Question: a reduction of 30 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 940 , what is the reduced price for kg ?

<gadget id="calculator">940 * 30</gadget>
<output>28_200</output>

<gadget id="calculator">28_200 / 100</gadget>
<output>282</output>

<gadget id="calculator">282 / 6</gadget>
<output>47</output>
<result>47</result>

Choices:
A. 72
B. 47
C. 40
D. 28
E. 20

divide(divide(multiply(940, 30), const_100), 6)

Explanation: "940 * ( 30 / 100 ) = 282 - - - - 6 ? - - - - 1 = > rs . 47 answer : b"


Question: a certain company reported that the revenue on sales increased 30 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">(9/5) - (13/10)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) / (13/10)</gadget>
<output>5/13 = around 0.384615</output>

<gadget id="calculator">(5/13) * 100</gadget>
<output>500/13 = around 38.461538</output>
<result>500/13 = around 38.461538</result>

Choices:
A. 50 %
B. 40 %
C. 35 %
D. 32 %
E. 39 %

multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(30, const_100))), add(const_1, divide(30, const_100))), const_100)

Explanation: assume the revenue in 2000 to be 100 . then in 2003 it would be 130 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 130 ) / 130 = 50 / 130 = 39 % answer : e .


Question: if a man lost 5 % by selling oranges at the rate of 8 a rupee at how many a rupee must he sell them to gain 52 % ?

<gadget id="calculator">100 - 5</gadget>
<output>95</output>

<gadget id="calculator">95 * 8</gadget>
<output>760</output>

<gadget id="calculator">100 + 52</gadget>
<output>152</output>

<gadget id="calculator">760 / 152</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 5
B. 8
C. 7
D. 4
E. 2

divide(multiply(subtract(const_100, 5), 8), add(const_100, 52))

Explanation: "95 % - - - - 8 152 % - - - - ? 95 / 152 * 8 = 5 answer : a"


Question: there are 32 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?

<gadget id="calculator">32 + 2</gadget>
<output>34</output>

<gadget id="calculator">34 - 1</gadget>
<output>33</output>

<gadget id="calculator">34 * 33</gadget>
<output>1_122</output>
<result>1_122</result>

Choices:
A. 1800
B. 1820
C. 1150
D. 1122
E. 1900

multiply(add(32, const_2), subtract(add(32, const_2), const_1))

Explanation: the total number of stations = 34 from 34 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 34 p 2 ways . 34 p 2 = 34 * 33 = 1122 answer : d


Question: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 5 , ab = 5 and ac = 11 , what is the length of ae ?

<gadget id="calculator">11 - 5</gadget>
<output>6</output>

<gadget id="calculator">6 / 2</gadget>
<output>3</output>

<gadget id="calculator">11 + 3</gadget>
<output>14</output>

<gadget id="calculator">14 + 5</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 19
B. 21
C. 23
D. 25
E. 27

add(add(11, divide(subtract(11, 5), 2)), 5)

Explanation: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 5 = 19 the answer is a ."


Question: a can run 288 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?

<gadget id="calculator">288 / 32</gadget>
<output>9</output>

<gadget id="calculator">9 * 28</gadget>
<output>252</output>

<gadget id="calculator">288 - 252</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 38 metre
B. 28 metre
C. 23 metre
D. 15 metre
E. 36 metre

subtract(288, multiply(divide(288, 32), 28))

Explanation: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 288 / 32 = 9 m / s distance covered by b in 4 seconds = speed ã — time = 9 ã — 4 = 36 metre i . e . , a beat b by 36 metre answer is e"


Question: if x / y = 7 / 4 , then ( x + y ) / ( x - y ) = ?

<gadget id="calculator">7 + 4</gadget>
<output>11</output>

<gadget id="calculator">7 - 4</gadget>
<output>3</output>

<gadget id="calculator">11 / 3</gadget>
<output>11/3 = around 3.666667</output>
<result>11/3 = around 3.666667</result>

Choices:
A. 5
B. 11 / 3
C. - 1 / 6
D. - 1 / 5
E. - 5

Explanation: "any x and y satisfying x / y = 7 / 4 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 4 , then ( x + y ) / ( x - y ) = ( 7 + 4 ) / ( 7 - 4 ) = 11 / 3 . answer : b ."


Question: of the families in city x in 1956 , 25 percent owned a personal computer . the number of families in city x owning a computer in 1960 was 15 percent greater than it was in 1956 , and the total number of families in city x was 5 percent greater in 1956 than it was in 1960 . what percent of the families in city x owned a personal computer in 1960 ?

<gadget id="calculator">15 + 100</gadget>
<output>115</output>

<gadget id="calculator">115 * 25</gadget>
<output>2_875</output>

<gadget id="calculator">2_875 / 100</gadget>
<output>115/4 = around 28.75</output>

<gadget id="calculator">100 + 5</gadget>
<output>105</output>

<gadget id="calculator">(115/4) / 105</gadget>
<output>23/84 = around 0.27381</output>

<gadget id="calculator">100 * (23/84)</gadget>
<output>575/21 = around 27.380952</output>
<result>575/21 = around 27.380952</result>

Choices:
A. 50 %
B. 51.22 %
C. 5.26 %
D. 7.20 %
E. 27.38 %

multiply(const_100, divide(divide(multiply(add(15, const_100), 25), const_100), add(const_100, 5)))

Explanation: "say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 number of families owning computer in 1960 = 25 * 115 / 100 = 28.75 number of families in 1960 = 105 the percentage = 28.75 / 105 * 100 = 27.38 % . option : e"


Question: if the cost price is 91 % of sp then what is the profit %

<gadget id="calculator">100 - 91</gadget>
<output>9</output>

<gadget id="calculator">9 / 91</gadget>
<output>9/91 = around 0.098901</output>

<gadget id="calculator">(9/91) * 100</gadget>
<output>900/91 = around 9.89011</output>
<result>900/91 = around 9.89011</result>

Choices:
A. 9.89 %
B. 8.90 %
C. 9.00 %
D. 8.00 %
E. 9.27 %

multiply(divide(subtract(const_100, 91), 91), const_100)

Explanation: "sol . sp = rs 100 : then cp = rs 91 : profit = rs 9 . profit = { ( 9 / 91 ) * 100 } % = 9.89 % answer is a ."


Question: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 24 , find the sum of money ?

<gadget id="calculator">24 / 40</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">100 + 65</gadget>
<output>165</output>

<gadget id="calculator">165 + 40</gadget>
<output>205</output>

<gadget id="calculator">(3/5) * 205</gadget>
<output>123</output>
<result>123</result>

Choices:
A. 288
B. 262
C. 72
D. 123
E. 267

multiply(divide(24, 40), add(add(const_100, 65), 40))

Explanation: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 24 41 - - - - ? = > rs . 123 answer : d"


Question: tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?

<gadget id="calculator">4 - 1</gadget>
<output>3</output>

<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 6
B. 7
C. 12
D. 16
E. 24

Explanation: number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e


Question: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 44000 . what is the share of c ?

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 3</gadget>
<output>2</output>

<gadget id="calculator">(2/3) + 2</gadget>
<output>8/3 = around 2.666667</output>

<gadget id="calculator">(8/3) + 1</gadget>
<output>11/3 = around 3.666667</output>

<gadget id="calculator">1 / (11/3)</gadget>
<output>3/11 = around 0.272727</output>

<gadget id="calculator">44_000 * (3/11)</gadget>
<output>12_000</output>
<result>12_000</result>

Choices:
A. rs . 12000
B. rs . 13375
C. rs . 11750
D. rs . 11625
E. none of these

multiply(44000, inverse(add(add(divide(2, 3), multiply(divide(2, 3), 3)), const_1)))

Explanation: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 44000 ] = rs . 12000 answer : option a"


Question: a sum of rs . 100 is lent at simple interest of 3 % p . a . for the first month , 9 % p . a . for the second month , 27 % p . a . for the third month and so on . what is the total amount of interest earned at the end of the year approximately

<gadget id="calculator">3 ** 12</gadget>
<output>531_441</output>

<gadget id="calculator">531_441 - 1</gadget>
<output>531_440</output>

<gadget id="calculator">531_440 * 3</gadget>
<output>1_594_320</output>

<gadget id="calculator">12 * 2</gadget>
<output>24</output>

<gadget id="calculator">1_594_320 / 24</gadget>
<output>66_430</output>
<result>66_430</result>

Choices:
A. rs . 797160
B. rs . 791160
C. rs . 65930
D. rs . 66430
E. rs . 67430

divide(multiply(subtract(power(3, const_12), const_1), 3), multiply(const_12, const_2))

Explanation: total amount of interest is i = p / 100 * 1 [ 3 / 12 + 9 / 12 + 27 / 12 … . 312 / 12 where p = 100 ; i = 1 / 12 ( 3 + 9 + … . . 312 ) i = 1 / 12 ( 3 ( 312 - 1 ) ) / 3 - 1 = 531440 * 3 / 12 * 2 = rs . 66430 answer : d


Question: suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 4
B. 6
C. 9
D. 10
E. 12

Explanation: the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the “ back ” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b .


Question: a man bought 10 crates of mangoes for $ 40 total . if he lost 2 of the crates , at what price would he have to sell each of the remaining crates in order to earn a total profit of 20 percent of the total cost ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">40 * (1/5)</gadget>
<output>8</output>

<gadget id="calculator">40 + 8</gadget>
<output>48</output>

<gadget id="calculator">10 - 2</gadget>
<output>8</output>

<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<result>6</result>

Choices:
A. $ 6
B. $ 8
C. $ 10
D. $ 12
E. $ 14

divide(add(40, multiply(40, divide(20, const_100))), subtract(10, 2))

Explanation: as given , after lost , the remaining 8 crates total cost = $ 40 so , 1 crate cost = 40 / 8 = 5 to get 20 % profit , 1 crate cost should be = 5 + 5 * 20 / 100 = $ 6 answer : a


Question: a number increased by 30 % gives 650 . the number is ?

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">650 / (13/10)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 200
B. 300
C. 400
D. 500
E. 600

divide(650, add(const_1, divide(30, const_100)))

Explanation: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 650 ( 130 ã — 5 = 650 ) 100 % - - - - - - - > 400 ( 100 ã — 5 = 500 ) option ' d '"


Question: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 20 days .

<gadget id="calculator">20 / 10</gadget>
<output>2</output>

<gadget id="calculator">2 * 4</gadget>
<output>8</output>

<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12 days .
B. 17 days .
C. 18 days .
D. 19 days .
E. 20 days .

subtract(20, multiply(divide(20, 10), 4))

Explanation: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 20 * 6 / 10 = 12 days . answer : a"


Question: if ' x ' is a positive integer exactly divisible by 6 or 15 but not divisible by 12 . what could possibly be the value of ' x ' ?

<gadget id="calculator">6 * 15</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 120
B. 60
C. 36
D. 90
E. 54

Explanation: 120 and 60 are both divisible by 6 and 15 but also by 12 . so they are not the right answer . 36 and 54 are both clearly not divisible by 15 ( not correct ) 90 is both divisible by 6 and 15 but not by 12 . answer : ( d ) 90


Question: on a sum of money , the simple interest for 2 years is rs . 324 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is

<gadget id="calculator">324 / 2</gadget>
<output>162</output>

<gadget id="calculator">340 - 162</gadget>
<output>178</output>

<gadget id="calculator">178 - 162</gadget>
<output>16</output>

<gadget id="calculator">100 * 16</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 / 162</gadget>
<output>800/81 = around 9.876543</output>
<result>800/81 = around 9.876543</result>

Choices:
A. 15 %
B. 14.25 %
C. 9.87 %
D. 10.5 %
E. 11.5 %

divide(multiply(const_100, subtract(subtract(340, divide(324, 2)), divide(324, 2))), divide(324, 2))

Explanation: "the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 324 = 16 ( r ã — si ) / ( 2 ã — 100 ) = 16 ( r ã — 324 ) / ( 2 ã — 100 ) = 16 r = 9.87 % answer : option c"


Question: a taxi leaves point a 2 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .

<gadget id="calculator">2 * 20</gadget>
<output>40</output>

<gadget id="calculator">40 + 40</gadget>
<output>80</output>

<gadget id="calculator">2 + 2</gadget>
<output>4</output>

<gadget id="calculator">4 - 2</gadget>
<output>2</output>

<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 42
B. 48
C. 44
D. 50
E. 40

divide(add(multiply(2, 20), multiply(2, 20)), subtract(add(2, 2), 2))

Explanation: "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 4 hrs and taxi a total of 2 hrs . hence 4 * ( v - 20 ) = 2 v 4 v - 80 = 2 v 2 v = 80 v = 40 mph e"


Question: monica planned her birthday party . she prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra . after the party , it turned out that one of the guests did n ' t come but every one of the guests that did come ate 6 muffins and 6 muffins remained . how many guests did monica plan on ?

<gadget id="calculator">6 + 6</gadget>
<output>12</output>

<gadget id="calculator">12 - 2</gadget>
<output>10</output>

<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2 .
B. 4 .
C. 5 .
D. 6 .
E. 7 .

Explanation: let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a


Question: a boy rides his bicycle 10 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately ?

<gadget id="calculator">12 + 10</gadget>
<output>22</output>

<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 10.7 km / hr
B. 10.8 km / hr
C. 17.8 km / hr
D. 10.5 km / hr
E. 30.8 km / hr

Explanation: total distance traveled = 10 + 12 = 22 km / hr . total time taken = 10 / 12 + 12 / 10 = 61 / 30 hrs . average speed = 22 * 30 / 61 = 10.8 km / hr . answer : b


Question: if 3 ^ x = 2 , then 3 ^ ( 4 x + 3 ) =

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>

<gadget id="calculator">log(3)</gadget>
<output>log(3) = around 1.098612</output>

<gadget id="calculator">log(2) / log(3)</gadget>
<output>log(2)/log(3) = around 0.63093</output>

<gadget id="calculator">4 * (log(2)/log(3))</gadget>
<output>4*log(2)/log(3) = around 2.523719</output>

<gadget id="calculator">(4*log(2)/log(3)) + 3</gadget>
<output>4*log(2)/log(3) + 3 = around 5.523719</output>

<gadget id="calculator">3 ** (4*log(2)/log(3) + 3)</gadget>
<output>3**(4*log(2)/log(3) + 3) = around 432</output>
<result>3**(4*log(2)/log(3) + 3) = around 432</result>

Choices:
A. 429
B. 454
C. 432
D. 438
E. 108

power(3, add(multiply(4, divide(log(const_2), log(const_3))), 3))

Explanation: 3 ^ x = 2 3 ^ 4 x = 2 ^ 4 3 ^ 4 x = 16 3 ^ ( 4 x + 3 ) = 3 ^ 4 x * 3 ^ 3 = 16 * 27 = 432 answer : c


Question: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 360 meters , after what time will they meet at the starting point ?

<gadget id="calculator">8 + 7</gadget>
<output>15</output>

<gadget id="calculator">360 / 15</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 20 sec
B. 15 sec
C. 30 sec
D. 24 sec
E. 1 min

Explanation: "they meet every 360 / 7 + 8 = 24 sec answer is d"


Question: a van takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) * 6</gadget>
<output>9</output>

<gadget id="calculator">540 / 9</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 40 kmph
B. 50 kmph
C. 60 kmph
D. 75 kmph
E. 860 kmph

Explanation: "time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )"


Question: if an object travels 90 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )

<gadget id="calculator">90 / 5_280</gadget>
<output>3/176 = around 0.017045</output>

<gadget id="calculator">1 / 3_600</gadget>
<output>1/3_600 = around 0.000278</output>

<gadget id="calculator">2 * (1/3_600)</gadget>
<output>1/1_800 = around 0.000556</output>

<gadget id="calculator">(3/176) / (1/1_800)</gadget>
<output>675/22 = around 30.681818</output>
<result>675/22 = around 30.681818</result>

Choices:
A. 30.68
B. 32.34
C. 34.56
D. 36.72
E. 38.95

divide(divide(90, 5280), multiply(2, divide(1, const_3600)))

Explanation: "90 feet / 2 seconds = 45 feet / second ( 45 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 30.68 ( approximately ) the answer is a ."


Question: the population of a village is 13400 . it increases annually at the rate of 21 % p . a . what will be its population after 2 years ?

Choices:
A. 10000
B. 12000
C. 19619
D. 18989
E. 14400

multiply(13400, power(add(const_1, divide(21, const_100)), 2))

Explanation: "formula : ( after = 100 denominator ago = 100 numerator ) 13400 × 121 / 100 × 121 / 100 = 19619 c"


Question: a box measuring 49 inches long by 21 inches wide by 14 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?

<gadget id="calculator">49 * 21</gadget>
<output>1_029</output>

<gadget id="calculator">1_029 * 14</gadget>
<output>14_406</output>

<gadget id="calculator">14 / 2</gadget>
<output>7</output>

<gadget id="calculator">7 ** 3</gadget>
<output>343</output>

<gadget id="calculator">14_406 / 343</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 17
B. 42
C. 54
D. 108
E. 864

divide(multiply(multiply(49, 21), 14), volume_cube(divide(14, const_2)))

Explanation: "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is ."


Question: sonika deposited rs . 7000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">9_200 - 7_000</gadget>
<output>2_200</output>

<gadget id="calculator">2_200 / 3</gadget>
<output>2_200/3 = around 733.333333</output>

<gadget id="calculator">(2_200/3) / 7_000</gadget>
<output>11/105 = around 0.104762</output>

<gadget id="calculator">(1/50) + (11/105)</gadget>
<output>131/1_050 = around 0.124762</output>

<gadget id="calculator">(131/1_050) * 7_000</gadget>
<output>2_620/3 = around 873.333333</output>

<gadget id="calculator">(2_620/3) * 3</gadget>
<output>2_620</output>

<gadget id="calculator">2_620 + 7_000</gadget>
<output>9_620</output>
<result>9_620</result>

Choices:
A. 9680
B. 2277
C. 9620
D. 2774
E. 1212

add(multiply(multiply(add(divide(2, const_100), divide(divide(subtract(9200, 7000), 3), 7000)), 7000), 3), 7000)

Explanation: "( 7000 * 3 * 2 ) / 100 = 420 9200 - - - - - - - - 9620 answer : c"


Question: a ’ s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?

<gadget id="calculator">20 - 13</gadget>
<output>7</output>

<gadget id="calculator">7 / 20</gadget>
<output>7/20 = around 0.35</output>
<result>7/20 = around 0.35</result>

Choices:
A. 1 / 17
B. 3 / 17
C. 1 / 10
D. 7 / 20
E. 3 / 10

Explanation: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 13 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 13 meters ) to reach the finish line . so b should get a head start of 7 / 20 th of the race . answer ( d )"


Question: what is the largest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 - 1</gadget>
<output>9_999</output>

<gadget id="calculator">lcm(15, 25)</gadget>
<output>75</output>

<gadget id="calculator">lcm(75, 40)</gadget>
<output>600</output>

<gadget id="calculator">lcm(600, 75)</gadget>
<output>600</output>

<gadget id="calculator">9_999 % 600</gadget>
<output>399</output>

<gadget id="calculator">9_999 - 399</gadget>
<output>9_600</output>
<result>9_600</result>

Choices:
A. 9600
B. 5200
C. 362
D. 958
E. 258

subtract(subtract(multiply(const_100, const_100), const_1), reminder(subtract(multiply(const_100, const_100), const_1), lcm(lcm(lcm(15, 25), 40), 75)))

Explanation: explanation : largest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , largest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : a


Question: what will be the cost of building a fence around a square plot with area equal to 64 sq ft , if the price per foot of building the fence is rs . 58 ?

<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>

<gadget id="calculator">4 * 8</gadget>
<output>32</output>

<gadget id="calculator">32 * 58</gadget>
<output>1_856</output>
<result>1_856</result>

Choices:
A. 3944
B. 2882
C. 2999
D. 1856
E. 2121

Explanation: "let the side of the square plot be a ft . a 2 = 64 = > a = 8 length of the fence = perimeter of the plot = 4 a = 32 ft . cost of building the fence = 32 * 58 = rs . 1856 . answer : d"


Question: a 6 litre sol is 20 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 6</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">2 * (6/5)</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">6 - (12/5)</gadget>
<output>18/5 = around 3.6</output>
<result>18/5 = around 3.6</result>

Choices:
A. a . 0.6
B. b . 1
C. c . 2.1
D. d . 3.6
E. e . 5.4

subtract(6, multiply(const_2, multiply(divide(20, const_100), 6)))

Explanation: "20 % of 6 = 1.2 50 % of 6 = 3 shortage is 1.8 so we need to have 1.8 / 50 % to get 50 % alcohol content . = 3.6 d"


Question: if 45 % of z is 60 % of y and y is 75 % of x , what percent of x is z ?

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(9/20) / (3/5)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) / (3/4)</gadget>
<output>1</output>

<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 200
B. 160
C. 100
D. 65
E. 50

multiply(divide(divide(75, const_100), divide(divide(45, const_100), divide(60, const_100))), const_100)

Explanation: "( 45 / 100 ) z = ( 60 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 60 / 100 ) * ( 3 / 4 ) x i . e . z = ( 60 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1 ) x = ( 100 / 100 ) x i . e . z is 100 % of x answer : option c"


Question: how many odd 3 - digit integers greater than 800 are there such that all their digits are different ?

<gadget id="calculator">3 + 2</gadget>
<output>5</output>

<gadget id="calculator">3 + 5</gadget>
<output>8</output>

<gadget id="calculator">8 * 4</gadget>
<output>32</output>

<gadget id="calculator">1 * 5</gadget>
<output>5</output>

<gadget id="calculator">5 * 8</gadget>
<output>40</output>

<gadget id="calculator">32 + 40</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 40
B. 56
C. 72
D. 81
E. 104

add(multiply(add(3, add(const_3, const_2)), const_4), multiply(multiply(const_1, add(const_3, const_2)), add(3, add(const_3, const_2))))

Explanation: in the range 800 - 900 : 1 choice for the first digit : 8 ; 5 choices for the third digit : 1 , 3 , 5 , 7 , 9 ( as the number is odd ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 5 * 8 = 40 . in the range 900 - 999 : 1 choice for the first digit : 9 ; 4 choices for the third digit : 1 , 3 , 5 , 7 ( 9 is out as it ' s the first digit ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 4 * 8 = 32 . total : 40 + 32 = 72 . answer : c


Question: the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?

<gadget id="calculator">7 - 2</gadget>
<output>5</output>

<gadget id="calculator">40 / 5</gadget>
<output>8</output>

<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 14
B. 16
C. 18
D. 20
E. 22

Explanation: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 40 x = 8 and the number of spinsters is 2 ( 8 ) = 16 . the answer is b ."


Question: 33 1 / 3 % of 240 ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">33 + (1/3)</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">(100/3) * 240</gadget>
<output>8_000</output>

<gadget id="calculator">8_000 / 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 80
B. 90
C. 110
D. 120
E. 130

divide(multiply(add(33, divide(1, 3)), 240), const_100)

Explanation: "33 1 / 3 % = 1 / 3 1 / 3 × 240 = 80 a )"


Question: one pump drains one - half of a pond in 7 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?

<gadget id="calculator">7 * 2</gadget>
<output>14</output>

<gadget id="calculator">1 / 14</gadget>
<output>1/14 = around 0.071429</output>

<gadget id="calculator">1 - (1/14)</gadget>
<output>13/14 = around 0.928571</output>

<gadget id="calculator">1 / (13/14)</gadget>
<output>14/13 = around 1.076923</output>
<result>14/13 = around 1.076923</result>

Choices:
A. 1 hour
B. 1.1 hour
C. 3 hours
D. 5 hours
E. 6 hours

divide(const_1, subtract(const_1, divide(const_1, multiply(7, const_2))))

Explanation: "first pump drains 1 / 2 of the tank in 7 hours so 14 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 14 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 14 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 14 + 1 / a ) = 1 / 2 solving u get a = 14 / 13 = 1.1 hence answer is b"


Question: what is the area of square field whose side of length 18 m ?

<gadget id="calculator">18 ** 2</gadget>
<output>324</output>
<result>324</result>

Choices:
A. 225 sq m
B. 186 sq m
C. 586 sq m
D. 324 sq m
E. 296 sq m

Explanation: "18 * 18 = 324 sq m answer : d"


Question: how much is 80 % of 40 is greater than 4 / 5 of 30 ?

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">40 * (4/5)</gadget>
<output>32</output>

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) * 30</gadget>
<output>24</output>

<gadget id="calculator">32 - 24</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 12
B. 27
C. 8
D. 12
E. 81

subtract(multiply(40, divide(80, const_100)), multiply(divide(4, 5), 30))

Explanation: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 32 - 24 = 8 answer : c"


Question: how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ?

<gadget id="calculator">60 / 5</gadget>
<output>12</output>

<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 4
B. 6
C. 11
D. 12
E. 15

Explanation: "the odd numbers less than 60 are 1 , 3,5 , . . . 59 some of them are equal to product of 5 and odd number hence odd multiples of 5 which are less than 60 are 5,15 , 25,35 , 45,55 ( total = 6 ) ; answer : b"


Question: in a sports club with 30 members , 17 play badminton and 18 play tennis and 2 do not play either . how many members play both badminton and tennis ?

<gadget id="calculator">17 + 18</gadget>
<output>35</output>

<gadget id="calculator">35 + 2</gadget>
<output>37</output>

<gadget id="calculator">37 - 30</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7
B. 8
C. 9
D. 10
E. 11

Explanation: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 18 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"


Question: working at their respective constant rates , machine a makes 100 copies in 15 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?

<gadget id="calculator">100 / 15</gadget>
<output>20/3 = around 6.666667</output>

<gadget id="calculator">150 / 10</gadget>
<output>15</output>

<gadget id="calculator">(20/3) + 15</gadget>
<output>65/3 = around 21.666667</output>

<gadget id="calculator">(65/3) * 30</gadget>
<output>650</output>
<result>650</result>

Choices:
A. 250
B. 425
C. 650
D. 700
E. 750

Explanation: "machine a can produce 100 * 30 / 15 = 200 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 650 copies . c is the answer"


Question: one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .

<gadget id="calculator">17 ** 2</gadget>
<output>289</output>

<gadget id="calculator">15 ** 2</gadget>
<output>225</output>

<gadget id="calculator">289 - 225</gadget>
<output>64</output>

<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>

<gadget id="calculator">15 * 8</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 120
B. 147
C. 251
D. 451
E. 258

rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2))))

Explanation: "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a"


Question: a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scale ?

<gadget id="calculator">24 - 6</gadget>
<output>18</output>

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">60 - 30</gadget>
<output>30</output>

<gadget id="calculator">40 / 30</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">18 * (4/3)</gadget>
<output>24</output>

<gadget id="calculator">24 + 24</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 20
B. 36
C. 48
D. 60
E. 84

add(multiply(subtract(24, 6), divide(subtract(100, 60), subtract(60, 30))), 24)

Explanation: first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c


Question: the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number .

<gadget id="calculator">184 * 3</gadget>
<output>552</output>

<gadget id="calculator">3 + 4</gadget>
<output>7</output>

<gadget id="calculator">7 * 3</gadget>
<output>21</output>

<gadget id="calculator">21 * 8</gadget>
<output>168</output>

<gadget id="calculator">552 + 168</gadget>
<output>720</output>

<gadget id="calculator">7 + 3</gadget>
<output>10</output>

<gadget id="calculator">720 / 10</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 72
B. 64
C. 84
D. 12
E. 92

divide(add(multiply(184, const_3), multiply(multiply(add(const_3, const_4), const_3), 8)), add(add(const_3, const_4), const_3))

Explanation: let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 .


Question: the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ?

<gadget id="calculator">200 + 102</gadget>
<output>302</output>

<gadget id="calculator">302 / 2</gadget>
<output>151</output>

<gadget id="calculator">200 - 102</gadget>
<output>98</output>

<gadget id="calculator">98 / 2</gadget>
<output>49</output>

<gadget id="calculator">49 + 1</gadget>
<output>50</output>

<gadget id="calculator">151 * 50</gadget>
<output>7_550</output>
<result>7_550</result>

Choices:
A. 5100
B. 7550
C. 10100
D. 15500
E. 20100

multiply(divide(add(200, 102), const_2), add(divide(subtract(200, 102), const_2), const_1))

Explanation: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b"


Question: how many litres of pure acid are there in 15 litres of a 20 % solution

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 15</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 4
B. 5
C. 2
D. 3
E. 1

Explanation: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 15 * 20 / 100 = 3 answer : option d


Question: rs . 385 were divided among x , y , z in such a way that x had rs . 20 more than y and z had rs 15 more than x . how much was y ’ s share ?

<gadget id="calculator">20 + 20</gadget>
<output>40</output>

<gadget id="calculator">15 + 40</gadget>
<output>55</output>

<gadget id="calculator">385 - 55</gadget>
<output>330</output>

<gadget id="calculator">330 / 3</gadget>
<output>110</output>

<gadget id="calculator">110 + 20</gadget>
<output>130</output>

<gadget id="calculator">15 + 130</gadget>
<output>145</output>
<result>145</result>

Choices:
A. rs . 130
B. rs . 145
C. rs . 154
D. rs . 160
E. rs . 164

Explanation: let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r ’ s share = rs ( 110 + 35 ) = rs . 145 b


Question: when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16

<gadget id="calculator">12 + 3</gadget>
<output>15</output>

<gadget id="calculator">2 + 4</gadget>
<output>6</output>

<gadget id="calculator">15 + 6</gadget>
<output>21</output>

<gadget id="calculator">21 / 16</gadget>
<output>21/16 = around 1.3125</output>

<gadget id="calculator">floor(21/16)</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 1
B. 3
C. 4
D. 5
E. 2

floor(divide(add(add(const_12, const_3), add(const_2, const_4)), 16))

Explanation: case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a


Question: a group of men decided to do a work in 20 days , but 8 of them became absent . if the rest of the group did the work in 28 days , find the original number of men ?

<gadget id="calculator">8 * 28</gadget>
<output>224</output>

<gadget id="calculator">28 - 20</gadget>
<output>8</output>

<gadget id="calculator">224 / 8</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 60
B. 28
C. 40
D. 50
E. 25

divide(multiply(8, 28), subtract(28, 20))

Explanation: "original number of men = 8 * 28 / ( 28 - 20 ) = 28 answer is b"


Question: three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ?

<gadget id="calculator">280 - 180</gadget>
<output>100</output>

<gadget id="calculator">100 - 36</gadget>
<output>64</output>

<gadget id="calculator">64 / 2</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 5 square meters
B. 32 square meters
C. 42 square meters
D. 83.3 square meters
E. 120 square meters

divide(subtract(subtract(280, 180), 36), const_2)

Explanation: "280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) ."


Question: mr . x , a mathematician , defines a number as ' connected with 6 if it is divisible by 6 or if the sum of its digits is 6 , or if 6 is one of the digits of the number . other numbers are all ' not connected with 6 ' . as per this definition , the number of integers from 1 to 60 ( both inclusive ) which are not connected with 6 is

<gadget id="calculator">10 + 3</gadget>
<output>13</output>

<gadget id="calculator">13 + 4</gadget>
<output>17</output>

<gadget id="calculator">60 - 17</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 18
B. 22
C. 42
D. 43
E. 45

subtract(60, add(add(const_10, const_3), const_4))

Explanation: explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such uncommon numbers . numbers from 1 to 60 , which have 6 as one of the digits are 6 , 16 , 26 , 36 , 46 , 56 , 60 . clearly , there are 4 such uncommon numbers . so , numbers ' not connected with 6 ' = 60 - ( 10 + 3 + 4 ) = 43 . answer : d


Question: a camera lens filter kit containing 5 filters sells for $ 67.50 . if the filters are purchased individually , 2 of them are priced at $ 7.45 each , 2 at $ 10.05 each , 1 at $ 14.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?

<gadget id="calculator">2 * 7.45</gadget>
<output>14.9</output>

<gadget id="calculator">2 * 10.05</gadget>
<output>20.1</output>

<gadget id="calculator">14.9 + 20.1</gadget>
<output>35</output>

<gadget id="calculator">14.5 + 35</gadget>
<output>49.5</output>

<gadget id="calculator">67.5 - 49.5</gadget>
<output>18</output>

<gadget id="calculator">18 * 100</gadget>
<output>1_800</output>

<gadget id="calculator">1_800 / 67.5</gadget>
<output>26.666667</output>
<result>26.666667</result>

Choices:
A. 25.66 %
B. 26.66 %
C. 27.66 %
D. 28.66 %
E. 29.66 %

Explanation: "cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b ."


Question: if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ? .

<gadget id="calculator">20 / 2</gadget>
<output>10</output>

<gadget id="calculator">2 ** 2</gadget>
<output>4</output>

<gadget id="calculator">20 / 4</gadget>
<output>5</output>

<gadget id="calculator">10 + 5</gadget>
<output>15</output>

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>

<gadget id="calculator">20 / 16</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">floor(5/4)</gadget>
<output>1</output>

<gadget id="calculator">15 + 1</gadget>
<output>16</output>

<gadget id="calculator">2 ** 3</gadget>
<output>8</output>

<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">floor(5/2)</gadget>
<output>2</output>

<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 10
B. 12
C. 15
D. 18
E. 20

add(add(add(divide(20, 2), divide(20, power(2, const_2))), floor(divide(20, power(power(2, const_2), 2)))), floor(divide(20, power(2, const_3))))

Explanation: 20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d


Question: a man performs 1 / 2 of the total journey by rail , 1 / 4 by bus and the remaining 4 km on foot . his total journey is

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 18 km
B. 16 km
C. 12 km
D. 24 km
E. 25 km

Explanation: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b"


Question: what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?

<gadget id="calculator">5 * 2</gadget>
<output>10</output>

<gadget id="calculator">10 * 3</gadget>
<output>30</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">30 - 6</gadget>
<output>24</output>

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

<gadget id="calculator">10 * 9</gadget>
<output>90</output>

<gadget id="calculator">24 / 90</gadget>
<output>4/15 = around 0.266667</output>
<result>4/15 = around 0.266667</result>

Choices:
A. 1 / 15
B. 2 / 15
C. 4 / 15
D. 7 / 15
E. none of these

divide(subtract(multiply(multiply(5, const_2), 3), multiply(3, const_2)), multiply(multiply(5, const_2), multiply(3, 3)))

Explanation: "explanation : since every third number starting from 10 will be divisible by 3 , so total number of numbers divisible by 3 are 90 / 3 = 30 numbers which are divisible by 3 and 5 both are numbers which are multiple of 15 . for the range 10 to 99 , 15 is the first number divisible by 15 and 90 is the last number . so total number of numbers divisible by 15 are : ( 90 - 15 ) / 15 + 1 = 5 + 1 = 6 number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6 . so number of numbers divisible by 3 and not by 5 are : 30 - 6 = 24 so total probability = 24 / 90 = 4 / 15 answer : c"


Question: bhanu spends 30 % of his income on petrol on scooter 21 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">300 / (3/10)</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 300</gadget>
<output>700</output>

<gadget id="calculator">21 / 100</gadget>
<output>21/100 = around 0.21</output>

<gadget id="calculator">700 * (21/100)</gadget>
<output>147</output>
<result>147</result>

Choices:
A. 2287
B. 140
C. 128
D. 797
E. 147

multiply(subtract(divide(300, divide(30, const_100)), 300), divide(21, const_100))

Explanation: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 21 % ( 700 ) = rs . 147 answer : e"


Question: one - third less than 25 % of 180 is equal to :

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 180</gadget>
<output>45</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 45</gadget>
<output>15</output>

<gadget id="calculator">45 - 15</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 15
B. 30
C. 35
D. 40
E. 45

subtract(multiply(divide(25, const_100), 180), multiply(divide(const_1, const_3), multiply(divide(25, const_100), 180)))

Explanation: "lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b"


Question: in arun ’ s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun ’ s weight is greater than 60 kg but less than 70 kg . his mother ’ s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what is the average of different probable weights of arun ?

<gadget id="calculator">68 - 1</gadget>
<output>67</output>

<gadget id="calculator">67 - 1</gadget>
<output>66</output>

<gadget id="calculator">67 + 66</gadget>
<output>133</output>

<gadget id="calculator">133 + 68</gadget>
<output>201</output>

<gadget id="calculator">201 / 3</gadget>
<output>67</output>
<result>67</result>

Choices:
A. 66 kg
B. 67 kg
C. 68 kg
D. 69 kg
E. none of these

divide(add(add(subtract(68, const_1), subtract(subtract(68, const_1), const_1)), 68), const_3)

Explanation: explanation : let arun ’ s weight by x kg . according to arun , 65 < x < 72 according to arun ’ s brother , 60 < x < 70 . according to arun ’ s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b


Question: there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?

<gadget id="calculator">binomial(8, 4)</gadget>
<output>70</output>

<gadget id="calculator">binomial(5, 4)</gadget>
<output>5</output>

<gadget id="calculator">70 - 5</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 40
B. 45
C. 50
D. 55
E. 65

Explanation: approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e


Question: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 500 . then his monthly salary is

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">500 * 5</gadget>
<output>2_500</output>
<result>2_500</result>

Choices:
A. rs . 2500
B. rs . 3500
C. rs . 1500
D. rs . 500
E. rs . 2000

Explanation: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 500 â ‡ ” 20 / 100 x = 500 â ‡ ” x = 500 ã — 5 = 2500 . answer a"


Question: robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert borrowed rs . 7280 / - from company . but robert forget that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the incentive amount given to robert ?

<gadget id="calculator">18_500 - 7_280</gadget>
<output>11_220</output>
<result>11_220</result>

Choices:
A. 9500
B. 12500
C. 10780
D. 10500
E. 8600

Explanation: "total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c"


Question: the food in a camp lasts for 40 men for 20 days . if 10 more men join , how many days will the food last ?

<gadget id="calculator">40 * 20</gadget>
<output>800</output>

<gadget id="calculator">40 + 10</gadget>
<output>50</output>

<gadget id="calculator">800 / 50</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 22 days
B. 30 days
C. 23 days
D. 16 days
E. 17 days

Explanation: one man can consume the same food in 40 * 20 = 800 days . 10 more men join , the total number of men = 50 the number of days the food will last = 800 / 50 = 16 days . answer : d


Question: a trader bought a car at 30 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

<gadget id="calculator">100 + 50</gadget>
<output>150</output>

<gadget id="calculator">70 * 150</gadget>
<output>10_500</output>

<gadget id="calculator">10_500 / 100</gadget>
<output>105</output>

<gadget id="calculator">105 / 100</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) - 1</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 7 %
B. 62 %
C. 12 %
D. 19 %
E. 5 %

multiply(subtract(divide(divide(multiply(subtract(const_100, 30), add(const_100, 50)), const_100), const_100), const_1), const_100)

Explanation: "original price = 100 cp = 70 s = 70 * ( 150 / 100 ) = 105 100 - 105 = 5 % answer : e"


Question: in a weight - lifting competition , the total weight of joe ' s two lifts was 450 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?

<gadget id="calculator">450 + 300</gadget>
<output>750</output>

<gadget id="calculator">750 / 3</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 250
B. 275
C. 325
D. 350
E. 400

Explanation: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 450 pounds . we sum the two variables to obtain : f + s = 450 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 450 3 f = 750 f = 250 answer is a ."


Question: a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 108 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

<gadget id="calculator">150 - 108</gadget>
<output>42</output>

<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>

<gadget id="calculator">1 - (13/20)</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">42 / (7/20)</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 40
B. 60
C. 80
D. 100
E. 120

divide(subtract(150, 108), subtract(const_1, divide(65, const_100)))

Explanation: "the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 108 books , thus the number of un - returned books is 150 - 108 = 42 books . 0.35 x = 42 x = 120 the answer is e ."


Question: ramu rides his bike at an average speed of 45 km / hr and reaches his desitination in 4 hours . somu covers the same distance in 6 hours . if ramu covered his journey at an average speed which was 9 km / hr less and somu covered his journey at an average speed which was 10 km / hr more , then the difference in their times taken to reach the destination would be ( in minutes ) .

<gadget id="calculator">45 * 4</gadget>
<output>180</output>

<gadget id="calculator">45 - 9</gadget>
<output>36</output>

<gadget id="calculator">180 / 36</gadget>
<output>5</output>

<gadget id="calculator">180 / 6</gadget>
<output>30</output>

<gadget id="calculator">30 + 10</gadget>
<output>40</output>

<gadget id="calculator">180 / 40</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">5 - (9/2)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 60</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 23 minutes
B. 30 minutes
C. 43 minutes
D. 23 minutes
E. 33 minutes

multiply(subtract(divide(multiply(45, 4), subtract(45, 9)), divide(multiply(45, 4), add(divide(multiply(45, 4), 6), 10))), const_60)

Explanation: distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b


Question: elena purchased brand x pens for $ 5.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?

<gadget id="calculator">4 * 12</gadget>
<output>48</output>

<gadget id="calculator">48 - 42</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 4
B. 5
C. 6
D. 7
E. 8

Explanation: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c ."


Question: in order to fence a square manish fixed 48 poles . if the distance between two poles , is 2 metres then what will be the area of the square so formed ?

<gadget id="calculator">48 / 2</gadget>
<output>24</output>

<gadget id="calculator">24 ** 2</gadget>
<output>576</output>
<result>576</result>

Choices:
A. 133 cm 2
B. 276 cm 2
C. 2500 cm 2
D. 576 cm 2
E. none of these

Explanation: let the side of the square be x m . ∴ perimeter of the square = 48 × 2 = 4 x ∴ x = 24 m ∴ area = ( 24 ) 2 = 576 m 2 answer d


Question: find the area of a parallelogram with base 20 cm and height 10 cm ?

<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 290 cm 2
B. 380 cm 2
C. 270 cm 2
D. 280 cm 2
E. 200 cm 2

Explanation: area of a parallelogram = base * height = 20 * 10 = 200 cm 2 answer : e


Question: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 84 liters of drink a to convert it to drink b ?

<gadget id="calculator">4 + 3</gadget>
<output>7</output>

<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>

<gadget id="calculator">(4/7) * 84</gadget>
<output>48</output>

<gadget id="calculator">48 * 4</gadget>
<output>192</output>

<gadget id="calculator">192 / 3</gadget>
<output>64</output>

<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(3/7) * 84</gadget>
<output>36</output>

<gadget id="calculator">64 - 36</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 24
B. 28
C. 32
D. 36
E. 40

subtract(divide(multiply(multiply(divide(4, add(4, 3)), 84), 4), 3), multiply(divide(3, add(4, 3)), 84))

Explanation: "in 84 liters of drink a , there are 48 liters of milk and 36 liters of juice . with 48 liters of milk , we need a total of 64 liters of juice to make drink b . we need to add 28 liters of juice . the answer is b ."


Question: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ?

<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 1
B. 3
C. 5
D. 7
E. 9

Explanation: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b"


Question: in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is

<gadget id="calculator">12 * 620</gadget>
<output>7_440</output>

<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">11 + (3/4)</gadget>
<output>47/4 = around 11.75</output>

<gadget id="calculator">(47/4) * 620</gadget>
<output>7_285</output>

<gadget id="calculator">7_440 - 7_285</gadget>
<output>155</output>
<result>155</result>

Choices:
A. 150
B. 200
C. 155
D. 350
E. none

subtract(multiply(12, 620), multiply(add(11, divide(9, 12)), 620))

Explanation: "sol . let the number of grils be x . then , number of boys = ( 620 - x ) . then , ( 11 3 / 4 × 620 ) ⇔ 11 x + 12 ( 620 - x ) ⇔ x = 7440 - 7285 ⇔ 155 . answer c"


Question: two trains are moving in opposite directions with speed of 60 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds

<gadget id="calculator">1.1 + 0.9</gadget>
<output>2</output>

<gadget id="calculator">60 + 90</gadget>
<output>150</output>

<gadget id="calculator">2 / 150</gadget>
<output>1/75 = around 0.013333</output>

<gadget id="calculator">(1/75) * 3_600</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 40
B. 42
C. 44
D. 46
E. 48

Explanation: "relative speed = 60 + 90 = 150 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 150 hr = 1 / / 75 hr = 3600 / 75 seconds = 1200 / 25 = 240 / 5 = 48 seconds answer is e ."


Question: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 14 km / hr respectively . they will meet for the first time in ?

<gadget id="calculator">20 + 14</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 50 min
B. 40 min
C. 34 min
D. 25 min
E. 20 min

Explanation: clearly , the two will meet when they are 1000 m apart to be 20 + 14 = 34 km apart , they take 1 hour to be 1000 m apart , they take 34 * 1000 / 1000 = 34 min . answer is c


Question: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 90 and rs . 80 respectively . the sum is :

<gadget id="calculator">90 * 80</gadget>
<output>7_200</output>

<gadget id="calculator">90 - 80</gadget>
<output>10</output>

<gadget id="calculator">7_200 / 10</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 1360
B. 1450
C. 720
D. 1800
E. none

divide(multiply(90, 80), subtract(90, 80))

Explanation: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 90 * 80 / ( 90 - 80 ) = rs . 720 . answer c"


Question: if shreehari walks in the speed of 4.5 km / hr from his house , in what time will he reach his school which is 750 m long from his house ?

<gadget id="calculator">750 / 1_000</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) / 4.5</gadget>
<output>0.166667</output>

<gadget id="calculator">0.166667 * 60</gadget>
<output>10.00002</output>
<result>10.00002</result>

Choices:
A. 5
B. 30
C. 10
D. 12
E. 15

multiply(divide(divide(750, const_1000), 4.5), const_60)

Explanation: speed = 4.5 * 5 / 18 = 1.25 m / sec time taken = 750 / 1.25 = 600 sec ie . 10 mins . answer : c


Question: if x is a number such that x ^ 2 + 2 x - 24 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =

<gadget id="calculator">4 + 24</gadget>
<output>28</output>

<gadget id="calculator">2 + 5</gadget>
<output>7</output>

<gadget id="calculator">28 / 7</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 4
B. - 4
C. - 3
D. - 6
E. 1

Explanation: x ^ 2 + 2 x - 24 = ( x + 6 ) ( x - 4 ) = 0 then x = - 6 or x = 4 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 4 . the answer is a .


Question: a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is

<gadget id="calculator">4 + 1</gadget>
<output>5</output>

<gadget id="calculator">5 * 510</gadget>
<output>2_550</output>

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">25 * 240</gadget>
<output>6_000</output>

<gadget id="calculator">2_550 + 6_000</gadget>
<output>8_550</output>

<gadget id="calculator">8_550 / 30</gadget>
<output>285</output>
<result>285</result>

Choices:
A. 250
B. 276
C. 280
D. 285
E. none

divide(add(multiply(add(const_4, const_1), 510), multiply(multiply(add(const_4, const_1), add(const_4, const_1)), 240)), 30)

Explanation: sol . since the month begins with a sunday , so there will be five sundays in the month . ∴ required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d


Question: a horse chases a pony 8 hours after the pony runs . horse takes 12 hours to reach the pony . if the average speed of the horse is 320 kmph , what s the average speed of the pony ?

<gadget id="calculator">12 * 320</gadget>
<output>3_840</output>

<gadget id="calculator">12 + 8</gadget>
<output>20</output>

<gadget id="calculator">3_840 / 20</gadget>
<output>192</output>
<result>192</result>

Choices:
A. 182 kmph
B. 192 kmph
C. 193 kmph
D. 196 kmph
E. 190 kmph

Explanation: pony take 20 hours and horse take 12 hours . . . then distance chased by them is 320 * 12 . so speed of pony is ( 320 * 12 ) / 20 = 192 kmph . answer is b


Question: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 10 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?

<gadget id="calculator">10 + 15</gadget>
<output>25</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">50 / (5/4)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 39.52 $
B. 40.63 $
C. 41.63 $
D. 42.15 $
E. 41.15 $

divide(50, add(divide(add(10, 15), const_100), const_1))

Explanation: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.10 x = 50 x = 39.52 hence , the correct option is a"


Question: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150 ?

<gadget id="calculator">150 / 2</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 10
B. 25
C. 50
D. 75
E. 100

Explanation: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 150 / 2 = 75 answer is d"


Question: a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?

<gadget id="calculator">60 - 15</gadget>
<output>45</output>

<gadget id="calculator">15 / 45</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>

Choices:
A. 1 / 4
B. 1 / 3
C. 1 / 2
D. 1
E. 3

Explanation: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 15 ) / ( 15 - 0 ) = 3 / 1 1 / x = 3 / 1 x = 1 / 3 answer : b"


Question: a certain car uses one gallon of gasoline every 32 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/20) * 4</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 / 32</gadget>
<output>1/32 = around 0.03125</output>

<gadget id="calculator">4 * (1/32)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/5) + (1/8)</gadget>
<output>13/40 = around 0.325</output>

<gadget id="calculator">8 * (1/32)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(13/40) - (1/4)</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(3/40) / (1/4)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 15 %
B. 20 %
C. 22.5 %
D. 25 %
E. 30 %

multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 32))), multiply(8, divide(const_1, 32))), multiply(8, divide(const_1, 32))), const_100)

Explanation: "4 miles on the highway = 4 / 32 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 32 + 4 / 20 = 13 / 40 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 13 / 40 - 8 / 32 ) / ( 8 / 32 ) = 0.30 . answer : e ."


Question: a retailer sold an appliance for $ 100 . if the retailer ' s gross profit on the appliance was 25 percent of the retailer ' s cost for the appliance , how many dollars was the retailer ' s gross profit ?

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">1 / (5/4)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>

<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<result>20</result>

Choices:
A. $ 10
B. $ 16
C. $ 20
D. $ 24
E. $ 25

subtract(100, multiply(divide(const_1, add(divide(25, 100), const_1)), 100))

Explanation: let p be the original price paid by the retailer . 1.25 * p = 100 p = 80 the profit is $ 20 . the answer is c .


Question: 24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?

<gadget id="calculator">4 * 25</gadget>
<output>100</output>

<gadget id="calculator">100 - 24</gadget>
<output>76</output>

<gadget id="calculator">4 * 5</gadget>
<output>20</output>

<gadget id="calculator">20 - 1</gadget>
<output>19</output>

<gadget id="calculator">76 / 19</gadget>
<output>4</output>

<gadget id="calculator">24 - 4</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 5
B. 10
C. 15
D. 20
E. 25

subtract(24, divide(subtract(multiply(4, 25), 24), subtract(multiply(4, 5), 1)))

Explanation: easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to t ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice t will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice t = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice v = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d


Question: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 15 percent of the test takers answered neither question correctly , what percent answered both correctly ?

<gadget id="calculator">85 + 75</gadget>
<output>160</output>

<gadget id="calculator">160 + 15</gadget>
<output>175</output>

<gadget id="calculator">175 - 100</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 60 %
B. 65 %
C. 70 %
D. 75 %
E. 80 %

subtract(add(add(85, 75), 15), const_100)

Explanation: { total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 75 - { both correctly } + 15 { both correctly } = 75 . answer : d .


Question: find the least number of complete years in which a sum of money put out at 25 % compound interest will be more than double of itself ?

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">log(5/4)</gadget>
<output>log(5/4) = around 0.223144</output>

<gadget id="calculator">log(2) / log(5/4)</gadget>
<output>log(2)/log(5/4) = around 3.106284</output>

<gadget id="calculator">(log(2)/log(5/4)) + 1</gadget>
<output>1 + log(2)/log(5/4) = around 4.106284</output>

<gadget id="calculator">floor(1 + log(2)/log(5/4))</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 6 years
B. 9 years
C. 5 years
D. 4 years
E. 6 years

floor(add(divide(log(const_2), log(add(const_1, divide(25, const_100)))), const_1))

Explanation: "4 years answer : d"


Question: mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 24 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?

<gadget id="calculator">24 + 22</gadget>
<output>46</output>

<gadget id="calculator">46 + 5</gadget>
<output>51</output>

<gadget id="calculator">51 - 29</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 18
B. 19
C. 22
D. 20
E. 19

Explanation: "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : c"


Question: 7 m - 20 = 2 m , then m + 7 is equal to ?

<gadget id="calculator">7 - 2</gadget>
<output>5</output>

<gadget id="calculator">20 / 5</gadget>
<output>4</output>

<gadget id="calculator">4 + 7</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 9
B. 10
C. 11
D. 12
E. 13

Explanation: 7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c


Question: the smallest value of n , for which 2 n + 1 is not a prime number is

<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 3
B. 4
C. 5
D. 6
E. 7

Explanation: "sol . = ( 2 × 1 + 1 ) = 3 , = ( 2 × 3 + 1 ) = 7 , = ( 2 × 4 + 1 ) = 9 , which is not prime . therefore n = 4 . answer b"


Question: two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ?

<gadget id="calculator">100 / 500</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20 %
B. 25 %
C. 40 %
D. 50 %
E. 80 %

Explanation: two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a


Question: in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 1 / 4 of the way by bus , and the remaining 5 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/3) + (1/4)</gadget>
<output>7/12 = around 0.583333</output>

<gadget id="calculator">1 - (7/12)</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">1 / (5/12)</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">5 * (12/5)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 13
B. 17
C. 42
D. 15
E. 12

multiply(5, inverse(subtract(1, add(divide(1, 3), divide(1, 4)))))

Explanation: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 5 x - 1 / 2 x - 3 / 5 x = 5 x = 12 km option : e"


Question: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 10 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?

<gadget id="calculator">1 + 10</gadget>
<output>11</output>

<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>
<result>11/2 = around 5.5</result>

Choices:
A. 8 mph
B. 5.5 mph
C. 3.5 mph
D. 4 mph
E. 0.5 mph

Explanation: ( 1 mph + 10 mph ) / 2 = 5.5 mph correct option is : b


Question: j is 25 % less than p and 20 % less than t . t is x % less than p . what is the value of x ?

<gadget id="calculator">25 * 25</gadget>
<output>625</output>

<gadget id="calculator">625 / 100</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>

Choices:
A. 93.5
B. 90
C. 6.75
D. 6.25
E. 2

Explanation: "let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d"


Question: denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination .

<gadget id="calculator">4_000 - 75</gadget>
<output>3_925</output>

<gadget id="calculator">3_925 / 4_000</gadget>
<output>157/160 = around 0.98125</output>
<result>157/160 = around 0.98125</result>

Choices:
A. 1
B. 159 / 160
C. 157 / 160
D. 4 3 / 160
E. 0

Explanation: when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 39263999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well . we ' ll get 3925 / 4000 = 157 / 160 . answer : c .


Question: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">8 / (1/2)</gadget>
<output>16</output>

<gadget id="calculator">16 / 12</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">0.33 * 100</gadget>
<output>33</output>

<gadget id="calculator">(4/3) * 33</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 0.33
B. 0.44
C. 0.55
D. 44
E. 55

multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100))

Explanation: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d"


Question: two spheres of their radios in the ratio 4 : 3 . find its volumes ratio ?

<gadget id="calculator">4/3 * pi * (4 ** 3)</gadget>
<output>256*pi/3 = around 268.082573</output>

<gadget id="calculator">4/3 * pi * (3 ** 3)</gadget>
<output>36*pi = around 113.097336</output>

<gadget id="calculator">(256*pi/3) / (36*pi)</gadget>
<output>64/27 = around 2.37037</output>
<result>64/27 = around 2.37037</result>

Choices:
A. 64 : 13
B. 13 : 64
C. 27 : 64
D. 64 : 27
E. none of them

Explanation: sphere volume ( v ) = 4 / 3 π r ( power 3 ) : 4 / 3 π r ( power 3 ) = 4 ( power 3 ) : 3 ( power 3 ) = 64 : 27 answer is d .


Question: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ?

<gadget id="calculator">1_536 ** 2</gadget>
<output>2_359_296</output>

<gadget id="calculator">3 * 2_359_296</gadget>
<output>7_077_888</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">7_077_888 ** (1/3)</gadget>
<output>192</output>

<gadget id="calculator">192 / 1.5</gadget>
<output>128</output>
<result>128</result>

Choices:
A. 34
B. 65
C. 88
D. 90
E. 128

divide(power(multiply(const_3, power(1536, const_2)), divide(const_1, const_3)), 1.5)

Explanation: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer"


Question: sum of the squares of 3 no . is 276 and the sum of their products taken two at a time is 150 . find the sum ?

<gadget id="calculator">150 * 2</gadget>
<output>300</output>

<gadget id="calculator">276 + 300</gadget>
<output>576</output>

<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 22
B. 18
C. 26
D. 24
E. 32

Explanation: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = â ˆ š 576 = 24 answer d"


Question: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 14 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 14 questions did zachary answer correctly ?

<gadget id="calculator">14 - 2</gadget>
<output>12</output>

<gadget id="calculator">2 * 12</gadget>
<output>24</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">24 - 6</gadget>
<output>18</output>

<gadget id="calculator">18 + 31</gadget>
<output>49</output>

<gadget id="calculator">3 + 2</gadget>
<output>5</output>

<gadget id="calculator">49 / 5</gadget>
<output>49/5 = around 9.8</output>
<result>49/5 = around 9.8</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 10

divide(add(subtract(multiply(2, subtract(14, 2)), multiply(3, 2)), 31), add(3, 2))

Explanation: i got two equations : 3 x - 2 y = 25 x + y = 14 3 x - 2 ( 14 - x ) = 25 3 x - 28 + 2 x = 25 5 x = 53 x = 10.6 or between 10 and 11 . ( ans e )


Question: bhaman travelled for 15 hours . he covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph . find the distance travelled by bhaman ?

<gadget id="calculator">2 * 40</gadget>
<output>80</output>

<gadget id="calculator">80 / 10</gadget>
<output>8</output>

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">20 / 10</gadget>
<output>2</output>

<gadget id="calculator">8 + 2</gadget>
<output>10</output>

<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">8 * 2</gadget>
<output>16</output>

<gadget id="calculator">16 * 10</gadget>
<output>160</output>

<gadget id="calculator">(3/2) * 160</gadget>
<output>240</output>
<result>240</result>

Choices:
A. 240
B. 230
C. 260
D. 220
E. 340

multiply(divide(15, add(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10))), multiply(multiply(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10)), const_10))

Explanation: let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a


Question: in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?

<gadget id="calculator">100 - 40</gadget>
<output>60</output>

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) * 60</gadget>
<output>45</output>

<gadget id="calculator">60 - 45</gadget>
<output>15</output>

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>

<gadget id="calculator">(7/8) * 40</gadget>
<output>35</output>

<gadget id="calculator">40 - 35</gadget>
<output>5</output>

<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20 %
B. 23 %
C. 15 %
D. 18 %
E. 16 %

add(subtract(subtract(const_100, 40), multiply(divide(3, 4), subtract(const_100, 40))), subtract(40, multiply(divide(7, 8), 40)))

Explanation: fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a .


Question: three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in .

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(2/3) * (1/8)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 11 hours
B. 12 hours
C. 15 hours
D. 16 hours
E. 17 hours

inverse(multiply(divide(const_2, const_3), divide(const_1, 8)))

Explanation: the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b


Question: john makes $ 40 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?

<gadget id="calculator">70 - 40</gadget>
<output>30</output>

<gadget id="calculator">30 / 40</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 16 %
B. 16.66 %
C. 76.69 %
D. 76.98 %
E. 75 %

multiply(divide(subtract(70, 40), 40), const_100)

Explanation: "increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e"


Question: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?

<gadget id="calculator">5 + 1</gadget>
<output>6</output>

<gadget id="calculator">6 * 6_500</gadget>
<output>39_000</output>

<gadget id="calculator">6_435 + 6_927</gadget>
<output>13_362</output>

<gadget id="calculator">13_362 + 6_855</gadget>
<output>20_217</output>

<gadget id="calculator">20_217 + 7_230</gadget>
<output>27_447</output>

<gadget id="calculator">27_447 + 6_562</gadget>
<output>34_009</output>

<gadget id="calculator">39_000 - 34_009</gadget>
<output>4_991</output>
<result>4_991</result>

Choices:
A. 4551
B. 4771
C. 4991
D. 4881
E. 4661

Explanation: "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer is c ."


Question: calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10 % of its volume is occupied by mortar ?

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">10 * (1/25)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 6</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(12/5) * (9/10)</gadget>
<output>54/25 = around 2.16</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(1/4) * (3/20)</gadget>
<output>3/80 = around 0.0375</output>

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(3/80) * (2/25)</gadget>
<output>3/1_000 = around 0.003</output>

<gadget id="calculator">(54/25) / (3/1_000)</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 720
B. 600
C. 660
D. 6000
E. none of these

divide(multiply(multiply(multiply(10, divide(4, const_100)), 6), subtract(const_1, divide(10, const_100))), multiply(multiply(divide(25, const_100), divide(15, const_100)), divide(8, const_100)))

Explanation: explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a


Question: the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ?

<gadget id="calculator">8 * 48</gadget>
<output>384</output>

<gadget id="calculator">384 / 24</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 12
B. 14
C. 15
D. 16
E. 20

Explanation: hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d


Question: one night a certain hotel rented 3 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>

<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">20 / 40</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 50 %
B. 55 %
C. 60 %
D. 65 %
E. 70 %

multiply(divide(multiply(subtract(const_1, divide(2, 3)), multiply(divide(3, 5), const_100)), subtract(const_100, multiply(divide(3, 5), const_100))), const_100)

Explanation: the rooms which were not rented is 2 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 2 / 5 ) = 1 / 2 = 50 % the answer is a .


Question: in what time will a train 180 m long cross an electric pole , it its speed be 144 km / hr ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>

<gadget id="calculator">180 / 40</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>

Choices:
A. 2.5 sec
B. 1.9 sec
C. 8.9 sec
D. 4.5 sec
E. 2.9 sec

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 180 / 40 = 4.5 sec . answer : d"


Question: the average monthly salary of 25 employees in an organisation is rs . 2500 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?

<gadget id="calculator">2_500 + 200</gadget>
<output>2_700</output>

<gadget id="calculator">25 + 1</gadget>
<output>26</output>

<gadget id="calculator">2_700 * 26</gadget>
<output>70_200</output>

<gadget id="calculator">2_500 * 25</gadget>
<output>62_500</output>

<gadget id="calculator">70_200 - 62_500</gadget>
<output>7_700</output>
<result>7_700</result>

Choices:
A. rs . 7700
B. rs . 3618
C. rs . 3600
D. rs . 3619
E. rs . 3610

subtract(multiply(add(2500, 200), add(25, const_1)), multiply(2500, 25))

Explanation: "manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a"


Question: we had $ 1400 left after spending 30 % of the money that we took for shopping . how much money did we start with ?

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">1_400 / (7/10)</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. $ 2000
B. $ 2100
C. $ 2200
D. $ 2300
E. $ 2400

divide(1400, subtract(const_1, divide(30, const_100)))

Explanation: "let x be the amount of money we started with . 0.7 x = 1400 x = 2000 the answer is a ."


Question: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 94 % water by weight . what is the new weight of the cucumbers , in pounds ?

<gadget id="calculator">100 - 99</gadget>
<output>1</output>

<gadget id="calculator">100 - 94</gadget>
<output>6</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) * 100</gadget>
<output>50/3 = around 16.666667</output>
<result>50/3 = around 16.666667</result>

Choices:
A. 2
B. 16
C. 92
D. 96
E. 98

multiply(divide(subtract(100, 99), subtract(100, 94)), 100)

Explanation: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 94 % water and 6 % of non - water , so now 1 pound of non - water composes 6 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.06 = 16 pounds . answer : b ."


Question: in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party .

<gadget id="calculator">105 * 2</gadget>
<output>210</output>

<gadget id="calculator">210 * 4</gadget>
<output>840</output>

<gadget id="calculator">840 + 1</gadget>
<output>841</output>

<gadget id="calculator">841 ** (1/2)</gadget>
<output>29</output>

<gadget id="calculator">29 + 1</gadget>
<output>30</output>

<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 14
B. 12
C. 13
D. 15
E. 16

divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2)

Explanation: "let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d"


Question: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?

<gadget id="calculator">60 / 2</gadget>
<output>30</output>

<gadget id="calculator">30 - 5</gadget>
<output>25</output>

<gadget id="calculator">20 / 1.5</gadget>
<output>13.333333</output>

<gadget id="calculator">60 / 13.333333</gadget>
<output>4.5</output>

<gadget id="calculator">25 - 4.5</gadget>
<output>20.5</output>
<result>20.5</result>

Choices:
A. 20.5
B. 15
C. 25.5
D. 30
E. 60

subtract(subtract(divide(const_60, const_2), 5), divide(const_60, divide(20, 1.5)))

Explanation: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 5 x = 20.5 minutes answer : a"


Question: a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 / 6</gadget>
<output>5_000/3 = around 1_666.666667</output>

<gadget id="calculator">(5_000/3) * 3</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 50
B. 30
C. 20
D. 40
E. 10

divide(multiply(divide(multiply(const_10, const_1000), 6), 3), const_100)

Explanation: let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a


Question: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 10 hours a day , the number of men required ?

<gadget id="calculator">12 * 10</gadget>
<output>120</output>

<gadget id="calculator">120 * 8</gadget>
<output>960</output>

<gadget id="calculator">8 * 10</gadget>
<output>80</output>

<gadget id="calculator">960 / 80</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 10 days
B. 12 days
C. 13 days
D. 11 days
E. 9 days

divide(multiply(multiply(12, 10), 8), multiply(8, 10))

Explanation: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 10 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 10 × 8 = 12 days b )"


Question: there are 240 doctors and nurses at a hospital . if the ratio of doctors to nurses is 3 to 7 , how many nurses are at the hospital ?

<gadget id="calculator">3 + 7</gadget>
<output>10</output>

<gadget id="calculator">240 / 10</gadget>
<output>24</output>

<gadget id="calculator">24 * 7</gadget>
<output>168</output>
<result>168</result>

Choices:
A. 168
B. 172
C. 176
D. 180
E. 184

Explanation: "the number of nurses at the hospital is ( 7 / 10 ) * 240 = 168 . the answer is a ."