Question: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?

<gadget id="calculator">1_200 / 30</gadget>
<output>40</output>

<gadget id="calculator">30 + 40</gadget>
<output>70</output>

<gadget id="calculator">30 ** 2</gadget>
<output>900</output>

<gadget id="calculator">40 ** 2</gadget>
<output>1_600</output>

<gadget id="calculator">900 + 1_600</gadget>
<output>2_500</output>

<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>

<gadget id="calculator">70 + 50</gadget>
<output>120</output>

<gadget id="calculator">120 * 10</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 2387
B. 1298
C. 1128
D. 1237
E. 1200

Explanation: "l * 30 = 1200 l = 40 40 + 30 + 50 = 120 120 * 10 = 1200 e"


Question: the length of a rectangle is 2 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?

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

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

Choices:
A. 30 square inches
B. 75 square inches
C. 68 square inches
D. 89 square inches
E. 32 square inches

Explanation: "if the width is 4 in and the length is 2 times the width , then the length is 2 * 4 = 8 in the area is given by 4 * 8 = 32 square inches correct answer e"


Question: the ratio between the sale price and the cost price of an article is 7 : 4 . what is the ratio between the profit and the cost price of that article ?

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

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

Choices:
A. 3 : 4
B. 1 : 2
C. 2 : 5
D. 3 : 5
E. 25

Explanation: "c . p . = rs . 4 x and s . p . = rs . 7 x . then , gain = rs . 3 x required ratio = 3 x : 4 x = 3 : 4 a"


Question: barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">(3/50) * 2_400</gadget>
<output>144</output>

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">2_400 * (1/20)</gadget>
<output>120</output>

<gadget id="calculator">144 - 120</gadget>
<output>24</output>

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/25) - (3/50)</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">24 / (1/50)</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. 1200
B. 3000
C. 1000
D. 3600
E. 2400

divide(subtract(multiply(divide(6, const_100), 2400), multiply(2400, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100)))

Explanation: "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.02 = 1200 ans : ` ` a ' '"


Question: difference between a two - digit number and the number obtained by interchanging the two digits is 36 , what is the difference between two numbers

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

<gadget id="calculator">36 / 9</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 2
B. 4
C. 8
D. 12
E. 14

Explanation: explanation : let the ten digit be x , unit digit is y . then ( 10 x + y ) - ( 10 y + x ) = 36 = > 9 x - 9 y = 36 = > x - y = 4 . option b


Question: the average score of a cricketer in 6 matches is 27 and in other 4 matches is 32 . then find the average score in all the 10 matches ?

<gadget id="calculator">6 * 27</gadget>
<output>162</output>

<gadget id="calculator">4 * 32</gadget>
<output>128</output>

<gadget id="calculator">162 + 128</gadget>
<output>290</output>

<gadget id="calculator">290 / 10</gadget>
<output>29</output>
<result>29</result>

Choices:
A. 25
B. 27
C. 30
D. 29
E. 42

divide(add(multiply(6, 27), multiply(4, 32)), 10)

Explanation: "average in 10 matches = ( 6 * 27 + 4 * 32 ) / 6 + 4 = 162 + 128 / 10 = 290 / 10 = 29 answer is d"


Question: rs . 900 amounts to rs . 920 in 3 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?

Choices:
A. rs . 1056
B. rs . 1001
C. rs . 2056
D. rs . 1026
E. rs . 1856

multiply(power(add(const_1, divide(3, const_100)), 3), 900)

Explanation: "( 900 * 3 * 3 ) / 100 = 81 920 + 81 = 1001 answer : b"


Question: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 136 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

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

<gadget id="calculator">(1/10) + (3/4)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">136 / (17/20)</gadget>
<output>160</output>

<gadget id="calculator">160 - 136</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 24
B. 33
C. 55
D. 77
E. 88

subtract(divide(136, add(divide(10, const_100), divide(3, 4))), 136)

Explanation: let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 136 = > . 1 x + 3 / 4 x = 136 = > x = 160 160 - 136 = pure gala = 24 . a


Question: at a monthly meeting , 1 / 3 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>

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

<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(1/6) * (2/3)</gadget>
<output>1/9 = around 0.111111</output>

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

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

<gadget id="calculator">(1/5) * (1/3)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/9) + (1/15)</gadget>
<output>8/45 = around 0.177778</output>
<result>8/45 = around 0.177778</result>

Choices:
A. 1 / 6
B. 2 / 15
C. 3 / 20
D. 7 / 30
E. 8 / 45

add(multiply(subtract(const_1, divide(5, 6)), subtract(const_1, divide(1, 3))), multiply(subtract(const_1, divide(4, 5)), divide(1, 3)))

Explanation: "males who did not arrive on time are 1 / 5 * 1 / 3 = 1 / 15 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 3 = 1 / 9 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 15 + 1 / 9 = 8 / 45 the answer is e ."


Question: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 30 % . what would have been the percentage of profit earned if no discount was offered ?

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

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

<gadget id="calculator">130 / 95</gadget>
<output>26/19 = around 1.368421</output>

<gadget id="calculator">100 * (26/19)</gadget>
<output>2_600/19 = around 136.842105</output>
<result>2_600/19 = around 136.842105</result>

Choices:
A. 140
B. 120
C. 130
D. 136.8
E. 150

multiply(const_100, divide(add(const_100, 30), subtract(const_100, 5)))

Explanation: "let c . p . be $ 100 . then , s . p . = $ 130 let marked price be $ x . then , 95 / 100 x = 130 x = 13000 / 95 = $ 136.8 now , s . p . = $ 136.8 , c . p . = $ 100 profit % = 136.8 % . d"


Question: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 300 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?

<gadget id="calculator">lcm(300, 200)</gadget>
<output>600</output>

<gadget id="calculator">600 / 300</gadget>
<output>2</output>

<gadget id="calculator">600 / 200</gadget>
<output>3</output>

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

Choices:
A. 3
B. 5
C. 7
D. 9
E. 11

Explanation: "the smallest amount that the company can spend is the lcm of 300 and 200 , which is 600 for each , which is total 1200 . the number of 1 st type of computers which costing $ 300 = 600 / 300 = 2 . the number of 2 nd type of computers which costing $ 200 = 600 / 200 = 3 . total = 2 + 3 = 5 answer is b ."


Question: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 14 is divided by 12 .

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

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>

<gadget id="calculator">14 + 25</gadget>
<output>39</output>

<gadget id="calculator">12 * 3</gadget>
<output>36</output>

<gadget id="calculator">39 - 36</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 6
B. 1
C. 3
D. 8
E. 7

subtract(add(14, power(add(const_1, const_4), 2)), multiply(12, 3))

Explanation: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c ."


Question: a man has some hens and cows . if the number of heads be 42 and the number of feet equals 124 , then the number of hens will be

<gadget id="calculator">42 * 4</gadget>
<output>168</output>

<gadget id="calculator">168 - 124</gadget>
<output>44</output>

<gadget id="calculator">44 / 2</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 22
B. 24
C. 26
D. 20
E. 28

divide(subtract(multiply(42, const_4), 124), const_2)

Explanation: "explanation : let number of hens = h and number of cows = c number of heads = 42 = > h + c = 42 - - - ( equation 1 ) number of feet = 124 = > 2 h + 4 c = 124 = > h + 2 c = 62 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 62 - 42 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 42 = > h = 42 - 20 = 22 i . e . , number of hens = 22 answer : a"


Question: find large number from below question the difference of two numbers is 1385 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

<gadget id="calculator">1_385 - 15</gadget>
<output>1_370</output>

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

<gadget id="calculator">1_370 / 5</gadget>
<output>274</output>

<gadget id="calculator">274 * 6</gadget>
<output>1_644</output>
<result>1_644</result>

Choices:
A. 1235
B. 1345
C. 1678
D. 1767
E. 1659

multiply(divide(subtract(1385, 15), subtract(6, const_1)), 6)

Explanation: "let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 large number = 274 + 1385 = 1659 e"


Question: convert 0.30 in to a vulgar fraction ?

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

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

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

<gadget id="calculator">100 * 0.3</gadget>
<output>30</output>

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

Choices:
A. 18 / 50
B. 16 / 50
C. 3 / 10
D. 19 / 50
E. none

divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.3), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))

Explanation: answer 0.30 = 30 / 100 = 3 / 10 correct option : c


Question: a room is 30 m long and 24 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :

<gadget id="calculator">30 * 24</gadget>
<output>720</output>

<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>

<gadget id="calculator">2 * (30 + 24)</gadget>
<output>108</output>

<gadget id="calculator">1_440 / 108</gadget>
<output>40/3 = around 13.333333</output>

<gadget id="calculator">30 * 24 * (40/3)</gadget>
<output>9_600</output>
<result>9_600</result>

Choices:
A. 9.6 m 3
B. 96 m 3
C. 960 m 3
D. 9600 m 3
E. 96000 m 3

volume_rectangular_prism(30, 24, divide(multiply(rectangle_area(30, 24), const_2), rectangle_perimeter(30, 24)))

Explanation: let the height be h 2 ( 30 + 24 ) x h – 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d


Question: if $ 120 invested at a certain rate of simple interest amounts to $ 180 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?

<gadget id="calculator">150 * 6</gadget>
<output>900</output>

<gadget id="calculator">180 - 120</gadget>
<output>60</output>

<gadget id="calculator">60 * 120</gadget>
<output>7_200</output>

<gadget id="calculator">7_200 / 120</gadget>
<output>60</output>

<gadget id="calculator">60 / 3</gadget>
<output>20</output>

<gadget id="calculator">900 * 20</gadget>
<output>18_000</output>

<gadget id="calculator">18_000 / 120</gadget>
<output>150</output>

<gadget id="calculator">150 + 150</gadget>
<output>300</output>
<result>300</result>

Choices:
A. $ 190
B. $ 180
C. $ 200
D. $ 240
E. $ 300

add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(180, 120), 120), 120), 3)), 120))

Explanation: "120 amounts to 180 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 180 120 + 120 * ( r / 100 ) * ( 3 ) = 140 = > r = 50 / 3 150 in 6 years = principal + interest = 300 answer is e ."


Question: the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ?

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) * 1.2</gadget>
<output>1.8</output>
<result>1.8</result>

Choices:
A. $ 1.80
B. $ 2.00
C. $ 2.40
D. $ 2.70
E. $ 3.00

Explanation: the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a .


Question: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , the how old is b ?

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

<gadget id="calculator">35 * 2</gadget>
<output>70</output>

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

<gadget id="calculator">70 / 5</gadget>
<output>14</output>
<result>14</result>

Choices:
A. 7
B. 9
C. 8
D. 14
E. 10

divide(multiply(subtract(37, const_2), const_2), add(const_4, const_1))

Explanation: explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 ⇒ 5 x = 35 ⇒ x = 7 . hence , b ' s age = 2 x = 14 years . answer : d


Question: if c and t are positive integers , ct + c + t can not be

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

Choices:
A. 5
B. 6
C. 7
D. 8
E. 9

Explanation: let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b


Question: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately

Choices:
A. 2972
B. 4567
C. 4235
D. 4547
E. 4675

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 2)

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 2 ) = rs . 2972 . answer : option a"


Question: a man swims downstream 30 km and upstream 12 km taking 3 hours each time , what is the speed of the man in still water ?

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

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

<gadget id="calculator">4 + 10</gadget>
<output>14</output>

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

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

divide(add(divide(12, 3), divide(30, 3)), const_2)

Explanation: "30 - - - 3 ds = 10 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 10 + 4 ) / 2 = 7 answer : b"


Question: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 7 x km .

<gadget id="calculator">40 * 7</gadget>
<output>280</output>

<gadget id="calculator">40 / 40</gadget>
<output>1</output>

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

<gadget id="calculator">80 / 20</gadget>
<output>4</output>

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

<gadget id="calculator">280 / 5</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 56
B. 18
C. 24
D. 19
E. 12

divide(multiply(40, 7), add(divide(40, 40), divide(multiply(2, 40), 20)))

Explanation: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 7 x / ( x / 8 ) = 56 kmph answer : a"


Question: if the average of 6 digits is 16 and the average of 4 of them is 10 , calculate the average of the remaining 2 numbers ?

<gadget id="calculator">6 * 16</gadget>
<output>96</output>

<gadget id="calculator">4 * 10</gadget>
<output>40</output>

<gadget id="calculator">96 - 40</gadget>
<output>56</output>

<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 36
B. 35
C. 28
D. 33
E. 21

divide(subtract(multiply(6, 16), multiply(4, 10)), 2)

Explanation: "explanation : total of the 6 digits - 6 * 16 = 96 total of the 4 digits - 4 * 10 = 40 total of the remaining 2 digits - 96 - 40 = 56 average of the remaining 2 numbers = 56 / 2 = 28 answer : c"


Question: a company pays 20.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?

<gadget id="calculator">20.5 * 50</gadget>
<output>1_025</output>

<gadget id="calculator">1_025 / 100</gadget>
<output>41/4 = around 10.25</output>

<gadget id="calculator">(41/4) * 100</gadget>
<output>1_025</output>

<gadget id="calculator">1_025 / 25</gadget>
<output>41</output>
<result>41</result>

Choices:
A. 25
B. 66
C. 18
D. 19
E. 41

divide(multiply(divide(multiply(20.5, 50), const_100), const_100), 25)

Explanation: "explanation : dividend on 1 share = ( 20.5 * 50 ) / 100 = rs . 10.25 rs . 25 is income on an investment of rs . 100 rs . 10.25 is income on an investment of rs . ( 10.25 * 100 ) / 25 = rs . 41 answer : e"


Question: how many diagonals does a 59 - sided convex polygon have ?

Choices:
A. 1168
B. 1652
C. 2452
D. 3304
E. 4256

divide(factorial(59), multiply(factorial(subtract(59, const_2)), factorial(const_2)))

Explanation: a 59 - sided convex polygon has 59 vertices . if we examine a single vertex , we can see that we can connect it with 56 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be ( 59 ) ( 56 ) = 3304 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3304 by 2 to get 1652 . the answer is b .


Question: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 33 % . what would have been the percentage of profit earned if no discount was offered ?

<gadget id="calculator">100 + 33</gadget>
<output>133</output>

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

<gadget id="calculator">133 / 95</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">100 * (7/5)</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 140
B. 120
C. 130
D. 110
E. 150

multiply(const_100, divide(add(const_100, 33), subtract(const_100, 5)))

Explanation: "let c . p . be $ 100 . then , s . p . = $ 133 let marked price be $ x . then , 95 / 100 x = 133 x = 13300 / 95 = $ 140 now , s . p . = $ 140 , c . p . = $ 100 profit % = 40 % . a"


Question: calculate how long it will take a swimmer to swim a distance of 10 km against the current of a river which flows at 3 km / hr , given that he can swim in still water at 5 km / h

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

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

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

Explanation: "swim in still water at = 5 speed of river = 3 us = 5 - 3 = 2 distance = 10 t = 10 / 2 = 5 answer : c"


Question: a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was :

<gadget id="calculator">84 * 8</gadget>
<output>672</output>

<gadget id="calculator">672 + 85</gadget>
<output>757</output>

<gadget id="calculator">757 - 92</gadget>
<output>665</output>
<result>665</result>

Choices:
A. 665
B. 376
C. 998
D. 1277
E. 1991

Explanation: explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665


Question: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 20 seconds . how long does it tick at 12 ′ o clock

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

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

<gadget id="calculator">12 - 1</gadget>
<output>11</output>

<gadget id="calculator">4 * 11</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 47
B. 76
C. 44
D. 66
E. 11

multiply(divide(20, subtract(6, const_1)), subtract(12, const_1))

Explanation: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 20 / 5 = 4 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 4 = 44 secs . answer : c"


Question: the price of a t . v . set worth rs . 30000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?

<gadget id="calculator">30_000 - 1_000</gadget>
<output>29_000</output>
<result>29_000</result>

Choices:
A. 22678
B. 26699
C. 29000
D. 19000
E. 26711

Explanation: "money paid in cash = rs . 1000 balance payment = ( 30000 - 1000 ) = rs . 29000 answer : c"


Question: 55 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :

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

<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * pi</gadget>
<output>pi/4 = around 0.785398</output>

<gadget id="calculator">55 / (pi/4)</gadget>
<output>220/pi = around 70.028175</output>
<result>220/pi = around 70.028175</result>

Choices:
A. 84 m
B. 88 m
C. 120 m
D. 70 m
E. none

divide(55, multiply(power(divide(1, const_2), const_2), const_pi))

Explanation: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 55 ⇔ = [ 55 * 20 * 20 * 7 / 22 ] = 7000 cm = 70 m . answer d"


Question: a metallic sheet is of rectangular shape with dimensions 48 m x 34 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :

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

<gadget id="calculator">48 - 16</gadget>
<output>32</output>

<gadget id="calculator">34 - 16</gadget>
<output>18</output>

<gadget id="calculator">32 * 18 * 8</gadget>
<output>4_608</output>
<result>4_608</result>

Choices:
A. 4830
B. 5120
C. 4608
D. 7500
E. 8960

volume_rectangular_prism(subtract(48, multiply(8, const_2)), subtract(34, multiply(8, const_2)), 8)

Explanation: "l = ( 48 - 16 ) m = 32 m , b = ( 34 - 16 ) m = 18 m , h = 8 m . volume of the box = ( 32 x 18 x 8 ) m 3 = 4608 m 3 . answer : option c"


Question: a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?

<gadget id="calculator">0.7 * 4</gadget>
<output>2.8</output>

<gadget id="calculator">6.3 - 2.8</gadget>
<output>3.5</output>

<gadget id="calculator">3.5 / 0.5</gadget>
<output>7</output>

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

Choices:
A. 12
B. 13
C. 11
D. 14
E. 5

add(divide(subtract(6.3, multiply(0.7, const_4)), 0.5), const_4)

Explanation: some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c


Question: if 25 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?

<gadget id="calculator">880 / 100</gadget>
<output>44/5 = around 8.8</output>

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">(44/5) * 75</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 500
B. 600
C. 620
D. 640
E. 660

multiply(divide(880, const_100), subtract(const_100, 25))

Explanation: "we know 25 % people study biology , therefore the no of people not studying = 100 - 25 = 75 % > therefore the people not studying biology out of a total 880 people are = 75 % of 880 > ( 75 / 100 ) * 880 = 660 people e"


Question: find large number from below question the difference of two numbers is 1380 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

<gadget id="calculator">1_380 - 15</gadget>
<output>1_365</output>

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

<gadget id="calculator">1_365 / 5</gadget>
<output>273</output>

<gadget id="calculator">273 * 6</gadget>
<output>1_638</output>
<result>1_638</result>

Choices:
A. 1245
B. 1345
C. 1455
D. 1577
E. 1653

multiply(divide(subtract(1380, 15), subtract(6, const_1)), 6)

Explanation: "let the smaller number be x . then larger number = ( x + 1380 ) . x + 1380 = 6 x + 15 5 x = 1365 x = 273 large number = 273 + 1380 = 1653 e"


Question: tough and tricky questions : word problems . operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 8 , when a # b = 100 ?

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

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

<gadget id="calculator">5 + 8</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 5
B. 8
C. 10
D. 13
E. 17

Explanation: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d


Question: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 240 6 ounces servings of orange juice ?

<gadget id="calculator">240 * 6</gadget>
<output>1_440</output>

<gadget id="calculator">1_440 / 12</gadget>
<output>120</output>

<gadget id="calculator">120 / 4</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 25
B. 34
C. 50
D. 67
E. 30

divide(divide(multiply(240, 6), 12), const_4)

Explanation: "its e . total juice rquired = 240 * 6 = 1440 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1440 / 48 = 30 . answer e"


Question: mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 38400 , how much amount per month would he have spent on clothes and transport ?

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

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>

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

<gadget id="calculator">38_400 / (1/5)</gadget>
<output>192_000</output>

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">192_000 / 12</gadget>
<output>16_000</output>

<gadget id="calculator">16_000 * (1/5)</gadget>
<output>3_200</output>
<result>3_200</result>

Choices:
A. 4038
B. 8076
C. 3200
D. 4845.6
E. none of these

multiply(divide(divide(38400, divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)), multiply(const_3, const_4)), divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100))

Explanation: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 38400 ⁄ 12 = 3200 answer c"


Question: daniel went to a shop and bought things worth rs . 50 , out of which 90 paise went on sales tax on taxable purchases . if the tax rate was 15 % , then what was the cost of the tax free items ?

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">50 - (9/10)</gadget>
<output>491/10 = around 49.1</output>

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

<gadget id="calculator">(491/10) - 6</gadget>
<output>431/10 = around 43.1</output>
<result>431/10 = around 43.1</result>

Choices:
A. 19.7
B. 20
C. 43.1
D. 21.5
E. 22

subtract(subtract(50, divide(90, const_100)), divide(90, 15))

Explanation: total cost of the items he purchased = rs . 50 given that out of this rs . 50 , 90 paise is given as tax = > total tax incurred = 90 paise = rs . 90 / 100 let the cost of the tax free items = x given that tax rate = 15 % ∴ ( 50 − 90 / 100 − x ) 15 / 100 = 90 / 100 ⇒ 15 ( 50 − 0.9 − x ) = 90 ⇒ ( 50 − 0.9 − x ) = 6 ⇒ x = 50 − 0.9 − 6 = 43.1 c


Question: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3410 , r will receive

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

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

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

<gadget id="calculator">25 + 6</gadget>
<output>31</output>

<gadget id="calculator">6 / 31</gadget>
<output>6/31 = around 0.193548</output>

<gadget id="calculator">3_410 * (6/31)</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 660
B. 700
C. 800
D. 900
E. none of these

multiply(3410, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3410 * ( 6 / 31 ) = 110 * 6 = 660 . answer : option a"


Question: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets ?

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

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

<gadget id="calculator">24 - 12</gadget>
<output>12</output>

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

Choices:
A. 4
B. 6
C. 8
D. 10
E. 12

divide(subtract(multiply(multiply(3, 4), 2), multiply(3, 4)), 2)

Explanation: let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 1 * 6 = 6 days to produce 1 w widgets . answer : b


Question: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 175 , how many coins of each type are there ?

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

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

<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">175 / (7/4)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 20 coins
B. 30 coins
C. 50 coins
D. 100 coins
E. none of these

divide(175, add(add(inverse(const_4), inverse(const_2)), const_1))

Explanation: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 175 ⇒ 1.75 x = 175 ⇒ x = 100 coins answer d"


Question: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5000 . the amount invested by y is

<gadget id="calculator">5_000 * 6</gadget>
<output>30_000</output>

<gadget id="calculator">30_000 / 2</gadget>
<output>15_000</output>
<result>15_000</result>

Choices:
A. rs . 45,000
B. rs . 50,000
C. rs . 60,000
D. rs . 15,000
E. none

Explanation: solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d


Question: little john had $ 16.10 . he spent $ 3.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?

<gadget id="calculator">2.2 + 2.2</gadget>
<output>4.4</output>

<gadget id="calculator">3.25 + 4.4</gadget>
<output>7.65</output>

<gadget id="calculator">16.1 - 7.65</gadget>
<output>8.45</output>
<result>8.45</result>

Choices:
A. $ 6.45
B. $ 8.35
C. $ 8.75
D. $ 8.85
E. $ 8.45

Explanation: john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 16.10 - 7.65 = $ 8.45 answer : e


Question: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 10 pumps work to empty the tank in 1 day ?

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

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

<gadget id="calculator">48 / 10</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>

Choices:
A. 4.8
B. 3.6
C. 1.1
D. 1.2
E. 1.3

Explanation: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 10 pumps then 48 / 10 = 4.8 hrs . answer : a"


Question: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?

<gadget id="calculator">4 * pi</gadget>
<output>4*pi = around 12.566371</output>

<gadget id="calculator">3 / pi</gadget>
<output>3/pi = around 0.95493</output>

<gadget id="calculator">(4*pi) * (3/pi)</gadget>
<output>12</output>

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

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

<gadget id="calculator">6 + 3</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 6 / π
B. 9 / π
C. 6
D. 9
E. 12

add(divide(multiply(multiply(4, const_pi), divide(3, const_pi)), 2), multiply(const_pi, divide(3, const_pi)))

Explanation: given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !


Question: if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n .

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

<gadget id="calculator">342 + (1/4)</gadget>
<output>1_369/4 = around 342.25</output>

<gadget id="calculator">(1_369/4) ** (1/2)</gadget>
<output>37/2 = around 18.5</output>
<result>37/2 = around 18.5</result>

Choices:
A. 17
B. 18
C. 19
D. 20
E. 21

Explanation: we write n ! = n * ( n - 1 ) ( n - 2 ! ) therefore n ! / ( n - 2 ) ! = n ( n - 1 ) * ( n - 2 ) ! / ( n - 2 ) ! = n ( n - 1 ) . - - > n ( n - 1 ) = 342 - - > n ^ 2 - n - 342 = 0 - - > n ^ 2 - 19 n + 18 n - 342 = 0 - - > n ( n - 19 ) + 18 ( n - 19 ) = 0 - - > ( n - 19 ) ( n + 18 ) = 0 therefore n - 19 = 0 ; n + 18 = 0 ; ( i . e ) n = 19 ; n = - 18 we want positive integer . so , n = 19 . answer : c


Question: a person has 100 $ in 10 $ and 5 $ bill . if the 5 $ bill quantity is twice that of 10 $ bill . what is quantity of 10 $ .

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

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

Choices:
A. 2
B. 6
C. 7
D. 8
E. 5

Explanation: let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e


Question: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 5 of whom are females , by how much does the index for the females exceed the index for the males in the group ?

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

<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">5 / 20</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(3/4) - (1/4)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 0.05
B. 0.0625
C. 0.5
D. 0.25
E. 0.6

subtract(divide(subtract(20, 5), 20), divide(5, 20))

Explanation: "index for females = ( 20 - 5 ) / 20 = 3 / 4 = 0.75 index for males = ( 20 - 15 / 20 = 1 / 4 = 0.25 index for females exceeds males by 0.75 - 0.25 = 0.5 answer : c"


Question: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 12 meters , and the interior of tank b has a height of 12 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?

<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">10 / 12</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(36/25) * (5/6)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) * 100</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 80 %
B. 90 %
C. 100 %
D. 110 %
E. 120 %

multiply(multiply(power(divide(12, 10), const_2), divide(10, 12)), const_100)

Explanation: "the radius of tank a is 12 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 144 / ( 4 * pi ^ 2 ) = 360 / ( pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 12 * pi * 100 / ( 4 * pi ^ 2 ) = 300 / ( pi ) tank a / tank b = 360 / 300 = 12 / 10 = 120 % the answer is e ."


Question: eric throws 2 dice , and his score is the sum of the values shown . sandra throws one dice and her score is the square of the value shown . what is the probabilty that sandras score will be strictly higher than erics score ? ?

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

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>

<gadget id="calculator">36 - 10</gadget>
<output>26</output>

<gadget id="calculator">3 + 26</gadget>
<output>29</output>

<gadget id="calculator">29 + 36</gadget>
<output>65</output>

<gadget id="calculator">65 + 36</gadget>
<output>101</output>

<gadget id="calculator">101 + 36</gadget>
<output>137</output>

<gadget id="calculator">36 * 6</gadget>
<output>216</output>

<gadget id="calculator">137 / 216</gadget>
<output>137/216 = around 0.634259</output>
<result>137/216 = around 0.634259</result>

Choices:
A. 137 / 216
B. 137 / 218
C. 137 / 217
D. 136 / 216
E. 138 / 216

divide(add(add(add(add(const_3, subtract(power(multiply(2, const_3), const_2), const_10)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), multiply(power(multiply(2, const_3), const_2), multiply(2, const_3)))

Explanation: sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a


Question: if $ 910 are divided between worker a and worker b in the ratio 5 : 9 , what is the share that worker b will get ?

<gadget id="calculator">5 + 9</gadget>
<output>14</output>

<gadget id="calculator">910 / 14</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 62.27 %
B. 63.28 %
C. 64.29 %
D. 65.31 %
E. 66.32 %

Explanation: worker b will get 9 / 14 = 64.29 % the answer is c .


Question: someone on a skateboard is traveling 8 miles per hour . how many feet does she travel in 5 seconds ? ( 1 mile = 5280 feet )

<gadget id="calculator">8 * 5_280</gadget>
<output>42_240</output>

<gadget id="calculator">42_240 / 3_600</gadget>
<output>176/15 = around 11.733333</output>

<gadget id="calculator">5 * (176/15)</gadget>
<output>176/3 = around 58.666667</output>
<result>176/3 = around 58.666667</result>

Choices:
A. 60 ft
B. 52 ft
C. 53 ft
D. 55 ft
E. 58.65 ft

multiply(5, divide(multiply(8, 5280), const_3600))

Explanation: "per second = > 8 * 5280 ft / 60 * 60 = 11.73 ft 5 seconds = > 11.73 * 5 = 58.65 ft answer : e"


Question: a car traveling at a certain constant speed takes 30 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 30 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">3_600 * (1/30)</gadget>
<output>120</output>

<gadget id="calculator">120 + 30</gadget>
<output>150</output>

<gadget id="calculator">150 / 3_600</gadget>
<output>1/24 = around 0.041667</output>

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

Choices:
A. 16
B. 18
C. 20
D. 22
E. 24

divide(1, divide(add(multiply(const_3600, divide(1, 30)), 30), const_3600))

Explanation: "30 * t = 1 km = > t = 1 / 30 km / h v * ( t + 30 / 3600 ) = 1 v ( 1 / 30 + 30 / 3600 ) = 1 v ( 150 / 3600 ) = 1 v = 24 km / h the answer is e ."


Question: of the families in city x in 1998 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2002 was 20 percent greater than it was in 1998 , and the total number of families in city x was 8 percent greater in 2002 than it was in 1998 . what percent of the families in city x owned a personal computer in 2002 ?

<gadget id="calculator">20 + 100</gadget>
<output>120</output>

<gadget id="calculator">120 * 30</gadget>
<output>3_600</output>

<gadget id="calculator">3_600 / 100</gadget>
<output>36</output>

<gadget id="calculator">100 + 8</gadget>
<output>108</output>

<gadget id="calculator">36 / 108</gadget>
<output>1/3 = around 0.333333</output>

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

Choices:
A. 50.12 %
B. 52.66 %
C. 56.33 %
D. 33.33 %
E. 74.12 %

multiply(const_100, divide(divide(multiply(add(20, const_100), 30), const_100), add(const_100, 8)))

Explanation: say a 100 families existed in 1998 then the number of families owning a computer in 1998 - 30 number of families owning computer in 2002 = 30 * 120 / 100 = 36 number of families in 2002 = 108 the percentage = 36 / 108 * 100 = 33.33 % . option : d


Question: recently , i decided to walk down an escalator of a tube station . i did some quick calculation in my mind . i found that if i walk down 20 ` ` 6 steps , i require thirty seconds to reach the bottom . however , if i am able to step down thirty ` ` 4 stairs , i would only require eighteen seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time i step off the last step at the bottom ?

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

<gadget id="calculator">30 + 4</gadget>
<output>34</output>

<gadget id="calculator">20 + 6</gadget>
<output>26</output>

<gadget id="calculator">34 - 26</gadget>
<output>8</output>

<gadget id="calculator">6 * 3</gadget>
<output>18</output>

<gadget id="calculator">30 - 18</gadget>
<output>12</output>

<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 18</gadget>
<output>12</output>

<gadget id="calculator">34 + 12</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 43
B. 44
C. 45
D. 40
E. 46

add(add(multiply(const_3, const_10), 4), multiply(divide(subtract(add(multiply(const_3, const_10), 4), add(20, 6)), subtract(multiply(const_3, const_10), multiply(6, const_3))), multiply(6, const_3)))

Explanation: 26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto . means he covered 8 steps ( i . e . 34 - 26 ) in 12 ( i . e 30 - 18 ) seconds the spped of the boy is 8 steps in 12 seconds after further simplyfy . . 2 steps in 3 seconds after 34 steps only 18 seconds , means 12 more steps are left total steps are 34 + 12 = 46 answer : e


Question: if y > 0 , ( 2 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

<gadget id="calculator">2 / 20</gadget>
<output>1/10 = around 0.1</output>

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

<gadget id="calculator">(1/10) + (3/10)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">100 * (2/5)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40 %
B. 50 %
C. 60 %
D. 70 %
E. 80 %

multiply(const_100, add(divide(2, 20), divide(3, 10)))

Explanation: "soln : - can be reduced to y / 10 + 3 y / 10 = 2 y / 5 = 40 % answer : a"


Question: at a loading dock , each worker on the night crew loaded 2 / 3 as many boxes as each worker on the day crew . if the night crew has 5 / 6 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?

<gadget id="calculator">6 * 3</gadget>
<output>18</output>

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

<gadget id="calculator">18 + 10</gadget>
<output>28</output>

<gadget id="calculator">18 / 28</gadget>
<output>9/14 = around 0.642857</output>
<result>9/14 = around 0.642857</result>

Choices:
A. 6 / 11
B. 7 / 12
C. 8 / 13
D. 9 / 14
E. 11 / 15

divide(multiply(6, 3), add(multiply(6, 3), multiply(2, 5)))

Explanation: let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 5 x / 6 ) ( 2 y / 3 ) = 5 xy / 9 the total number of boxes is xy + 5 xy / 9 = 14 xy / 9 the fraction loaded by the day crew is xy / ( 14 xy / 9 ) = 9 / 14 the answer is d .


Question: if a train , travelling at a speed of 90 kmph , crosses a pole in 6 sec , then the length of train is ?

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>

<gadget id="calculator">25 * 6</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 281 m
B. 112 m
C. 117 m
D. 125 m
E. 150 m

Explanation: "e e = 90 * 5 / 18 * 6 = 150 m"


Question: find the number of different prime factors of 25650

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

Choices:
A. 4
B. 2
C. 3
D. 5
E. 6

Explanation: explanation : l . c . m of 25650 = 2 x 3 x 3 x 3 x 5 x 5 x 19 3 , 2 , 5,19 number of different prime factors is 4 . answer : option a


Question: the mean of 50 observations was 36 . it was found later that an observation 58 was wrongly taken as 43 . the corrected new mean is ?

<gadget id="calculator">36 * 50</gadget>
<output>1_800</output>

<gadget id="calculator">50 - 2</gadget>
<output>48</output>

<gadget id="calculator">48 - 43</gadget>
<output>5</output>

<gadget id="calculator">1_800 + 5</gadget>
<output>1_805</output>

<gadget id="calculator">1_805 / 50</gadget>
<output>361/10 = around 36.1</output>
<result>361/10 = around 36.1</result>

Choices:
A. 36.7
B. 36.1
C. 36.5
D. 36.9
E. 36.3

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 43)), 50)

Explanation: "correct sum = ( 36 * 50 + 58 - 43 ) = 1815 . correct mean = 1815 / 50 = 36.3 answer : e"


Question: in a school of 450 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?

<gadget id="calculator">44 + 28</gadget>
<output>72</output>

<gadget id="calculator">72 + 10</gadget>
<output>82</output>

<gadget id="calculator">100 - 82</gadget>
<output>18</output>

<gadget id="calculator">450 * 18</gadget>
<output>8_100</output>

<gadget id="calculator">8_100 / 100</gadget>
<output>81</output>
<result>81</result>

Choices:
A. 72
B. 75
C. 80
D. 81
E. 90

divide(multiply(450, subtract(const_100, add(add(44, 28), 10))), const_100)

Explanation: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 450 * 18 / 100 = 81 answer : d"


Question: find the volume and surface area of a cuboid 16 m long , 14 m broad and 7 m high .

<gadget id="calculator">16 * 7</gadget>
<output>112</output>

<gadget id="calculator">16 * 14</gadget>
<output>224</output>

<gadget id="calculator">14 * 7</gadget>
<output>98</output>

<gadget id="calculator">224 + 98</gadget>
<output>322</output>

<gadget id="calculator">112 + 322</gadget>
<output>434</output>

<gadget id="calculator">434 * 2</gadget>
<output>868</output>
<result>868</result>

Choices:
A. 878 cm ^ 2
B. 858 cm ^ 2
C. 838 cm ^ 2
D. 868 cm ^ 2
E. none of them

multiply(add(multiply(16, 7), add(multiply(16, 14), multiply(14, 7))), const_2)

Explanation: volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d


Question: 3 - twentieths of the members of a social club are retirees who are also bridge players , 5 - twentieths of the members are retirees , and one - half of the members are bridge players . if 120 of the members are neither retirees nor bridge players , what is the total number of members in the social club ?

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

<gadget id="calculator">120 - 20</gadget>
<output>100</output>

<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 240
B. 300
C. 200
D. 400
E. 480

multiply(subtract(120, multiply(5, const_4)), const_2)

Explanation: { total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c


Question: the total marks obtained by a student in mathematics and physics is 80 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .

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

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 40
B. 30
C. 25
D. 50
E. none of these .

Explanation: let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 80 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 80 + 20 ) / 2 = 50 . answer : d


Question: the perimeter of a triangle is 44 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?

<gadget id="calculator">(2.5 * 44) / 2</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 38 cm 2
B. 55 cm 2
C. 65 cm 2
D. 45 cm 2
E. 35 cm 2

Explanation: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : b"


Question: the principal that amounts to rs . 4903 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?

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

<gadget id="calculator">6 + (1/4)</gadget>
<output>25/4 = around 6.25</output>

<gadget id="calculator">(25/4) / 100</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">1 + (1/16)</gadget>
<output>17/16 = around 1.0625</output>

<gadget id="calculator">(17/16) ** 3</gadget>
<output>4_913/4_096 = around 1.199463</output>

<gadget id="calculator">4_903 / (4_913/4_096)</gadget>
<output>20_082_688/4_913 = around 4_087.662935</output>
<result>20_082_688/4_913 = around 4_087.662935</result>

Choices:
A. s . 3096
B. s . 4076
C. s . 4085
D. s . 4096
E. s . 5096

divide(4903, power(add(1, divide(add(6, divide(1, 4)), const_100)), 3))

Explanation: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4903 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4076 . answer : b"


Question: in a group of 95 students , 36 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?

<gadget id="calculator">36 + 32</gadget>
<output>68</output>

<gadget id="calculator">68 - 59</gadget>
<output>9</output>

<gadget id="calculator">36 - 9</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 9
B. 19
C. 23
D. 45
E. 27

Explanation: "number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 95 - 59 = 36 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 95 = 36 + 32 + 36 - x or x = 9 now , number of students taking only history will be h - x or 36 - 9 = 27 answer : - e"


Question: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 80 cents more than the commodity y ?

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

<gadget id="calculator">4.4 - 4.2</gadget>
<output>0.2</output>

<gadget id="calculator">(4/5) + 0.2</gadget>
<output>1</output>

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

<gadget id="calculator">(3/10) - 0.2</gadget>
<output>0.1</output>

<gadget id="calculator">1 / 0.1</gadget>
<output>10</output>

<gadget id="calculator">2_001 + 10</gadget>
<output>2_011</output>
<result>2_011</result>

Choices:
A. 2010 .
B. 2011 .
C. 2012 .
D. 2013 .
E. 2014 .

add(2001, divide(add(divide(80, const_100), subtract(4.40, 4.20)), subtract(divide(30, const_100), subtract(4.40, 4.20))))

Explanation: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 80 = $ 1.00 cents on commodity y , which will take 10 years . the answer is b ."


Question: there are 13 clubs in a full deck of 52 cards . in a certain game , you pick a card from a standard deck of 52 cards . if the card is a club , you win . if the card is not a club , the person replaces the card to the deck , reshuffles , and draws again . the person keeps repeating that process until he picks a club , and the point is to measure how many draws it took before the person picked a club and , thereby , won . what is the probability that one will pick the first club on the forth draw or later ?

<gadget id="calculator">52 - 13</gadget>
<output>39</output>

<gadget id="calculator">39 / 52</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) * (3/4)</gadget>
<output>9/16 = around 0.5625</output>

<gadget id="calculator">(9/16) * (3/4)</gadget>
<output>27/64 = around 0.421875</output>
<result>27/64 = around 0.421875</result>

Choices:
A. 1 / 2
B. 3 / 4
C. 7 / 8
D. 27 / 32
E. 27 / 64

multiply(multiply(divide(subtract(52, 13), 52), divide(subtract(52, 13), 52)), divide(subtract(52, 13), 52))

Explanation: favorable case = the club is picked in the third draw or later unfavorable cases = the club is picked in either first draw , second draw or third draws probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case 1 : probability of club picked in first draw = 13 / 52 = 1 / 4 unfavorable case 2 : probability of club picked in second draw ( i . e . first draw is not club ) = ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 unfavorable case 3 : probability of club picked in third draw ( i . e . first and 2 nd draws are not clubs ) = ( 39 / 52 ) * ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 3 / 4 ) * ( 1 / 4 ) = 9 / 64 total unfavorable probability = ( 1 / 4 ) + ( 3 / 16 ) + ( 9 / 64 ) = ( 16 / 64 ) + ( 12 / 64 ) + ( 9 / 64 ) = 37 / 64 i . e . , favorable probability = 1 - ( 37 / 64 ) = 27 / 64 answer : option e


Question: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 70 , and what number ?

<gadget id="calculator">20 + 40</gadget>
<output>60</output>

<gadget id="calculator">60 + 60</gadget>
<output>120</output>

<gadget id="calculator">5 * 3</gadget>
<output>15</output>

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

<gadget id="calculator">25 + 70</gadget>
<output>95</output>

<gadget id="calculator">120 - 95</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 15
B. 25
C. 35
D. 45
E. 55

subtract(add(add(20, 40), 60), add(add(multiply(5, const_3), 10), 70))

Explanation: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 answer : b"


Question: if 28 % of a number exceeds 18 % of it by 7.2 , then find the number ?

<gadget id="calculator">28 - 18</gadget>
<output>10</output>

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">7.2 / (1/10)</gadget>
<output>72</output>

<gadget id="calculator">72 + 18</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 50
B. 34
C. 55
D. 60
E. 90

add(divide(7.2, divide(subtract(28, 18), const_100)), 18)

Explanation: use the elimination method to find the correct option . of all the options only 90 fits 28 % of 90 = 25.2 18 % of 90 = 16.2 25.2 - 16.2 = 7.2 required number is 90 . answer : e


Question: how many factors of 60 are odd numbers greater than 1 ?

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

<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>3</result>

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

Explanation: prime factors of 60 are 2 ^ 2,3 ^ 1,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 1 + 1 ) ( 1 + 1 ) = 4 since we need odd divisors other than 1 = > 4 - 1 = 3 odd divisors d is the answer


Question: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent e of the distribution is less than m + d ?

<gadget id="calculator">100 - 68</gadget>
<output>32</output>

<gadget id="calculator">32 / 2</gadget>
<output>16</output>

<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 16 %
B. 32 %
C. 48 %
D. 84 %
E. 92 %

subtract(const_100, divide(subtract(const_100, 68), const_2))

Explanation: d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d


Question: village p ’ s population is 1150 greater than village q ' s population . if village q ’ s population were reduced by 200 people , then village p ’ s population would be 4 times as large as village q ' s population . what is village q ' s current population ?

<gadget id="calculator">200 * 4</gadget>
<output>800</output>

<gadget id="calculator">1_150 + 800</gadget>
<output>1_950</output>

<gadget id="calculator">1_950 / 3</gadget>
<output>650</output>
<result>650</result>

Choices:
A. 600
B. 625
C. 650
D. 675
E. 700

divide(add(1150, multiply(200, 4)), const_3)

Explanation: p = q + 1150 . p = 4 ( q - 200 ) . 4 ( q - 200 ) = q + 1150 . 3 q = 1950 . q = 650 . the answer is c .


Question: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours e would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?

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

<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/4) + (1/11)</gadget>
<output>15/44 = around 0.340909</output>

<gadget id="calculator">(15/44) / 15</gadget>
<output>1/44 = around 0.022727</output>

<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 22 hours
B. 30 hours
C. 44 hours
D. 60 hours
E. it can not be determined from the information above .

divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))

Explanation: say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job e in 44 hours . answer : c .


Question: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 50,000 after completion of one year . what will be madhu ' s share of profit ?

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

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

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

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

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

<gadget id="calculator">5 * 100</gadget>
<output>500</output>

<gadget id="calculator">500 * 100</gadget>
<output>50_000</output>

<gadget id="calculator">8_000 + 50_000</gadget>
<output>58_000</output>

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

<gadget id="calculator">4 * 3</gadget>
<output>12</output>

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">58_000 * (5/12)</gadget>
<output>72_500/3 = around 24_166.666667</output>
<result>72_500/3 = around 24_166.666667</result>

Choices:
A. rs . 27,000
B. rs . 24,000
C. rs . 25,000
D. rs . 36,000
E. none of these

multiply(add(multiply(multiply(multiply(const_4, 2), multiply(add(2, const_3), 2)), const_100), multiply(multiply(add(2, const_3), const_100), const_100)), divide(divide(multiply(add(2, const_3), 2), 2), multiply(const_4, const_3)))

Explanation: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 50,000 i . e . rs . 25,000 answer : c"


Question: in a certain school , the ratio of boys to girls is 5 to 13 . if there are 160 more girls than boys , how many boys are there ?

<gadget id="calculator">5 / 13</gadget>
<output>5/13 = around 0.384615</output>

<gadget id="calculator">1 - (5/13)</gadget>
<output>8/13 = around 0.615385</output>

<gadget id="calculator">160 / (8/13)</gadget>
<output>260</output>

<gadget id="calculator">260 - 160</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 100
B. 36
C. 45
D. 72
E. 117

subtract(divide(160, subtract(const_1, divide(5, 13))), 160)

Explanation: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 160 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 160 . so 1 part corresponds to 160 / 8 = 20 and so 5 parts correspond to 5 * 10 = 100 . a"


Question: ajay can walk 4 km in 1 hour . in how many hours he can walk 40 km ?

<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 5 hrs
B. 10 hrs
C. 15 hrs
D. 20 hrs
E. 30 hrs

Explanation: "1 hour he walk 4 km he walk 40 km in = 40 / 4 * 1 = 10 hours answer is b"


Question: ramesh has solved 108 questions in an examination . if he got only ‘ 0 ’ marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer .

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

<gadget id="calculator">(1/3) * 108</gadget>
<output>36</output>

<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">36 / (4/3)</gadget>
<output>27</output>

<gadget id="calculator">108 - 27</gadget>
<output>81</output>
<result>81</result>

Choices:
A. 78
B. 79
C. 80
D. 81
E. 82

subtract(108, divide(multiply(divide(1, 3), 108), add(const_1, divide(1, 3))))

Explanation: if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d


Question: what is the measure of the angle x made by the diagonals of the any adjacent sides of a cube .

<gadget id="calculator">180 / 3</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 30
B. 45
C. 60
D. 75
E. 90

Explanation: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c"


Question: after decreasing 15 % in the price of an article costs rs . 915 . find the actual cost of an article ?

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">915 / (17/20)</gadget>
<output>18_300/17 = around 1_076.470588</output>
<result>18_300/17 = around 1_076.470588</result>

Choices:
A. 915
B. 1000
C. 1076
D. 1067
E. 1760

divide(915, subtract(const_1, divide(15, const_100)))

Explanation: "cp * ( 85 / 100 ) = 915 cp = 10.76 * 100 = > cp = 1076 answer : c"


Question: dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 12 hours and then stops , how many hours will it take annie , working alone , to complete the job ?

<gadget id="calculator">12 / 15</gadget>
<output>4/5 = around 0.8</output>

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

<gadget id="calculator">(1/5) * 10</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 2
B. 4
C. 6
D. 8
E. 10

multiply(subtract(const_1, divide(12, 15)), 10)

Explanation: "dan can complete 1 / 15 of the job per hour . in 12 hours , dan completes 12 ( 1 / 15 ) = 4 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 1 / 5 / 1 / 10 = 2 hours . the answer is a ."


Question: a circle graph shows how the megatech corporation allocates its research and development budget : 17 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?

<gadget id="calculator">17 + 24</gadget>
<output>41</output>

<gadget id="calculator">41 + 15</gadget>
<output>56</output>

<gadget id="calculator">56 + 29</gadget>
<output>85</output>

<gadget id="calculator">85 + 8</gadget>
<output>93</output>

<gadget id="calculator">100 - 93</gadget>
<output>7</output>

<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>

<gadget id="calculator">7 * 360</gadget>
<output>2_520</output>

<gadget id="calculator">2_520 / 100</gadget>
<output>126/5 = around 25.2</output>
<result>126/5 = around 25.2</result>

Choices:
A. 8 °
B. 10 °
C. 26 °
D. 36 °
E. 52 °

divide(multiply(subtract(const_100, add(add(add(add(17, 24), 15), 29), 8)), divide(const_3600, const_10)), const_100)

Explanation: here all percentage when summed we need to get 100 % . as per data 17 + 24 + 15 + 29 + 8 = 93 % . so remaining 7 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 7 % will be 26 degrees . . imo option c .


Question: peter invests a sum of money and gets back an amount of $ 830 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?

<gadget id="calculator">854 - 830</gadget>
<output>24</output>

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>

<gadget id="calculator">(1/25) - (3/100)</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">24 / (1/100)</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 * (3/100)</gadget>
<output>72</output>

<gadget id="calculator">830 - 72</gadget>
<output>758</output>
<result>758</result>

Choices:
A. 670
B. 664
C. 698
D. 758
E. 700

subtract(830, multiply(divide(subtract(854, 830), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100)))

Explanation: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 830 = 24 interest earned for 3 years = 24 * 3 = 72 amount invested = 830 - 72 = 758 answer : d"


Question: the simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months . how much amount was borrowed ?

<gadget id="calculator">14 / 12</gadget>
<output>7/6 = around 1.166667</output>

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">(7/6) * (3/50)</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">(2/3) * (2/25)</gadget>
<output>4/75 = around 0.053333</output>

<gadget id="calculator">(7/100) - (4/75)</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">250 / (1/60)</gadget>
<output>15_000</output>
<result>15_000</result>

Choices:
A. 15000
B. 25000
C. 7500
D. 14500
E. none of these

divide(250, subtract(multiply(divide(14, const_12), divide(6, const_100)), multiply(divide(8, const_12), divide(8, const_100))))

Explanation: let the amount be x . from the question , x × 14 × 6 / 1200 − x × 8 × 8 / 1200 = 250 ∴ x = 15000 answer a


Question: if $ 120 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?

<gadget id="calculator">150 * 6</gadget>
<output>900</output>

<gadget id="calculator">240 - 120</gadget>
<output>120</output>

<gadget id="calculator">120 * 120</gadget>
<output>14_400</output>

<gadget id="calculator">14_400 / 120</gadget>
<output>120</output>

<gadget id="calculator">120 / 3</gadget>
<output>40</output>

<gadget id="calculator">900 * 40</gadget>
<output>36_000</output>

<gadget id="calculator">36_000 / 120</gadget>
<output>300</output>

<gadget id="calculator">150 + 300</gadget>
<output>450</output>
<result>450</result>

Choices:
A. $ 190
B. $ 180
C. $ 200
D. $ 340
E. $ 450

add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(240, 120), 120), 120), 3)), 120))

Explanation: "120 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 120 + 120 * ( r / 100 ) * ( 3 ) = 240 = > r = 100 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 450 answer is e ."


Question: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 9 : 6 : 5 , respectively , by weight . if 40 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?

<gadget id="calculator">9 * 2</gadget>
<output>18</output>

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

<gadget id="calculator">18 - 10</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 15
B. 12
C. 8
D. 6
E. 4

subtract(multiply(9, const_2), multiply(5, const_2))

Explanation: we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 9 x + 6 x + 5 x = 40 20 x = 40 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 5 ) ( 2 ) = 10 pounds of apples = ( 9 ) ( 2 ) = 18 thus we know that there are 18 – 10 = 8 more pounds of apples than grapes . answer is c .


Question: the population of a town increases 20 % and 25 % respectively in two consecutive years . after the growth the present population of the town is 1500 . then what is the population of the town 2 years ago ?

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

<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</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">(6/5) * (5/4)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">1_500 / (3/2)</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 1000
B. 1100
C. 1200
D. 1300
E. 1400

divide(1500, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

Explanation: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1500 * 100 / 120 * 100 / 125 = 1000 answer : option a"


Question: find the average of all the numbers between 6 and 34 which are divisible by 5 .

<gadget id="calculator">6 + 4</gadget>
<output>10</output>

<gadget id="calculator">34 - 4</gadget>
<output>30</output>

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

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

Choices:
A. 18
B. 20
C. 24
D. 30
E. 32

divide(add(add(6, const_4), subtract(34, const_4)), const_2)

Explanation: "solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 5 = 20 . answer b"


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 $ 0.24 , then how many 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">0.24 * 100</gadget>
<output>24</output>

<gadget id="calculator">(4/3) * 24</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 0.32
B. 0.44
C. 32
D. 44
E. 55

multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.24, 100))

Explanation: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 24 = 32 cents . answer : c ."


Question: a train running at the speed of 162 km / hr crosses a pole in 9 seconds . find the length of the train .

<gadget id="calculator">162 * 1_000</gadget>
<output>162_000</output>

<gadget id="calculator">162_000 / 3_600</gadget>
<output>45</output>

<gadget id="calculator">45 * 9</gadget>
<output>405</output>
<result>405</result>

Choices:
A. 150 meter
B. 286 meter
C. 186 meter
D. 405 meter
E. 265 meter

multiply(divide(multiply(162, const_1000), const_3600), 9)

Explanation: "speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time ( 45 ) * 9 = 405 meter answer : d"


Question: a student has to obtain 30 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?

<gadget id="calculator">150 + 30</gadget>
<output>180</output>

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

<gadget id="calculator">180 / (3/10)</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 750
B. 600
C. 650
D. 550
E. 500

divide(add(150, 30), divide(30, const_100))

Explanation: "let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b"


Question: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?

<gadget id="calculator">8 * 60</gadget>
<output>480</output>

<gadget id="calculator">5 * 480</gadget>
<output>2_400</output>

<gadget id="calculator">6 * 60</gadget>
<output>360</output>

<gadget id="calculator">480 / 360</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">2_400 / (1/3)</gadget>
<output>7_200</output>
<result>7_200</result>

Choices:
A. 5729
B. 5760
C. 7200
D. 2870
E. 2799

divide(multiply(5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1))

Explanation: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 5 = 7200 . answer : c"


Question: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 560 . how many green hats did we buy ?

<gadget id="calculator">85 * 6</gadget>
<output>510</output>

<gadget id="calculator">560 - 510</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 36
B. 50
C. 40
D. 42
E. 44

Explanation: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b ."


Question: the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1498 respectively . what is the rate of interest ?

<gadget id="calculator">1_498 - 1_400</gadget>
<output>98</output>

<gadget id="calculator">98 * 100</gadget>
<output>9_800</output>

<gadget id="calculator">9_800 / 1_400</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 3 %
B. 5 %
C. 7 %
D. 9 %
E. 11 %

divide(multiply(subtract(1498, 1400), const_100), 1400)

Explanation: "1498 - 1400 = 98 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 98 ) / ( 1400 ) = 7 % the answer is c ."


Question: a man can row 9 kmph in still water . when the river is running at 3.1 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

<gadget id="calculator">9 + 3.1</gadget>
<output>12.1</output>

<gadget id="calculator">9 - 3.1</gadget>
<output>5.9</output>

<gadget id="calculator">12.1 * 5.9</gadget>
<output>71.39</output>

<gadget id="calculator">12.1 + 5.9</gadget>
<output>18</output>

<gadget id="calculator">71.39 / 18</gadget>
<output>3.966111</output>

<gadget id="calculator">3.966111 * 2</gadget>
<output>7.932222</output>
<result>7.932222</result>

Choices:
A. 2.21
B. 2.48
C. 9.24
D. 7.29
E. 7.94

multiply(divide(multiply(add(9, 3.1), subtract(9, 3.1)), add(add(9, 3.1), subtract(9, 3.1))), const_2)

Explanation: "m = 9 s = 3.1 ds = 12.1 us = 5.9 x / 12.1 + x / 5.9 = 1 x = 3.97 d = 3.97 * 2 = 7.94 answer : e"


Question: a man invests some money partly in 12 % stock at 105 and partly in 8 % stock at 88 . to obtain equal dividends from both , he must invest the money in the ratio :

<gadget id="calculator">105 * 2</gadget>
<output>210</output>

<gadget id="calculator">88 * 3</gadget>
<output>264</output>

<gadget id="calculator">210 / 264</gadget>
<output>35/44 = around 0.795455</output>
<result>35/44 = around 0.795455</result>

Choices:
A. 31 : 44
B. 31 : 27
C. 16 : 15
D. 35 : 44
E. 35 : 27

divide(multiply(105, const_2), multiply(88, const_3))

Explanation: "n case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer : option d"


Question: a man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?

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

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

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

<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">15 - (15/2)</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">(15/2) / 1</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>

Choices:
A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 15 / 2 minutes

divide(subtract(15, divide(15, divide(add(5, 15), subtract(15, 5)))), const_1)

Explanation: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 15 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 15 , d = 15 b - 15 c ; every 5 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 15 b - 15 c = 5 b + 5 c , - - > b = 2 c , - - > d = 15 b - 15 b / 2 = 15 b / 2 . interval = \ frac { d } { b } = \ frac { 15 / 2 b } { b } = 15 / 2 answer : e ( 15 / 2 minutes ) ."


Question: rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ?

<gadget id="calculator">75 * 60</gadget>
<output>4_500</output>

<gadget id="calculator">4_500 / 100</gadget>
<output>45</output>

<gadget id="calculator">10 * 70</gadget>
<output>700</output>

<gadget id="calculator">700 / 100</gadget>
<output>7</output>

<gadget id="calculator">30 * 40</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>

<gadget id="calculator">7 + 12</gadget>
<output>19</output>

<gadget id="calculator">35 * 60</gadget>
<output>2_100</output>

<gadget id="calculator">2_100 / 100</gadget>
<output>21</output>

<gadget id="calculator">19 + 21</gadget>
<output>40</output>

<gadget id="calculator">45 - 40</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 5
B. 6
C. 7
D. 8
E. 9

subtract(divide(multiply(75, 60), const_100), add(add(divide(multiply(10, 70), const_100), divide(multiply(30, 40), const_100)), divide(multiply(35, 60), const_100)))

Explanation: explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a


Question: a number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?

<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>
<result>7/3 = around 2.333333</result>

Choices:
A. 25 / 9
B. 7 / 3
C. 5 / 3
D. 3 / 5
E. 9 / 25

Explanation: "sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b"


Question: one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?

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

<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">(5/6) / 6</gadget>
<output>5/36 = around 0.138889</output>

<gadget id="calculator">1 - (5/36)</gadget>
<output>31/36 = around 0.861111</output>

<gadget id="calculator">1 / (31/36)</gadget>
<output>36/31 = around 1.16129</output>
<result>36/31 = around 1.16129</result>

Choices:
A. 32 / 31
B. 33 / 31
C. 34 / 31
D. 36 / 31
E. 0 / 31

divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))

Explanation: connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d


Question: in the manufacture of a certain product , 6 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">6 * (1/20)</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>

Choices:
A. 0.125 %
B. 0.3 %
C. 0.8 %
D. 1.25 %
E. 2.0 %

Explanation: "0.06 * 0.05 = 0.003 = 0.3 % the answer is b ."


Question: in a group of ducks and cows , the total number of legs are 26 more than twice the no . of heads . find the total no . of buffaloes .

<gadget id="calculator">26 / 2</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 11
B. 12
C. 13
D. 16
E. 18

Explanation: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c"


Question: a man walking at 3 / 4 th of the speed , reaches his office late by 2 hours . what is the usual time ?

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

<gadget id="calculator">(3/4) * 2</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) * (3/4)</gadget>
<output>9/8 = around 1.125</output>

<gadget id="calculator">(9/8) * 2</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">(3/2) - (9/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(9/4) / (3/8)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 5 hours
B. 3 hours
C. 6 hours
D. 12 hours
E. 15 hours

divide(multiply(multiply(multiply(divide(3, 4), 2), divide(3, 4)), 2), subtract(multiply(divide(3, 4), 2), multiply(multiply(divide(3, 4), 2), divide(3, 4))))

Explanation: at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c


Question: given a + b = 1 , find the value of 2 a + 2 b . two solutions are presented below . only one is correct , even though both yield the correct answer .

<gadget id="calculator">2 + 1</gadget>
<output>3</output>

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

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

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

Explanation: because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 × 1 = 2 . correct answer d


Question: a sum fetched total simple interest of 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?

<gadget id="calculator">100 * 4_016.25</gadget>
<output>401_625</output>

<gadget id="calculator">9 * 5</gadget>
<output>45</output>

<gadget id="calculator">401_625 / 45</gadget>
<output>8_925</output>
<result>8_925</result>

Choices:
A. 8925
B. 8032.5
C. 4462.5
D. 8900
E. none of these

divide(multiply(const_100, 4016.25), multiply(9, 5))

Explanation: "let the sums be p . now , 45 % of p = 4016.25 or , p = 8925 answer a"


Question: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 7 , 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 + 7</gadget>
<output>21</output>
<result>21</result>

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

add(add(11, divide(subtract(11, 5), 2)), 7)

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 + 7 = 21 the answer is b ."


Question: each of the integers from 1 to 17 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?

<gadget id="calculator">17 / 2</gadget>
<output>17/2 = around 8.5</output>

<gadget id="calculator">(17/2) + 1</gadget>
<output>19/2 = around 9.5</output>
<result>19/2 = around 9.5</result>

Choices:
A. 19
B. 12
C. 11
D. 10
E. 3

Explanation: "out of the 17 integers : 9 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )"


Question: the averge score of a cricketer for 10 matches is 45 runs . if the average for the first 6 matches is 48 . then find the average for the last 4 matches ?

<gadget id="calculator">45 * 10</gadget>
<output>450</output>

<gadget id="calculator">6 * 48</gadget>
<output>288</output>

<gadget id="calculator">450 - 288</gadget>
<output>162</output>

<gadget id="calculator">162 / 4</gadget>
<output>81/2 = around 40.5</output>
<result>81/2 = around 40.5</result>

Choices:
A. 43.25
B. 43
C. 38
D. 40.5
E. 36

divide(subtract(multiply(45, 10), multiply(6, 48)), 4)

Explanation: sum of last 4 matches = ( ( 10 × 45 ) – ( 6 × 48 ) = 162 average = 162 / 4 = 40.5 answer : d


Question: a shopkeeper fixes the marked price of an item 40 % above its cost price . the percentage of discount allowed to gain 8 % is

<gadget id="calculator">8 + 100</gadget>
<output>108</output>

<gadget id="calculator">40 + 100</gadget>
<output>140</output>

<gadget id="calculator">108 / 140</gadget>
<output>27/35 = around 0.771429</output>

<gadget id="calculator">(27/35) * 100</gadget>
<output>540/7 = around 77.142857</output>

<gadget id="calculator">100 - (540/7)</gadget>
<output>160/7 = around 22.857143</output>
<result>160/7 = around 22.857143</result>

Choices:
A. 23.85 %
B. 22.85 %
C. 21.85 %
D. 20.85 %
E. none of these

subtract(const_100, multiply(divide(add(8, const_100), add(40, const_100)), const_100))

Explanation: "explanation : let the cost price = rs 100 then , marked price = rs 140 required gain = 8 % , so selling price = rs 108 discount = 140 - 108 = 32 discount % = ( 32 / 140 ) * 100 = 22.85 % option b"


Question: how long does a train 60 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?

<gadget id="calculator">60 + 80</gadget>
<output>140</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">140 / (50/3)</gadget>
<output>42/5 = around 8.4</output>
<result>42/5 = around 8.4</result>

Choices:
A. 5.8 sec
B. 8.4 sec
C. 12.4 sec
D. 6.8 sec
E. 1.8 sec

divide(add(60, 80), multiply(60, const_0_2778))

Explanation: "b 16.8 sec d = 60 + 80 = 140 m s = 60 * 5 / 18 = 50 / 3 t = 140 * 3 / 50 = 8.4 sec answer is b"


Question: a circle graph shows how the budget of a certain company was spent : 55 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?

<gadget id="calculator">55 + 9</gadget>
<output>64</output>

<gadget id="calculator">64 + 5</gadget>
<output>69</output>

<gadget id="calculator">69 + 4</gadget>
<output>73</output>

<gadget id="calculator">73 + 2</gadget>
<output>75</output>

<gadget id="calculator">100 - 75</gadget>
<output>25</output>

<gadget id="calculator">360 * 25</gadget>
<output>9_000</output>

<gadget id="calculator">9_000 / 100</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 18 °
B. 36 °
C. 54 °
D. 72 °
E. 90 °

divide(multiply(const_360, subtract(const_100, add(add(add(add(55, 9), 5), 4), 2))), const_100)

Explanation: "the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e ."


Question: which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 10 is 4 ?

<gadget id="calculator">lcm(7, 12)</gadget>
<output>84</output>

<gadget id="calculator">lcm(84, 10)</gadget>
<output>420</output>

<gadget id="calculator">gcd(1_856, 420)</gadget>
<output>4</output>

<gadget id="calculator">4 * 420</gadget>
<output>1_680</output>

<gadget id="calculator">4 + 1_680</gadget>
<output>1_684</output>

<gadget id="calculator">1_856 - 1_684</gadget>
<output>172</output>
<result>172</result>

Choices:
A. 168
B. 172
C. 182
D. 140
E. 160

Explanation: first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b


Question: how many bricks , each measuring 25 cm * 11.25 cm * 6 cm , will be needed to build a wall 8 m * 6 m * 22.5 m

<gadget id="calculator">8 * 100</gadget>
<output>800</output>

<gadget id="calculator">6 * 100</gadget>
<output>600</output>

<gadget id="calculator">800 * 600</gadget>
<output>480_000</output>

<gadget id="calculator">480_000 * 22.5</gadget>
<output>10_800_000</output>

<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>

<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>

<gadget id="calculator">10_800_000 / 1_687.5</gadget>
<output>6_400</output>
<result>6_400</result>

Choices:
A. 6400
B. 3777
C. 2679
D. 2667
E. 1997

divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))

Explanation: "to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 ∗ 600 ∗ 22.5 / 25 ∗ 11.25 ∗ 6 = 6400 answer : a"