Question: two guys a and b leave point a and point b simultaneously and travel towards point b and point a on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will b take to cover the entire journey between point b and point a ?

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

<gadget id="calculator">4 + 4</gadget>
<output>8</output>

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

<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 65
B. 90
C. 70
D. 75
E. 80

add(50, multiply(add(const_4, const_1), add(const_4, const_4)))

Explanation: let x per minute be the speed of a and y per minute be the speed of b . after meeting at a point , a travels for 32 mins and b travels for 50 mins . so distance covered by each of them post point of crossing a = 32 x and b = 50 y the distance covered by a and b before they cross each would be distance covered by b and a post crossing respectively . therefore distance covered by b before he meets a = 32 x time taken by b cover 32 x distance = 32 x / y mins therefore total time taken by b = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of a and b = x + y therefore time taken before a and b meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by b reach destination after meeting a = 50 mins total travel time for b = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins b


Question: if 63 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

<gadget id="calculator">63 + 50</gadget>
<output>113</output>

<gadget id="calculator">113 + 20</gadget>
<output>133</output>

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

Choices:
A. 24 %
B. 27 %
C. 30 %
D. 33 %
E. 36 %

subtract(add(add(63, 50), 20), const_100)

Explanation: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 17 % = 33 % . the answer is d ."


Question: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 95 units raises the average to 55 units per day , what is the value of n ?

<gadget id="calculator">95 - 50</gadget>
<output>45</output>

<gadget id="calculator">55 - 50</gadget>
<output>5</output>

<gadget id="calculator">45 / 5</gadget>
<output>9</output>

<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<result>8</result>

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

subtract(divide(subtract(95, 50), subtract(55, 50)), const_1)

Explanation: "the average daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 95 - 55 = 40 n = 8 the answer is c ."


Question: how many seconds will a 300 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

<gadget id="calculator">63 - 3</gadget>
<output>60</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">300 / (50/3)</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 12 sec
B. 30 sec
C. 86 sec
D. 15 sec
E. 18 sec

divide(300, multiply(subtract(63, 3), const_0_2778))

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 300 * 3 / 50 = 18 sec . answer : e"


Question: abcd is a parallelogram . bd = 2 . the angles of triangle bcd are all equal . what is the perimeter of the parallelogram ?

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

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

Choices:
A. 12
B. 9 √ 3
C. 9
D. 8
E. 3 √ 3

Explanation: so , bc = bd = cd = ba = ad = 2 the parallelogram has 4 equal sides bc = cd = ba = ad = 2 so the perimeter of the parallelogram will be 2 * 4 = 8 hence answer will be ( d ) 2


Question: if the price of petrol increases by 40 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">100 / 140</gadget>
<output>5/7 = around 0.714286</output>

<gadget id="calculator">1 - (5/7)</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>

Choices:
A. 25 %
B. 20 %
C. 16.67 %
D. 28.6 %
E. none of these

multiply(subtract(const_1, divide(const_100, add(const_100, 40))), const_100)

Explanation: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 40 ) i . e 140 . now , his consumption should be reduced to : - = ( 140 − 100 ) / 140 ∗ 100 . hence , the consumption should be reduced to 28.6 % . answer : d"


Question: the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.8 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?

<gadget id="calculator">6 * 3.95</gadget>
<output>23.7</output>

<gadget id="calculator">2 * 3.8</gadget>
<output>7.6</output>

<gadget id="calculator">2 * 3.85</gadget>
<output>7.7</output>

<gadget id="calculator">7.6 + 7.7</gadget>
<output>15.3</output>

<gadget id="calculator">23.7 - 15.3</gadget>
<output>8.4</output>

<gadget id="calculator">8.4 / 2</gadget>
<output>4.2</output>
<result>4.2</result>

Choices:
A. 4.2
B. 4.4
C. 4.6
D. 5.6
E. 5.7

divide(subtract(multiply(6, 3.95), add(multiply(2, 3.8), multiply(2, 3.85))), 2)

Explanation: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.8 * 2 ) + ( 3.85 * 2 ) ] = 8.4 . required average = ( 8.4 / 2 ) = 4.2 . a"


Question: the average of 7 numbers is 24 . if each number be multiplied by 5 . find the average of new set of numbers ?

<gadget id="calculator">24 * 5</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 110
B. 122
C. 120
D. 125
E. 145

Explanation: "explanation : average of new numbers = 24 * 5 = 120 answer : option c"


Question: a cycle is bought for rs . 900 and sold for rs . 1080 , find the gain percent ?

<gadget id="calculator">1_080 - 900</gadget>
<output>180</output>

<gadget id="calculator">180 / 900</gadget>
<output>1/5 = around 0.2</output>

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

Choices:
A. 27 %
B. 20 %
C. 25 %
D. 40 %
E. 28 %

multiply(divide(subtract(1080, 900), 900), const_100)

Explanation: "900 - - - - 180 100 - - - - ? = > 20 % answer : b"


Question: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?

<gadget id="calculator">30 / 45</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">60 * (2/3)</gadget>
<output>40</output>

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

Choices:
A. 5
B. 10
C. 20
D. 30
E. 40

subtract(const_60, multiply(const_60, divide(30, 45)))

Explanation: "explanation : t = 15 / 45 * 60 = 20 answer : option c"


Question: if rs . 544 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?

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

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

<gadget id="calculator">(2/3) * (1/4)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) + (1/4)</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">(5/12) + 1</gadget>
<output>17/12 = around 1.416667</output>

<gadget id="calculator">544 / (17/12)</gadget>
<output>384</output>
<result>384</result>

Choices:
A. s . 300
B. s . 360
C. s . 389
D. s . 384
E. s . 323

divide(544, add(add(multiply(divide(2, 3), divide(1, 4)), divide(1, 4)), 1))

Explanation: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 544 * 2 / 17 = rs . 64 b ' s share = 544 * 3 / 17 = rs . 96 c ' s share = 544 * 12 / 17 = rs . 384 . answer : d"


Question: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?

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

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

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

<gadget id="calculator">20 / 40</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

Choices:
A. 0
B. 1 / 3
C. 2 / 5
D. 1 / 2
E. 3 / 5

divide(multiply(5, 4), multiply(5, multiply(4, 2)))

Explanation: we will have a negative product only if 1 , 2 , 3 , or 4 are selected from set t . p ( negative product ) = 4 / 8 = 1 / 2 the answer is d .


Question: a 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?

<gadget id="calculator">300 / 18</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) * 48</gadget>
<output>800</output>

<gadget id="calculator">800 - 300</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 500
B. 350
C. 828
D. 277
E. 122

subtract(multiply(speed(300, 18), 48), 300)

Explanation: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 489 = 50 / 3 3 x + 900 = 2400 = > x = 500 m . answer : a"


Question: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years . find the average age of the women ?

<gadget id="calculator">20 + 22</gadget>
<output>42</output>

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

<gadget id="calculator">42 + 16</gadget>
<output>58</output>

<gadget id="calculator">58 / 2</gadget>
<output>29</output>
<result>29</result>

Choices:
A. 87
B. 98
C. 30
D. 29
E. 37

divide(add(add(20, 22), multiply(8, 2)), const_2)

Explanation: "20 + 22 + 8 * 2 = 58 / 2 = 29 answer : d"


Question: if 20 % of x is 15 less than 15 % of 1500 , then x is ?

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

<gadget id="calculator">1_500 * (3/20)</gadget>
<output>225</output>

<gadget id="calculator">225 - 15</gadget>
<output>210</output>

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

<gadget id="calculator">210 / (1/5)</gadget>
<output>1_050</output>
<result>1_050</result>

Choices:
A. 872
B. 738
C. 837
D. 840
E. 1050

divide(subtract(multiply(1500, divide(15, const_100)), 15), divide(20, const_100))

Explanation: "20 % of x = x / 5 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 5 = 225 - 15 = > x / 5 = 210 = > x = 1050 . answer : e"


Question: if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?

<gadget id="calculator">70 * 5</gadget>
<output>350</output>

<gadget id="calculator">350 - 10</gadget>
<output>340</output>

<gadget id="calculator">340 / 5</gadget>
<output>68</output>

<gadget id="calculator">68 + 10</gadget>
<output>78</output>
<result>78</result>

Choices:
A. 50
B. 52
C. 69
D. 78
E. 84

add(divide(subtract(multiply(70, 5), 10), 5), 10)

Explanation: "sum of 5 integer ( a , b , c , d , e ) = 5 * 70 = 350 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 350 i . e . 5 a = 340 i . e . a = 68 i . e . largest e = 68 + 10 = 78 answer : option d"


Question: what is the normal price of an article sold at $ 72 after two successive discounts of 10 % and 20 % ?

<gadget id="calculator">100 - 10</gadget>
<output>90</output>

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

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

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

<gadget id="calculator">(9/10) * (4/5)</gadget>
<output>18/25 = around 0.72</output>

<gadget id="calculator">72 / (18/25)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. $ 92
B. $ 96
C. $ 100
D. $ 104
E. $ 108

divide(72, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100)))

Explanation: 0.8 * 0.9 * cost price = $ 72 cost price = $ 100 the answer is c .


Question: of the 200 stamps in a collection , 80 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?

<gadget id="calculator">80 + 50</gadget>
<output>130</output>

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

<gadget id="calculator">200 - 110</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 60
B. 90
C. 100
D. 130
E. 150

subtract(200, subtract(add(80, 50), 20))

Explanation: "20 stamps are both foreign and more than 10 years old . 60 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 60 + 30 ) = 90 the answer is b ."


Question: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 3 of the remaining paint . how many gallons of paint has joe used ?

<gadget id="calculator">360 / 4</gadget>
<output>90</output>

<gadget id="calculator">90 * 1</gadget>
<output>90</output>

<gadget id="calculator">360 - 90</gadget>
<output>270</output>

<gadget id="calculator">270 / 3</gadget>
<output>90</output>

<gadget id="calculator">90 + 90</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 18
B. 180
C. 175
D. 216
E. 250

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 3))

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 3 ) * 270 = 90 gallons total paint used = 180 gallons . option b"


Question: if a truck is traveling at a constant rate of 108 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )

<gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) / 108</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(1/180) * 3_600</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 24
C. 30
D. 36
E. 48

multiply(divide(divide(600, 1000), 108), const_3600)

Explanation: speed = 108 km / hr = > 108,000 m / hr in one minute = > 108000 / 60 = 1800 meters in one sec = > 1800 / 60 = 30 meters time = total distance need to be covered / avg . speed = > 600 / 30 = 20 and hence the answer : a


Question: what is the least number that should be added to 1054 , so the sum of the number is divisible by 23 ?

<gadget id="calculator">1_054 / 23</gadget>
<output>1_054/23 = around 45.826087</output>

<gadget id="calculator">floor(1_054/23)</gadget>
<output>45</output>

<gadget id="calculator">1 + 45</gadget>
<output>46</output>

<gadget id="calculator">46 - (1_054/23)</gadget>
<output>4/23 = around 0.173913</output>

<gadget id="calculator">(4/23) * 23</gadget>
<output>4</output>
<result>4</result>

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

multiply(subtract(add(const_1, floor(divide(1054, 23))), divide(1054, 23)), 23)

Explanation: "( 1054 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."


Question: two bullet trains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

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

<gadget id="calculator">120 / 10</gadget>
<output>12</output>

<gadget id="calculator">120 / 12</gadget>
<output>10</output>

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

<gadget id="calculator">240 / 22</gadget>
<output>120/11 = around 10.909091</output>
<result>120/11 = around 10.909091</result>

Choices:
A. 11 sec .
B. 15 sec .
C. 12 sec .
D. 17 sec .
E. 19 sec .

Explanation: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 12 m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = 22 m / sec . required time = ( 120 + 120 ) / 22 sec = 11 sec . a"


Question: 70 % of x is greater than 1 / 3 rd of x by 110 . what is x ?

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

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

<gadget id="calculator">(7/10) - (1/3)</gadget>
<output>11/30 = around 0.366667</output>

<gadget id="calculator">110 / (11/30)</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 100
B. 200
C. 300
D. 350
E. 400

divide(110, subtract(divide(70, const_100), divide(1, 3)))

Explanation: "7 x / 10 - x / 3 = 110 11 x / 30 = 110 x = 300 answer : c"


Question: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?

<gadget id="calculator">7 - 6</gadget>
<output>1</output>

<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">80 / (1/100)</gadget>
<output>8_000</output>
<result>8_000</result>

Choices:
A. 7000
B. 8000
C. 8800
D. 8900
E. 9000

divide(80, divide(subtract(7, 6), const_100))

Explanation: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 80 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 80 = > total appeared candidates in state b = 80 x 100 = 8000 = > total appeared candidates in state a = total appeared candidates in state b = 8000"


Question: the sector of a circle has perimeter of 144 cm and central angle 180 o . find its radius ?

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

<gadget id="calculator">20 + 2</gadget>
<output>22</output>

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

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">2 * (22/7)</gadget>
<output>44/7 = around 6.285714</output>

<gadget id="calculator">(44/7) * 180</gadget>
<output>7_920/7 = around 1_131.428571</output>

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

<gadget id="calculator">(7_920/7) / 360</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">(22/7) + 2</gadget>
<output>36/7 = around 5.142857</output>

<gadget id="calculator">144 / (36/7)</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 25 cm
B. 32 cm
C. 14 cm
D. 28 cm
E. 21 cm

divide(144, add(divide(multiply(multiply(const_2, divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), 180), divide(const_3600, const_10)), const_2))

Explanation: "let the radius is x cm perimeter of the sector = length of the arc + 2 ( radius ) 144 = ( 180 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 144 = 22 x / 7 + 2 x 144 = 36 x / 7 36 x = 1008 x = 28 answer : d"


Question: the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is ?

<gadget id="calculator">10 + 7</gadget>
<output>17</output>

<gadget id="calculator">2 * 17</gadget>
<output>34</output>

<gadget id="calculator">34 * 5</gadget>
<output>170</output>

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

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

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

<gadget id="calculator">9 + 3</gadget>
<output>12</output>

<gadget id="calculator">170 - 12</gadget>
<output>158</output>

<gadget id="calculator">158 * 3</gadget>
<output>474</output>
<result>474</result>

Choices:
A. rs . 229
B. rs . 429
C. rs . 129
D. rs . 474
E. rs . 111

multiply(subtract(multiply(multiply(2, add(10, 7)), 5), add(add(multiply(2, 3), multiply(2, 1.5)), multiply(2, 1.5))), 3)

Explanation: "area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d"


Question: ravi and kavi start a business by investing â ‚ ¹ 2000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .

<gadget id="calculator">2_000 / 72_000</gadget>
<output>1/36 = around 0.027778</output>
<result>1/36 = around 0.027778</result>

Choices:
A. 2 : 36
B. 5 : 36
C. 7 : 36
D. 1 : 36
E. 3 : 36

Explanation: "ratio of profit = ratio of investments = 2000 : 72000 = 1 : 36 answer : d"


Question: the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?

<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">1_000 / (5/4)</gadget>
<output>800</output>
<result>800</result>

Choices:
A. 620
B. 400
C. 45
D. 500
E. 800

divide(1000, add(const_1, divide(25, const_100)))

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 125 ) = rs . 800 . answer : e"


Question: john makes $ 60 a week from his job . he earns a raise and now makes $ 100 a week . what is the % increase ?

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

<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>

Choices:
A. 16 %
B. 66.67 %
C. 17 %
D. 17.61 %
E. 17.56 %

multiply(divide(subtract(100, 60), 60), const_100)

Explanation: "increase = ( 40 / 60 ) * 100 = ( 4 / 6 ) * 100 = 66.67 % . 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 153 , 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">153 / (17/20)</gadget>
<output>180</output>

<gadget id="calculator">180 - 153</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 22
B. 33
C. 55
D. 27
E. 88

subtract(divide(153, add(divide(10, const_100), divide(3, 4))), 153)

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 = 153 = > . 1 x + 3 / 4 x = 153 = > x = 180 180 - 153 = pure gala = 27 . d"


Question: a cistern 5 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :

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

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

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

<gadget id="calculator">(5/4) * 5</gadget>
<output>25/4 = around 6.25</output>

<gadget id="calculator">5 + (25/4)</gadget>
<output>45/4 = around 11.25</output>

<gadget id="calculator">2 * (45/4)</gadget>
<output>45/2 = around 22.5</output>

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

<gadget id="calculator">(45/2) + 20</gadget>
<output>85/2 = around 42.5</output>
<result>85/2 = around 42.5</result>

Choices:
A. 49 m 2
B. 42.5 m 2
C. 53.5 m 2
D. 55 m 2
E. 57 m 2

add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 4), multiply(add(divide(25, const_100), 1), 5))), multiply(4, 5))

Explanation: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 5 x 1.25 ) + 5 x 4 ] m 2 = 42.5 m 2 . answer : option b"


Question: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 63 , what is the total amount ?

<gadget id="calculator">100 / 45</gadget>
<output>20/9 = around 2.222222</output>

<gadget id="calculator">(20/9) * 63</gadget>
<output>140</output>

<gadget id="calculator">50 / 45</gadget>
<output>10/9 = around 1.111111</output>

<gadget id="calculator">(10/9) * 63</gadget>
<output>70</output>

<gadget id="calculator">140 + 70</gadget>
<output>210</output>

<gadget id="calculator">210 + 63</gadget>
<output>273</output>
<result>273</result>

Choices:
A. 115
B. 273
C. 117
D. 118
E. 119

add(add(multiply(divide(const_100, 45), 63), multiply(divide(50, 45), 63)), 63)

Explanation: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 63 39 - - - ? = > 273 answer : b"


Question: find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) )

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

<gadget id="calculator">3 - (1/3)</gadget>
<output>8/3 = around 2.666667</output>

<gadget id="calculator">1 / (8/3)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">3 + (3/8)</gadget>
<output>27/8 = around 3.375</output>

<gadget id="calculator">1 / (27/8)</gadget>
<output>8/27 = around 0.296296</output>

<gadget id="calculator">3 + (8/27)</gadget>
<output>89/27 = around 3.296296</output>

<gadget id="calculator">1 / (89/27)</gadget>
<output>27/89 = around 0.303371</output>
<result>27/89 = around 0.303371</result>

Choices:
A. 21 / 29
B. 27 / 89
C. 89 / 21
D. 29 / 21
E. none

divide(1, add(3, divide(1, add(3, divide(1, subtract(3, divide(1, 3)))))))

Explanation: 1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 b


Question: if a - b = 5 and a 2 + b 2 = 31 , find the value of ab .

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

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

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

Choices:
A. 9
B. 2
C. 3
D. 7
E. 12

Explanation: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 31 - 25 = 6 ab = 3 . answer : c"


Question: if circles x and y have the same area and circle x has a circumference of 18 π , half of the radius of circle y is :

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

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

Choices:
A. 16
B. 4.5
C. 4
D. 2
E. 1

Explanation: "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 18 * pi x = 9 thus y = 9 y / 2 = 4.5 ans : b"


Question: the present population of a town is 2000 . population increase rate is 20 % p . a . find the population of town after 1 years ?

<gadget id="calculator">2_000 * 20</gadget>
<output>40_000</output>

<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>

<gadget id="calculator">2_000 + 400</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 1000
B. 2400
C. 1500
D. 1600
E. 1250

Explanation: "p = 2000 r = 20 % required population of town = p ( 1 + r / 100 ) ^ t = 2000 ( 1 + 20 / 100 ) = 2000 ( 6 / 5 ) = 2400 answer is b"


Question: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 490 , krishan has ?

<gadget id="calculator">490 / 7</gadget>
<output>70</output>

<gadget id="calculator">70 * 17</gadget>
<output>1_190</output>

<gadget id="calculator">1_190 / 7</gadget>
<output>170</output>

<gadget id="calculator">170 * 17</gadget>
<output>2_890</output>
<result>2_890</result>

Choices:
A. rs . 2890
B. rs . 2330
C. rs . 1190
D. rs . 1620
E. rs . 2680

multiply(divide(multiply(divide(490, 7), 17), 7), 17)

Explanation: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 490 : n & there n = 289 x 490 / 49 = rs . 2890 answer : a"


Question: by selling an article for $ 195 , a person gains $ 45 . what is the gain % ?

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

<gadget id="calculator">195 - 45</gadget>
<output>150</output>

<gadget id="calculator">4_500 / 150</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 25 %
B. 30 %
C. 50 %
D. 20 %
E. 10 %

divide(multiply(45, const_100), subtract(195, 45))

Explanation: s . p . = $ 195 gain = $ 45 c . p . = 195 - 45 = 150 gain % = 45 / 150 * 100 % = 30 % answer is b


Question: by selling an article at rs . 600 , a profit of 60 % is made . find its cost price ?

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>

<gadget id="calculator">100 + 60</gadget>
<output>160</output>

<gadget id="calculator">60_000 / 160</gadget>
<output>375</output>
<result>375</result>

Choices:
A. 228
B. 267
C. 375
D. 480
E. 811

divide(multiply(600, const_100), add(const_100, 60))

Explanation: "sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 60 ) ] = 600 * [ 100 / 160 ] = rs . 375 answer : c"


Question: ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the number .

<gadget id="calculator">18 - 3</gadget>
<output>15</output>

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

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

Explanation: solution : let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y . . . . . . . ( 1 ) 10 x + y + 18 = 10 y + x . . . . ( 2 ) solving 1 st equation we get 2 x - y = 1 . . . . . ( 3 ) solving 2 nd equation we get y - x = 2 . . . . . ( 4 ) solving 3 and 4 , we get x = 3 and y = 5 answer : b


Question: how many 3 - digit integers between 311 and 401 , exclusive , are divisible by 3 when the tens digit and the hundered digit are switched ?

<gadget id="calculator">401 - 311</gadget>
<output>90</output>

<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30
B. 19
C. 22
D. 3
E. 90

Explanation: answer is 30 no of digits between 311 and 401 ( exclusive ) = 401 - 311 - 1 = 89 no intergers divisble by 3 = ~ 89 / 3 ~ 30 divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . e . g 372 is divisble by 3 ( becae 3 + 7 + 2 = 12 ( divisble by 3 ) ) switch digits 732 also divisble by 3 ( becae 7 + 3 + 2 = 12 ( divisble by 3 ) ) divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . you have right . so it is enough to proceed like usual to find the numbers in a given range that are divisible by 3 . so 399 - 312 / 3 + 1 = 30 . answer : a


Question: the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintain the original area ?

<gadget id="calculator">100 - 22</gadget>
<output>78</output>

<gadget id="calculator">78 / 100</gadget>
<output>39/50 = around 0.78</output>

<gadget id="calculator">1 - (39/50)</gadget>
<output>11/50 = around 0.22</output>

<gadget id="calculator">(11/50) / (39/50)</gadget>
<output>11/39 = around 0.282051</output>

<gadget id="calculator">(11/39) * 100</gadget>
<output>1_100/39 = around 28.205128</output>
<result>1_100/39 = around 28.205128</result>

Choices:
A. 14 %
B. 15 %
C. 28 %
D. 30 %
E. 35 %

multiply(divide(subtract(const_1, divide(subtract(const_100, 22), const_100)), divide(subtract(const_100, 22), const_100)), const_100)

Explanation: "sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28.2 % c"


Question: a car drives 60 miles on local roads at 20 mph , and 195 miles on the highway at 65 mph , what is the average speed of the entire trip ?

<gadget id="calculator">60 + 195</gadget>
<output>255</output>

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

<gadget id="calculator">195 / 65</gadget>
<output>3</output>

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

<gadget id="calculator">255 / 6</gadget>
<output>85/2 = around 42.5</output>
<result>85/2 = around 42.5</result>

Choices:
A. 36 mph
B. 40 mph
C. 44 mph
D. 43 mph
E. 58 mph

Explanation: "so the answer is plainly d . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 195 to 65 to find the needed time to cover 195 miles , so t = 3 hours so the total time for covering total distance would be 3 + 3 = 6 hours and total distance is 60 + 195 = 255 miles final stage : average speed is total distance divide to total time : 255 / 6 = 42.5 miles per hour rounded up to 43 mph . . . ."


Question: if x > 3000 , then the value of ( 1.2 x ) / ( 0.5 x - 406 ) is closest to ?

<gadget id="calculator">2 - 0.5</gadget>
<output>1.5</output>

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

Choices:
A. 1 / 6
B. 1 / 3
C. 10 / 21
D. 1 / 2
E. 3 / 1

Explanation: assume x = 3002 ( 1.2 x ) / ( 0.5 x - 406 ) = 3602.4 / ( 3002 * 0.5 - 406 ) = 3602.4 / 1095 = = 3 / 1 e


Question: a train passes a platform in 32 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is

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

<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>

<gadget id="calculator">32 - 20</gadget>
<output>12</output>

<gadget id="calculator">15 * 12</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 180 meter
B. 240 meter
C. 200 meter
D. 260 meter
E. none of these

multiply(multiply(const_0_2778, 54), subtract(32, 20))

Explanation: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 32 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 32 = > 300 + l = 15 × 32 = 480 = > l = 480 - 300 = 180 meter answer : option a"


Question: the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % ?

<gadget id="calculator">100 / 64</gadget>
<output>25/16 = around 1.5625</output>

<gadget id="calculator">100 - 12</gadget>
<output>88</output>

<gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>

<gadget id="calculator">(25/16) * (22/25)</gadget>
<output>11/8 = around 1.375</output>

<gadget id="calculator">(11/8) - 1</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>

Choices:
A. 33 %
B. 28.02 %
C. 37.5 %
D. 30.5 %
E. 22 %

multiply(subtract(multiply(divide(const_100, 64), divide(subtract(const_100, 12), const_100)), const_1), const_100)

Explanation: c 37.5 % let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 88 gain % = 24 / 64 * 100 = 37.5 % .


Question: 3 numbers are in the ratio 3 : 5 : 7 . the largest number value is 70 . find difference between smallest & largest number is ?

<gadget id="calculator">70 / 7</gadget>
<output>10</output>

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

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

Choices:
A. 40
B. 45
C. 35
D. 30
E. 50

subtract(70, multiply(divide(70, 7), 3))

Explanation: = = 3 : 5 : 7 total parts = 15 = the largest number value is 70 = the largest number is = 7 = then 7 parts - - - - - > 70 ( 7 * 10 = 70 ) = smallest number = 3 & largest number = 7 = difference between smallest number & largest number is = 7 - 3 = 4 = then 4 parts - - - - - > 40 ( 4 * 10 = 40 ) a


Question: in a 80 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :

<gadget id="calculator">7 / 56</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 80</gadget>
<output>10</output>

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

Choices:
A. 3 seconds
B. 12 seconds
C. 10 seconds
D. 18 seconds
E. 28 seconds

subtract(multiply(divide(7, 56), 80), 7)

Explanation: "b runs 56 m in 7 sec . = > b runs 80 m in 7 / 56 * 80 = 10 seconds since a beats b by 7 seconds , a runs 80 m in ( 10 - 7 ) = 3 seconds hence , a ' s time over the course = 3 seconds answer : a"


Question: there are 5 people who can build 5 houses in just 5 days . increase the amount of people to 100 . how long would it take these 100 people to build 100 houses ?

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

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

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

Explanation: it will take 5 days for 100 people to build 100 houses . 1 person can build 1 house in 5 days . so , 100 people can build 100 houses in 5 days . answer d


Question: the smallest number which when diminished by 2 , is divisible by 12 , 16 , 18 , 21 and 28 is

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

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

<gadget id="calculator">9 * 16</gadget>
<output>144</output>

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

<gadget id="calculator">144 * 7</gadget>
<output>1_008</output>

<gadget id="calculator">1_008 + 2</gadget>
<output>1_010</output>
<result>1_010</result>

Choices:
A. 1008
B. 1010
C. 1022
D. 1032
E. 1043

add(multiply(multiply(power(const_3, 2), power(2, const_4)), add(const_3, const_4)), const_2)

Explanation: required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 2 = 1008 + 2 = 1010 answer : b


Question: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours ?

<gadget id="calculator">8 / 6</gadget>
<output>4/3 = around 1.333333</output>

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

<gadget id="calculator">55 / 30</gadget>
<output>11/6 = around 1.833333</output>

<gadget id="calculator">60 * (11/6)</gadget>
<output>110</output>

<gadget id="calculator">110 - 45</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 50
B. 55
C. 60
D. 65
E. 70

subtract(multiply(multiply(45, divide(8, 6)), divide(55, 30)), 45)

Explanation: "45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers the answer is d ."


Question: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 12 feet between each tree . how many trees can be planted if the road is 157 feet long ?

<gadget id="calculator">157 - 1</gadget>
<output>156</output>

<gadget id="calculator">12 + 1</gadget>
<output>13</output>

<gadget id="calculator">156 / 13</gadget>
<output>12</output>
<result>13</result>

Choices:
A. 8
B. 9
C. 10
D. 11
E. 13

add(divide(subtract(157, const_1), add(12, const_1)), const_1)

Explanation: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 12 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 12 feet spaces will be t - 1 . then , the length of sidewalk required for 12 feet spaces will be 12 * ( t - 1 ) it is given that total lenght of sidewalk is 157 feet . or 12 ( t - 1 ) + t = 157 or 12 t - 12 + t = 157 or 13 t = 169 or t = 13 answer : - e"


Question: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 150 m long ?

<gadget id="calculator">150 / 1_000</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">360 / 1_000</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(3/20) + (9/25)</gadget>
<output>51/100 = around 0.51</output>

<gadget id="calculator">(51/100) / 45</gadget>
<output>17/1_500 = around 0.011333</output>

<gadget id="calculator">(17/1_500) * 3_600</gadget>
<output>204/5 = around 40.8</output>
<result>204/5 = around 40.8</result>

Choices:
A. 38 sec
B. 35 sec
C. 44 sec
D. 40.8 sec
E. none of these

multiply(divide(add(divide(150, const_1000), divide(360, const_1000)), 45), const_3600)

Explanation: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 150 = 510 meter time taken to cross the platform = 510 / ( 25 / 2 ) = 510 ã — 2 / 25 = 40.8 seconds answer : d"


Question: two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 7 . find the probability that both of them are selected .

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

<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(1/3) * (2/7)</gadget>
<output>2/21 = around 0.095238</output>
<result>2/21 = around 0.095238</result>

Choices:
A. 2 / 69
B. 2 / 21
C. 2 / 23
D. 2 / 29
E. 2 / 10

Explanation: explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 7 ) = 2 / 21 answer : b ) 2 / 21


Question: a box contains 22 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is

<gadget id="calculator">22 - 4</gadget>
<output>18</output>

<gadget id="calculator">binomial(18, 2)</gadget>
<output>153</output>

<gadget id="calculator">binomial(22, 2)</gadget>
<output>231</output>

<gadget id="calculator">153 / 231</gadget>
<output>51/77 = around 0.662338</output>

<gadget id="calculator">1 - (51/77)</gadget>
<output>26/77 = around 0.337662</output>
<result>26/77 = around 0.337662</result>

Choices:
A. 4 / 19
B. 7 / 19
C. 12 / 19
D. 21 / 99
E. 26 / 77

subtract(const_1, divide(choose(subtract(22, 4), const_2), choose(22, const_2)))

Explanation: "solution p ( none is defective ) = 18 c 2 / 22 c 2 = 51 / 77 p ( at least one is defective ) = ( 1 - 51 / 77 ) = 26 / 77 . answer e"


Question: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 8 times the probability that both events a and b occur . what is the probability that event a occurs ?

<gadget id="calculator">2 + 1</gadget>
<output>3</output>

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

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

<gadget id="calculator">3 / 18</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) * 2</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>

Choices:
A. 1 / 12
B. 1 / 8
C. 1 / 6
D. 1 / 3
E. 2 / 3

multiply(divide(add(const_2, const_1), add(multiply(8, const_2), const_2)), const_2)

Explanation: "let us say probability of a occurring is a . let us say probability of b occurring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 8 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 8 * 2 b * b 3 b - 2 b ^ 2 = 16 b ^ 2 3 b = 18 b ^ 2 b = 3 / 18 = 1 / 6 so , a = 2 b = 1 / 3 answer : d"


Question: if - 2 and - 3 are negative integers , then - 2 * - 3 + 2 is

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

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

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

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

Choices:
A. - 5
B. 8
C. - 6
D. - 3
E. - 8

Explanation: answer : b


Question: a can give b 50 meters start and c 100 meters start in a kilometer race . how much start can b give c in a kilometer race ?

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>

<gadget id="calculator">1_000 * 900</gadget>
<output>900_000</output>

<gadget id="calculator">1_000 - 50</gadget>
<output>950</output>

<gadget id="calculator">900_000 / 950</gadget>
<output>18_000/19 = around 947.368421</output>

<gadget id="calculator">1_000 - (18_000/19)</gadget>
<output>1_000/19 = around 52.631579</output>
<result>1_000/19 = around 52.631579</result>

Choices:
A. 111.12
B. 111.67
C. 111.64
D. 52.63
E. 101.12

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 100)), subtract(multiply(const_100, const_10), 50)))

Explanation: "a runs 1000 m while b runs 950 m and c runs 900 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 900 ) / 950 = 947.37 m . b can give c = 1000 - 947.37 = 52.63 m . answer : d"


Question: how many seconds will a 800 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?

<gadget id="calculator">63 - 3</gadget>
<output>60</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">800 / (50/3)</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 48
B. 52
C. 38
D. 42
E. 45

divide(800, multiply(subtract(63, 3), const_0_2778))

Explanation: "explanation : here distance d = 800 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = 800 x 18 / 60 x 5 = 48 sec . answer is a"


Question: if a - b = 8 and a ^ 2 + b ^ 2 = 164 , find the value of ab

<gadget id="calculator">164 ** (1/2)</gadget>
<output>2*sqrt(41) = around 12.806248</output>

<gadget id="calculator">(2*sqrt(41)) - 8</gadget>
<output>-8 + 2*sqrt(41) = around 4.806248</output>

<gadget id="calculator">(-8 + 2*sqrt(41)) / 2</gadget>
<output>-4 + sqrt(41) = around 2.403124</output>

<gadget id="calculator">8 + (-4 + sqrt(41))</gadget>
<output>4 + sqrt(41) = around 10.403124</output>

<gadget id="calculator">(4 + sqrt(41)) * (-4 + sqrt(41))</gadget>
<output>(-4 + sqrt(41))*(4 + sqrt(41)) = around 25</output>

<gadget id="calculator">((-4 + sqrt(41))*(4 + sqrt(41))) * 2</gadget>
<output>2*(-4 + sqrt(41))*(4 + sqrt(41)) = around 50</output>
<result>2*(-4 + sqrt(41))*(4 + sqrt(41)) = around 50</result>

Choices:
A. 10
B. 12
C. 50
D. 18
E. 19

multiply(multiply(add(8, divide(subtract(sqrt(164), 8), 2)), divide(subtract(sqrt(164), 8), 2)), 2)

Explanation: 2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 164 - 64 = 100 = > ab = 50 answer : c


Question: a sum fetched a total simple interest of rs . 929.20 at the rate of 8 p . c . p . a . in 5 years . what is the sum ?

<gadget id="calculator">929.2 * 100</gadget>
<output>92_920</output>

<gadget id="calculator">92_920 / 8</gadget>
<output>11_615</output>

<gadget id="calculator">11_615 / 5</gadget>
<output>2_323</output>
<result>2_323</result>

Choices:
A. 2323
B. 1223
C. 2563
D. 1853
E. 2353

divide(divide(multiply(929.20, const_100), 8), 5)

Explanation: "explanation : si = rs . 929.20 p = ? t = 5 years r = 8 % p = 100 × si / rt = 100 × 929.20 / 8 × 5 = rs . 2323 answer : option a"


Question: ? % of 360 = 151.2

<gadget id="calculator">151.2 * 100</gadget>
<output>15_120</output>

<gadget id="calculator">15_120 / 360</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 42
B. 36
C. 64
D. 72
E. none of these

Explanation: "? % of 360 = 151.2 or , ? = 151.2 × 100 / 360 = 42 answer a"


Question: the radius of a wheel is 22.5 cm . what is the distance covered by the wheel in making 500 resolutions ?

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

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

<gadget id="calculator">21 + 1</gadget>
<output>22</output>

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">(22/7) * 22.5</gadget>
<output>70.714286</output>

<gadget id="calculator">70.714286 * 2</gadget>
<output>141.428572</output>

<gadget id="calculator">141.428572 * 500</gadget>
<output>70_714.286</output>

<gadget id="calculator">70_714.286 / 100</gadget>
<output>707.14286</output>
<result>707.14286</result>

Choices:
A. 708 m
B. 707.14 m
C. 774 m
D. 714 m
E. 744 m

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.5), const_2), 500), const_100)

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.5 = 70714 cm = 707.14 m answer : b"


Question: how many cubes of 10 cm edge can be put in a cubical box of 1 m edge ?

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

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

<gadget id="calculator">(1/10) ** 3</gadget>
<output>1/1_000 = around 0.001</output>

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

Choices:
A. 1
B. 10
C. 100
D. 1000
E. none

Explanation: "sol . number of cubes = [ 100 * 100 * 100 / 10 * 10 * 10 ] = 1000 . answer d"


Question: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required ?

<gadget id="calculator">12 * 10</gadget>
<output>120</output>

<gadget id="calculator">120 * 8</gadget>
<output>960</output>

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

<gadget id="calculator">960 / 120</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8 days
B. 9 days
C. 11 days
D. 13 days
E. 15 days

divide(multiply(multiply(12, 10), 8), multiply(8, 15))

Explanation: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 10 = 8 days . a )"


Question: if a man lost 10 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?

<gadget id="calculator">100 - 10</gadget>
<output>90</output>

<gadget id="calculator">90 * 12</gadget>
<output>1_080</output>

<gadget id="calculator">100 + 44</gadget>
<output>144</output>

<gadget id="calculator">1_080 / 144</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>

Choices:
A. 6.5
B. 7.5
C. 7
D. 8
E. 2

divide(multiply(subtract(const_100, 10), 12), add(const_100, 44))

Explanation: 90 % - - - - 12 144 % - - - - ? 90 / 144 * 12 = 7.50 answer : b


Question: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

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

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

<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 10 : 5
B. 15 : 2
C. 20 : 2
D. 25 : 2
E. none of these

Explanation: "explanation : indian stamps are common to both ratios . multiply both ratios by factors such that the indian stamps are represented by the same number . us : indian = 5 : 2 , and indian : british = 5 : 1 . multiply the first by 5 , and the second by 2 . hence the two ratios can be combined and us : british = 25 : 2 now us : indian = 25 : 10 , and indian : british = 10 : 2 answer : d"


Question: a canteen requires 13 dozen bananas per day . how many bananas will it require for 9 weeks ?

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

<gadget id="calculator">9 * 7</gadget>
<output>63</output>

<gadget id="calculator">13 * 63</gadget>
<output>819</output>

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

<gadget id="calculator">819 * 12</gadget>
<output>9_828</output>
<result>9_828</result>

Choices:
A. 728
B. 9828
C. 1404
D. 9882
E. none

multiply(multiply(13, multiply(9, add(const_3, const_4))), multiply(const_3, const_4))

Explanation: requirement of bananas for 1 day in the canteen = 13 dozens ∴ requirement of bananas for 9 weeks i . e . 63 days = 63 × 13 dozens = 63 × 13 × 12 = 9828 . answer d


Question: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 11 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?

<gadget id="calculator">1_500 / 5</gadget>
<output>300</output>

<gadget id="calculator">11 - 3</gadget>
<output>8</output>

<gadget id="calculator">300 * 8</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. s 1200
B. s 1500
C. s 1600
D. s 1900
E. s 2400

multiply(divide(1500, 5), subtract(11, 3))

Explanation: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 11 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 3300 . hence , ( r - p ) = ( 3300 - 900 ) = 2400 answer : e"


Question: a shipment of 230 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?

<gadget id="calculator">84 - 1</gadget>
<output>83</output>

<gadget id="calculator">84 * 83</gadget>
<output>6_972</output>

<gadget id="calculator">230 - 1</gadget>
<output>229</output>

<gadget id="calculator">230 * 229</gadget>
<output>52_670</output>

<gadget id="calculator">6_972 / 52_670</gadget>
<output>3_486/26_335 = around 0.132371</output>
<result>3_486/26_335 = around 0.132371</result>

Choices:
A. 1 / 250
B. 1 / 84
C. 1 / 11
D. 9 / 68
E. 1 / 3

divide(multiply(84, subtract(84, const_1)), multiply(230, subtract(230, const_1)))

Explanation: "probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = ( 84 / 230 ) probability of chosing one defective phone from a lot of 229 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 229 ) combined probability of series of events = product of the probabilities = ( 84 / 230 ) * ( 83 / 229 ) 84 / 230 is close to ( 23 / 63 ) and ( 83 / 229 ) = ( 29 / 80 ) so answer is ( 23 / 63 ) * ( 29 / 80 ) = ( 9 / 68 ) so , answer will be d"


Question: a large box contains 20 small boxes and each small box contains 32 chocolate bars . how many chocolate bars are in the large box ?

<gadget id="calculator">20 * 32</gadget>
<output>640</output>
<result>640</result>

Choices:
A. 220
B. 490
C. 380
D. 450
E. 640

Explanation: "the only thing you have to do is a simple multiply we have : 20 * 32 = 640 correct answer is : e ) 640"


Question: in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25000 votes how many votes did candidate x received ?

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

<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/2) * (3/5)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(9/10) * 25_000</gadget>
<output>22_500</output>
<result>22_500</result>

Choices:
A. 18000
B. 22500
C. 24000
D. 26000
E. 32000

multiply(multiply(add(const_1, divide(1, 2)), subtract(const_1, divide(2, 5))), 25000)

Explanation: z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b .


Question: a train 800 m long can cross a pole in 10 sec and then find the speed of the train ?

<gadget id="calculator">800 / 1_000</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">10 / 3_600</gadget>
<output>1/360 = around 0.002778</output>

<gadget id="calculator">(4/5) / (1/360)</gadget>
<output>288</output>
<result>288</result>

Choices:
A. 280
B. 282
C. 284
D. 286
E. 288

divide(divide(800, const_1000), divide(10, const_3600))

Explanation: "length = speed * time speed = l / t s = 800 / 10 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 288 kmph answer : e"


Question: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is two times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?

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

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

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

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

<gadget id="calculator">18 / 8</gadget>
<output>9/4 = around 2.25</output>
<result>9/4 = around 2.25</result>

Choices:
A. 1 : 1
B. 2 : 3
C. 3 : 2
D. 9 : 4
E. 18 : 8

divide(multiply(multiply(2, 3), 3), multiply(multiply(2, 2), 2))

Explanation: water : soap = 3 : 2 soap : salt = 6 : 2 = > for 6 soap , salt = 2 = > for 2 soap , salt = ( 2 / 6 ) * 2 = 2 / 3 so , water : soap : salt = 3 : 2 : 2 / 3 = 18 : 12 : 4 after open container , water : soap : salt = 9 : 18 : 4 so , water : salt = 9 : 4 = 18 : 8 e


Question: a string of 30 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.1 , what is the probability that the string of light bulbs will fail during the time period t ?

<gadget id="calculator">1 - 0.1</gadget>
<output>0.9</output>

<gadget id="calculator">0.9 ** 30</gadget>
<output>0.042391</output>

<gadget id="calculator">1 - 0.042391</gadget>
<output>0.957609</output>
<result>0.957609</result>

Choices:
A. 0.1
B. ( 0.1 ) ^ 30
C. 1 - ( 0.1 ) ^ 30
D. ( 0.93 ) ^ 30
E. 1 - ( 0.90 ) ^ 30

subtract(const_1, power(subtract(const_1, 0.1), 30))

Explanation: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 30 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.1 = 0.90 the the probability that none of the 30 light bulbs fails is 0.90 ^ 30 . hence , the probability that at least one light bulb fails is 1 - 0.90 ^ 30 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 30 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.1 = 10 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."


Question: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?

<gadget id="calculator">12 + 4</gadget>
<output>16</output>

<gadget id="calculator">16 - 9</gadget>
<output>7</output>

<gadget id="calculator">7 + 1</gadget>
<output>8</output>

<gadget id="calculator">8 * 12</gadget>
<output>96</output>

<gadget id="calculator">96 * 30</gadget>
<output>2_880</output>

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

<gadget id="calculator">2_880 / 4</gadget>
<output>720</output>

<gadget id="calculator">720 * 3</gadget>
<output>2_160</output>

<gadget id="calculator">2_160 * 10</gadget>
<output>21_600</output>

<gadget id="calculator">720 * 6</gadget>
<output>4_320</output>

<gadget id="calculator">21_600 + 4_320</gadget>
<output>25_920</output>
<result>25_920</result>

Choices:
A. $ 24960
B. $ 25920
C. $ 28080
D. $ 28500
E. $ 29160

add(multiply(multiply(divide(multiply(multiply(add(subtract(add(const_12, const_4), 9), const_1), const_12), 30), add(3, const_1)), 3), 10), multiply(divide(multiply(multiply(add(subtract(add(const_12, const_4), 9), const_1), const_12), 30), add(3, const_1)), 6))

Explanation: from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive there are 8 * 12 = 96 five - minute intervals , thus total of 96 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 96 * 30 - - > x = 24 * 30 and 3 x = 3 * ( 24 * 30 ) = 24 * 90 . therefore , the total revenue from ticket sales that day was 24 * 30 * 6 + 24 * 90 * 10 = $ 25,920 . answer : b .


Question: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 105 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?

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

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

<gadget id="calculator">(1/2) * (1/4)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/2) + (1/8)</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">105 / (3/8)</gadget>
<output>280</output>
<result>280</result>

Choices:
A. 280
B. 320
C. 360
D. 420
E. 480

divide(105, subtract(1, add(divide(1, 2), multiply(divide(1, 2), divide(1, 4)))))

Explanation: "easy 280 is the answer . 3 / 4 ( x / 2 ) = 105 x = 105 * 8 / 3 = 280 . answer a"


Question: if 2 / 3 rd of the contents of a container evaporated on the 1 st day . and 1 / 4 th of the remaining evaporated on the second day . what part of the contents of the container is left at the end of the second day ?

<gadget id="calculator">4 * 1</gadget>
<output>4</output>

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

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

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

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

<gadget id="calculator">(1/4) * (2/3)</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

Choices:
A. 1 / 4
B. 1 / 12
C. 1 / 18
D. 1 / 6
E. 1 / 2

multiply(divide(subtract(multiply(4, 1), multiply(3, 1)), multiply(4, 1)), divide(2, 3))

Explanation: after first day , 1 / 3 of the contents remain . after second day , ( 1 / 3 ) - ( 1 / 4 ( 2 / 3 ) ) = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 of the contents remain answer : d


Question: the average of first 7 prime numbers is ?

<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 10.11
B. 11.11
C. 8.29
D. 13.11
E. 14.11

Explanation: "sum of 7 prime no . = 58 average = 58 / 7 = 8.29 answer : c"


Question: in a group of 28 junior high school students , 5 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?

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

<gadget id="calculator">28 - 15</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 7
B. 13
C. 9
D. 12
E. 10

Explanation: b 13 add 1 + 10 + 4 to get 15 . then subtract 21 from the total students ⇒ 28 – 15 = 13 . answer is b


Question: a , b , c can complete a piece of work in 3,9 and 15 days respectively . working together , they will complete the same work in how many days ?

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

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

<gadget id="calculator">4 + 4</gadget>
<output>8</output>

<gadget id="calculator">8 + 1</gadget>
<output>9</output>

<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>

<gadget id="calculator">(1/3) + (1/9)</gadget>
<output>4/9 = around 0.444444</output>

<gadget id="calculator">(1/15) + (4/9)</gadget>
<output>23/45 = around 0.511111</output>

<gadget id="calculator">1 / (23/45)</gadget>
<output>45/23 = around 1.956522</output>
<result>45/23 = around 1.956522</result>

Choices:
A. 45 / 23
B. 55 / 23
C. 61 / 57
D. 12 / 13
E. 22 / 23

inverse(add(inverse(15), add(inverse(const_3), inverse(add(add(const_4, const_4), const_1)))))

Explanation: ( a + b + c ) ' s 1 day work = ( 1 / 3 ) + ( 1 / 9 ) + ( 1 / 115 ) = 23 / 45 a , b , c together will complete the work in 45 / 23 days answer is a


Question: in a group of cows and chickens , the number of legs was 12 more than twice the number of heads . the number of cows was :

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

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

Choices:
A. 6
B. 7
C. 10
D. 12
E. 14

Explanation: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 12 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 12 = 4 x + 2 y . or , 2 x + 12 = 4 x [ subtracting 2 y from both sides ] . or , 12 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 12 = 2 x . or , x = 6 [ dividing by 2 on both sides ] . therefore , the number of cows = 6 . correct answer : a ) 6"


Question: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?

<gadget id="calculator">385 - 320</gadget>
<output>65</output>

<gadget id="calculator">65 / 320</gadget>
<output>13/64 = around 0.203125</output>

<gadget id="calculator">(13/64) * 100</gadget>
<output>325/16 = around 20.3125</output>
<result>325/16 = around 20.3125</result>

Choices:
A. 2 %
B. 17 %
C. 20 %
D. 65 %
E. 83 %

multiply(divide(subtract(385, 320), 320), const_100)

Explanation: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 320 ) / 320 ] x 100 65 / 320 x 100 13 / 64 x 100 ≈ 13 / 65 x 100 ≈ 1 / 5 x 100 ≈ 20 % . the answer is c ."


Question: if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab .

Choices:
A. 5
B. 10
C. 12
D. 14
E. 15

multiply(multiply(add(3, divide(subtract(sqrt(29), 3), 2)), divide(subtract(sqrt(29), 3), 2)), 2)

Explanation: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 ab = 10 . b )"


Question: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 182 cms . what was the ratio of men to women ?

<gadget id="calculator">180 - 170</gadget>
<output>10</output>

<gadget id="calculator">182 - 180</gadget>
<output>2</output>

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

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

divide(subtract(180, 170), subtract(182, 180))

Explanation: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 182 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 182 m ) / ( w + m ) = 180 170 w + 182 m = 180 w + 180 m 2 m = 10 w m = 5 w m / w = 5 / 1 the ratio of men to women is 5 to 1 . b"


Question: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 400 , by what percent is the price to be reduced ?

<gadget id="calculator">400 / 500</gadget>
<output>4/5 = around 0.8</output>

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

Choices:
A. 10 %
B. 15 %
C. 20 %
D. 25 %
E. 80 %

Explanation: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 400 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 400 ) * 100 / 500 = 80 % answer : option e"


Question: jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the number ' s sum will be 13 ?

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/6) * (1/7)</gadget>
<output>1/42 = around 0.02381</output>
<result>1/42 = around 0.02381</result>

Choices:
A. 3 / 14
B. 2 / 7
C. 1 / 3
D. 1 / 42
E. 12 / 21

multiply(divide(const_1, 6), divide(1, 7))

Explanation: both dice addition result is 13 = ( 6 + 7 ) probability that the number on first die is 6 = 1 / 6 probability that the number on second die is 7 = 1 / 7 probability that both dice addition result is 13 = 1 / 6 * 1 / 7 = 1 / 42 d


Question: if a = 105 and a ^ 3 = 21 * 25 * 315 * b , what is the value of b ?

<gadget id="calculator">105 ** 3</gadget>
<output>1_157_625</output>

<gadget id="calculator">21 * 25</gadget>
<output>525</output>

<gadget id="calculator">525 * 315</gadget>
<output>165_375</output>

<gadget id="calculator">1_157_625 / 165_375</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 35
B. 7
C. 45
D. 49
E. 54

divide(power(105, 3), multiply(multiply(21, 25), 315))

Explanation: first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 315 = 3 * 3 * 5 * 7 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 3 * 5 * 7 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 3 * 7 ^ 2 b = 7 correct answer b .


Question: boy sells a book for rs . 540 he gets a loss of 10 % , to gain 10 % , what should be the sp ?

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

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">540 / (9/10)</gadget>
<output>600</output>

<gadget id="calculator">600 * (1/10)</gadget>
<output>60</output>

<gadget id="calculator">600 + 60</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 430
B. 450
C. 550
D. 590
E. 660

add(divide(540, subtract(const_1, divide(10, const_100))), multiply(divide(540, subtract(const_1, divide(10, const_100))), divide(10, const_100)))

Explanation: "cost price = 540 / 90 x 100 = 600 to gain 10 % = 600 x 10 / 100 = 60 sp = cp + gain = 600 + 60 = 660 answer : e"


Question: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?

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

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

<gadget id="calculator">(1/3) * (1/2)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(1/6) * (3/8)</gadget>
<output>1/16 = around 0.0625</output>
<result>1/16 = around 0.0625</result>

Choices:
A. 1 / 16
B. 7 / 8
C. 9 / 64
D. 5 / 64
E. 3 / 64

multiply(multiply(divide(1, 3), divide(1, 2)), subtract(1, divide(5, 8)))

Explanation: "p ( xavier will solve ) = 1 / 3 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 3 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 16 . ans . a ."


Question: if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers i

<gadget id="calculator">0.08 * 100</gadget>
<output>8</output>

<gadget id="calculator">0.2 * 100</gadget>
<output>20</output>

<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 2 : 3
B. 2 : 5
C. 3 : 20
D. 20 : 3
E. none

divide(multiply(0.08, const_100), multiply(0.2, const_100))

Explanation: "sol . 0.2 a = 0.08 b â ‡ ” a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 â ˆ ´ a : b = 2 : 5 . answer b"


Question: a person want to give his money of $ 1800 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?

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

<gadget id="calculator">5 + 4</gadget>
<output>9</output>

<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 1_800</gadget>
<output>600</output>
<result>600</result>

Choices:
A. $ 700
B. $ 600
C. $ 900
D. $ 500
E. $ 400

multiply(divide(3, add(add(2, 3), 4)), 1800)

Explanation: "b ' s share = 1800 * 3 / 9 = $ 600 answer is b"


Question: in what time will a train 240 metres long cross an electric pole , if its speed be 126 km / hr ?

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

<gadget id="calculator">126 * (5/18)</gadget>
<output>35</output>

<gadget id="calculator">240 / 35</gadget>
<output>48/7 = around 6.857143</output>
<result>48/7 = around 6.857143</result>

Choices:
A. 6.75 sec
B. 6.85 sec
C. 6.55 sec
D. 6.44 sec
E. 7.85 sec

Explanation: "solution speed = ( 126 x 5 / 18 ) m / sec = 35 m / sec time taken = ( 240 / 35 ) sec = 6.85 sec . answer b"


Question: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 7 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?

<gadget id="calculator">1_720 - 600</gadget>
<output>1_120</output>

<gadget id="calculator">1_120 * 7</gadget>
<output>7_840</output>

<gadget id="calculator">7_840 / 100</gadget>
<output>392/5 = around 78.4</output>
<result>392/5 = around 78.4</result>

Choices:
A. $ 54.00
B. $ 78.40
C. $ 90.00
D. $ 100.80
E. $ 154.80

divide(multiply(subtract(1720, 600), 7), const_100)

Explanation: correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.07 ( $ 1120 ) = $ 78.40 . the correct answer is b .


Question: how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 200 m in length ?

<gadget id="calculator">110 + 200</gadget>
<output>310</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">310 / (50/3)</gadget>
<output>93/5 = around 18.6</output>
<result>93/5 = around 18.6</result>

Choices:
A. 18.6 sec
B. 14.9 sec
C. 12.4 sec
D. 16.8 sec
E. 11.8 sec

Explanation: "a 18.6 sec d = 110 + 200 = 310 m s = 60 * 5 / 18 = 50 / 3 t = 310 * 3 / 50 = 18.6 sec answer is a"


Question: excepting ‘ seldom ’ which means – rarely , infrequently and not often , is the antonym .

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

<gadget id="calculator">7 * 10</gadget>
<output>70</output>

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

<gadget id="calculator">70 + 6</gadget>
<output>76</output>

<gadget id="calculator">100 + 76</gadget>
<output>176</output>
<result>176</result>

Choices:
A. 22
B. 278
C. 267
D. 176
E. 971

add(const_100, add(multiply(add(const_3, const_4), const_10), add(const_3, const_3)))

Explanation: answer : d


Question: two pipes a and b can fill a tank in 24 minutes and 32 minutes respectively . if both the pipes are opened simultaneously , after how much time should b be closed so that the tank is full in 18 minutes ?

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

<gadget id="calculator">(1/24) * 18</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>

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

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

multiply(subtract(const_1, multiply(divide(const_1, 24), 18)), 32)

Explanation: pipe a will work for 18 minutes . suppose pipe b is closed after x minutes than we have 18 / 24 + x / 32 = 1 x = 8 minute . answer : d


Question: the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?

<gadget id="calculator">35 * 181</gadget>
<output>6_335</output>

<gadget id="calculator">6_335 - 166</gadget>
<output>6_169</output>

<gadget id="calculator">6_169 + 106</gadget>
<output>6_275</output>

<gadget id="calculator">6_275 / 35</gadget>
<output>1_255/7 = around 179.285714</output>

<gadget id="calculator">floor(1_255/7)</gadget>
<output>179</output>
<result>179</result>

Choices:
A. 187.89 cm
B. 179.29 cm
C. 123.98 cm
D. 149.98 cm
E. 146.89 cm

floor(divide(add(subtract(multiply(35, 181), 166), 106), 35))

Explanation: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"


Question: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 280 vote ’ s majority . what is the total number of votes polled ?

<gadget id="calculator">100 * 280</gadget>
<output>28_000</output>

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

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

<gadget id="calculator">28_000 / 40</gadget>
<output>700</output>
<result>700</result>

Choices:
A. 750
B. 700
C. 800
D. 850
E. none of these

divide(multiply(const_100, 280), subtract(70, subtract(const_100, 70)))

Explanation: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 7 = 280 ) 100 % - - - - - > 700 ( 100 * 7 = 700 ) answer : option b"


Question: a dishonest dealer professes to sell goods at the cost price but uses a weight of 990 grams per kg , what is his percent ?

<gadget id="calculator">100 / 990</gadget>
<output>10/99 = around 0.10101</output>

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

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

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">(10/99) * 1_000</gadget>
<output>10_000/99 = around 101.010101</output>

<gadget id="calculator">(10_000/99) - 100</gadget>
<output>100/99 = around 1.010101</output>
<result>100/99 = around 1.010101</result>

Choices:
A. 1.01 %
B. 25 %
C. 22 %
D. 29 %
E. 45 %

subtract(multiply(divide(const_100, 990), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

Explanation: "990 - - - 10 100 - - - ? = > 1.01 % answer : a"


Question: 50 % of x is greater than 1 / 3 rd of x by 110 . what is x ?

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

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

<gadget id="calculator">(1/2) - (1/3)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">110 / (1/6)</gadget>
<output>660</output>
<result>660</result>

Choices:
A. 100
B. 200
C. 300
D. 350
E. 660

divide(110, subtract(divide(50, const_100), divide(1, 3)))

Explanation: "5 x / 10 - x / 3 = 110 1 x / 6 = 110 x = 660 answer : e"


Question: the average age of a , b and c is 26 years . if the average age of a and c is 29 years , what is the age of b in years ?

<gadget id="calculator">26 * 3</gadget>
<output>78</output>

<gadget id="calculator">29 * 2</gadget>
<output>58</output>

<gadget id="calculator">78 - 58</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 19
B. 35
C. 20
D. 32
E. 21

subtract(multiply(26, const_3), multiply(29, const_2))

Explanation: "c 20 age of b = age of ( a + b + c ) – age of ( a + c ) = 26 × 3 – 29 × 2 = 78 – 58 = 20 years"


Question: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 25 % lemonade syrup ?

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

<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>

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

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(7/15) - (2/5)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/15) / (7/15)</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">(1/7) * 15</gadget>
<output>15/7 = around 2.142857</output>
<result>15/7 = around 2.142857</result>

Choices:
A. 1.5
B. 1.75
C. 2.14
D. 2.34
E. 2.64

multiply(divide(subtract(divide(7, add(8, 7)), divide(const_2, add(const_2, const_3))), divide(7, add(8, 7))), add(8, 7))

Explanation: "let the total solution is 150 l with 80 l water 70 l syrup . to make 25 % syrup solution , the result solution must have 112.5 l syrup and 37.5 l syrup . therefore we are taking 32.5 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 32.5 l syrup in 69.6 l solution we started by multiplying 10 now to get to the result we need to divide by 32.5 = > amount of solution to be replaced with water = ( 69.6 / 32.5 ) = 2.14 . correct option : c"


Question: in what time will a train 175 m long cross an electric pole , it its speed be 180 km / hr ?

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

<gadget id="calculator">180 * (5/18)</gadget>
<output>50</output>

<gadget id="calculator">175 / 50</gadget>
<output>7/2 = around 3.5</output>
<result>7/2 = around 3.5</result>

Choices:
A. 7.5
B. 6.5
C. 5.5
D. 4.5
E. 3.5

Explanation: "speed = 180 * 5 / 18 = 50 m / sec time taken = 175 / 50 = 3.5 sec . answer : e"


Question: 80 % of the population of a village is 64000 . the total population of the village is ?

<gadget id="calculator">100 / 80</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 64_000</gadget>
<output>80_000</output>
<result>80_000</result>

Choices:
A. 26799
B. 24000
C. 80000
D. 29973
E. 12312

Explanation: "x * ( 80 / 100 ) = 64000 x = 800 * 100 x = 80000 answer : c"


Question: the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ?

<gadget id="calculator">(5 * 42) / 2</gadget>
<output>105</output>
<result>105</result>

Choices:
A. 128 cm 2
B. 36.0 cm 2
C. 105 cm 2
D. 25 cm 2
E. 135 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 = 5.0 * 42 / 2 = 105 cm 2 answer : c"


Question: company c sells a line of 20 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?

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

<gadget id="calculator">1_200 * 20</gadget>
<output>24_000</output>

<gadget id="calculator">400 * 10</gadget>
<output>4_000</output>

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

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

<gadget id="calculator">9 * 1_000</gadget>
<output>9_000</output>

<gadget id="calculator">4_000 + 9_000</gadget>
<output>13_000</output>

<gadget id="calculator">24_000 - 13_000</gadget>
<output>11_000</output>
<result>11_000</result>

Choices:
A. 12000
B. 11000
C. 10000
D. 13000
E. 15000

subtract(multiply(multiply(const_12, const_100), 20), add(multiply(400, 10), multiply(subtract(subtract(20, 10), const_1), const_1000)))

Explanation: the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b .


Question: the total age of a and b is 12 year more than the total age of b and c . c is how many years younger than a ?

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

Choices:
A. 12
B. 24
C. data inadequate
D. none of these
E. 34

Explanation: "solution ( a + b ) - ( b + c ) = 12 ⇔ a - c = 12 . answer a"


Question: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 867 sq m , then what is the breadth of the rectangular plot ?

<gadget id="calculator">867 / 3</gadget>
<output>289</output>

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 19 m
B. 17 m
C. 10 m
D. 12 m
E. 18 m

Explanation: answer : option b explanation : let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 867 3 b 2 = 867 b 2 = 289 = 172 ( b > 0 ) b = 17 m . answer : option b


Question: in a fuel station the service costs $ 1.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?

<gadget id="calculator">65 * 120</gadget>
<output>7_800</output>

<gadget id="calculator">7_800 / 100</gadget>
<output>78</output>

<gadget id="calculator">65 + 78</gadget>
<output>143</output>

<gadget id="calculator">143 * 2</gadget>
<output>286</output>

<gadget id="calculator">286 * 0.6</gadget>
<output>171.6</output>

<gadget id="calculator">65 * 3</gadget>
<output>195</output>

<gadget id="calculator">195 * 0.6</gadget>
<output>117</output>

<gadget id="calculator">171.6 + 117</gadget>
<output>288.6</output>
<result>288.6</result>

Choices:
A. 122.6 $
B. 128.9 $
C. 243.7 $
D. 293.85 $
E. 312.12 $

add(multiply(multiply(add(65, divide(multiply(65, 120), const_100)), 2), 0.6), multiply(multiply(65, 3), 0.6))

Explanation: "service cost of 3 van and 2 truck = 1.05 * ( 3 + 2 ) = 5.25 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.6 = 288.6 total cost = fuel + service = 288.6 + 5.25 = 293.85 answer is d"


Question: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 34 % iodine solution ?

<gadget id="calculator">35 * 20</gadget>
<output>700</output>

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

<gadget id="calculator">7 * 34</gadget>
<output>238</output>

<gadget id="calculator">7 * 20</gadget>
<output>140</output>

<gadget id="calculator">238 - 140</gadget>
<output>98</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">20 * (2/5)</gadget>
<output>8</output>

<gadget id="calculator">8 - 7</gadget>
<output>1</output>

<gadget id="calculator">98 / 1</gadget>
<output>98</output>

<gadget id="calculator">98 + 35</gadget>
<output>133</output>
<result>133</result>

Choices:
A. 35
B. 49
C. 100
D. 105
E. 136

add(divide(subtract(multiply(divide(multiply(35, 20), const_100), 34), multiply(divide(multiply(35, 20), const_100), 20)), subtract(multiply(20, divide(40, const_100)), divide(multiply(35, 20), const_100))), 35)

Explanation: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 34 / 100 40 x + 700 = 34 x + 1220 6 x = 820 x = 136 lts correct option : e"


Question: a car runs 375 km in 3 hours . what ' s the car ' s speed ?

<gadget id="calculator">375 / 3</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 124
B. 125
C. 126
D. 127
E. none

Explanation: solution : 375 ÷ 3 = 125 answer b


Question: two men a and b working together complete a piece of work which it would have taken them respectively 12 and 18 days to complete if they worked separately . they received rs . 149.25 as their payment . find the share of a in the amount they received ?

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(1/12) + (1/18)</gadget>
<output>5/36 = around 0.138889</output>

<gadget id="calculator">(1/12) / (5/36)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) * 149.25</gadget>
<output>89.55</output>
<result>89.55</result>

Choices:
A. rs . 89.55
B. rs . 59.70
C. rs . 85.56
D. rs . 88.56
E. none of these

multiply(divide(inverse(12), add(inverse(12), inverse(18))), 149.25)

Explanation: lcm of 12 and 18 is 36 no of untits of a is 3 units no of units of b is 2 units then 5 - - > 149.25 3 - - - > ? ( 3 * 149.25 ) / 5 = 89.55 answer : a


Question: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 1 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?

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

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

<gadget id="calculator">12 / 9</gadget>
<output>4/3 = around 1.333333</output>

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

<gadget id="calculator">1 * 4</gadget>
<output>4</output>

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

<gadget id="calculator">(4/3) / 3</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>

Choices:
A. 9 : 8
B. 4 : 9
C. 3 : 2
D. 2 : 3
E. 1 : 2

divide(divide(multiply(const_4, 3), multiply(3, 3)), divide(multiply(3, const_4), multiply(1, const_4)))

Explanation: "the ratio of economy to luxury cars is 3 : 1 - - > e : l = 3 : 1 = 12 : 4 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 4 : 9 . answer : b ."


Question: the compound ratio of 7 : 6 , 3 : 2 and 4 : 5 ?

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

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

<gadget id="calculator">21 / 12</gadget>
<output>7/4 = around 1.75</output>

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

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

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

<gadget id="calculator">(7/4) / (6/5)</gadget>
<output>35/24 = around 1.458333</output>
<result>35/24 = around 1.458333</result>

Choices:
A. 7 : 5
B. 1 : 87
C. 1 : 6
D. 1 : 9
E. 1 : 2

divide(divide(multiply(7, 3), multiply(6, 2)), divide(multiply(3, 4), multiply(2, 5)))

Explanation: 7 / 6 * 3 / 2 * 4 / 5 = 7 / 5 7 : 5 answer : a


Question: there are 50 students in a class . if 14 % are absent on a particular day , find the number of students present in the class .

<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">1 - (7/50)</gadget>
<output>43/50 = around 0.86</output>

<gadget id="calculator">(43/50) * 50</gadget>
<output>43</output>
<result>43</result>

Choices:
A. 43
B. 36
C. 28
D. 129
E. 11

multiply(subtract(const_1, divide(14, const_100.0)), 50)

Explanation: "number of students absent on a particular day = 14 % of 50 i . e . , 14 / 100 × 50 = 7 therefore , the number of students present = 50 - 7 = 43 students . answer : a"


Question: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 31 kmph . of how many minutes does the train stop per hour ?

<gadget id="calculator">31 / 45</gadget>
<output>31/45 = around 0.688889</output>

<gadget id="calculator">60 * (31/45)</gadget>
<output>124/3 = around 41.333333</output>

<gadget id="calculator">60 - (124/3)</gadget>
<output>56/3 = around 18.666667</output>
<result>56/3 = around 18.666667</result>

Choices:
A. 18.6
B. 27
C. 12
D. 121
E. 28

subtract(const_60, multiply(const_60, divide(31, 45)))

Explanation: "explanation : t = 14 / 45 * 60 = 18.6 answer : option a"


Question: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 1 km / h , how many hours will the swimmer take to swim against the current for 6 km ?

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

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

Choices:
A. 1.2
B. 1.4
C. 1.6
D. 1.8
E. 2

Explanation: the swimmer can swim against the current at a speed of 4 - 1 = 3 km / h . the time it will take is 6 / 3 = 2 hours . the answer is e .


Question: calculate how long it will take a swimmer to swim a distance of 12 km against the current of a river which flows at 1.2 km / hr , given that he can swim in still water at 5 km / h

<gadget id="calculator">5 - 1.2</gadget>
<output>3.8</output>

<gadget id="calculator">12 / 3.8</gadget>
<output>3.157895</output>
<result>3.157895</result>

Choices:
A. 3.26
B. 3.16
C. 2.34
D. 3.98
E. 3.17

Explanation: "swim in still water at = 5 speed of river = 1.2 us = 5 - 1.2 = 3.8 distance = 12 t = 12 / 3.8 = 3.16 answer : b"


Question: find the value of ( 100 + 20 / 90 ) × 90

<gadget id="calculator">20 / 90</gadget>
<output>2/9 = around 0.222222</output>

<gadget id="calculator">(2/9) + 100</gadget>
<output>902/9 = around 100.222222</output>

<gadget id="calculator">(902/9) * 90</gadget>
<output>9_020</output>
<result>9_020</result>

Choices:
A. 4520
B. 9100
C. 9150
D. 8120
E. 9020

Explanation: "( 9000 + 20 ) / 90 * 90 = 9020 answer : e"


Question: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 112 . what was the number he chose ?

<gadget id="calculator">112 + 138</gadget>
<output>250</output>

<gadget id="calculator">250 / 2</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 123
B. 267
C. 125
D. 267
E. 120

Explanation: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 112 x = 125 answer : c"


Question: how many multiples of 3 are there between 15 and 246 ?

<gadget id="calculator">246 - 15</gadget>
<output>231</output>

<gadget id="calculator">231 / 3</gadget>
<output>77</output>

<gadget id="calculator">77 + 1</gadget>
<output>78</output>
<result>78</result>

Choices:
A. 128
B. 94
C. 89
D. 76
E. 60

add(divide(subtract(246, 15), 3), const_1)

Explanation: "it should be mentioned whether 15 and 246 are inclusive . if 15 and 246 are inclusive , then the answer is ( 246 - 15 ) / 3 + 1 = 78 . if 15 and 246 are not inclusive , then the answer is ( 243 - 18 ) / 3 + 1 = 76 . since oa is d , then we have not inclusive case ."