Question: if the length and breadth of a rectangular room are each increased by 1 m , then the area of floor is increased by 21 sq . m . if the length is creased by 1 m and breadth is decreased by 1 m , then the area is decreased by 5 sq . m . the perimeter of the floor is :

<gadget id="calculator">21 - 5</gadget>
<output>16</output>

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

<gadget id="calculator">21 - 1</gadget>
<output>20</output>

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

<gadget id="calculator">2 * (8 + 12)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 27
B. 35
C. 40
D. 49
E. 38

rectangle_perimeter(divide(subtract(21, 5), const_2), subtract(subtract(21, 1), divide(subtract(21, 5), const_2)))

Explanation: let length = x meters and breadth = y meters . then , ( x + 1 ) ( y + 1 ) - xy = 21 x + y = 20 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ 1 and , xy - [ ( x + 1 ) ( y - 1 ) ] = 5 x - y = 6 ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ ã ¢ â ‚ ¬ â ¦ . . 2 solving ( i ) and ( ii ) , we get : x = 13 and y = 7 so , length = 13 m and breadth = 7 m . perimeter = [ 2 ( 13 + 7 ) ] m = 40 m . answer : c


Question: a car is 15 minutes late by running at a speed of 4 / 5 th of its actual speed . the actual time taken by the car to cover that distance is :

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

Choices:
A. 30 minutes
B. 1 hour
C. 2 hours
D. 3 hours
E. none of these

Explanation: explanation : new speed = 4 / 5 th of its actual speed new time = 5 / 4 th of its actual time = > 5 / 4 t - t = 15 / 60 = 1 / 4 = > 1 / 4 t = 1 / 4 = > t = 1 hour answer : b


Question: the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 30 runs . find his average in all the 30 matches ?

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

<gadget id="calculator">30 * 10</gadget>
<output>300</output>

<gadget id="calculator">800 + 300</gadget>
<output>1_100</output>

<gadget id="calculator">20 + 10</gadget>
<output>30</output>

<gadget id="calculator">1_100 / 30</gadget>
<output>110/3 = around 36.666667</output>
<result>110/3 = around 36.666667</result>

Choices:
A. 31
B. 36.67
C. 88
D. 13
E. 12

divide(add(multiply(40, 20), multiply(30, 10)), add(20, 10))

Explanation: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 300 . total score of the batsman in the 30 matches = 1100 . average score of the batsman = 1100 / 30 = 36.67 . answer : b"


Question: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability t that the next couple the maitre ' d seats will not order dessert ?

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

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

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

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

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

<gadget id="calculator">(3/5) / (4/5)</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) * 100</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 20 %
B. 25 %
C. 40 %
D. 60 %
E. 75 %

multiply(subtract(const_1, divide(divide(60, multiply(multiply(const_2, const_5), multiply(const_2, const_5))), subtract(const_1, divide(20, multiply(multiply(const_2, const_5), multiply(const_2, const_5)))))), multiply(multiply(const_2, const_5), multiply(const_2, const_5)))

Explanation: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . t = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"


Question: anne bought doughnuts for a class breakfast party . she bought 6 chocolate doughnuts , 8 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?

<gadget id="calculator">6 + 8</gadget>
<output>14</output>

<gadget id="calculator">14 + 8</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 22
B. 36
C. 39
D. 21
E. 11

Explanation: "add the numbers of doughnuts . 6 + 8 + 8 = 22 . answer is a ."


Question: i sold a book at a profit of 10 % . had i sold it for $ 110 more , 15 % would have been gained . find the cost price ?

<gadget id="calculator">110 * 10</gadget>
<output>1_100</output>

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

<gadget id="calculator">1_100 / 5</gadget>
<output>220</output>

<gadget id="calculator">220 * 100</gadget>
<output>22_000</output>

<gadget id="calculator">22_000 / 10</gadget>
<output>2_200</output>
<result>2_200</result>

Choices:
A. $ 2000
B. $ 2200
C. $ 3000
D. $ 3120
E. $ 1540

divide(multiply(divide(multiply(110, 10), subtract(15, 10)), const_100), 10)

Explanation: 115 % of cost - 110 % of cost = $ 110 5 % of cost = $ 110 cost = 110 * 100 / 5 = $ 2200 answer is b


Question: 90 % of the population of a village is 36000 . the total population of the village is ?

<gadget id="calculator">100 / 90</gadget>
<output>10/9 = around 1.111111</output>

<gadget id="calculator">(10/9) * 36_000</gadget>
<output>40_000</output>
<result>40_000</result>

Choices:
A. 26799
B. 24000
C. 26682
D. 29973
E. 40000

Explanation: "x * ( 90 / 100 ) = 36000 x = 400 * 100 x = 40000 answer : e"


Question: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = ?

<gadget id="calculator">1.9 * 0.6</gadget>
<output>1.14</output>

<gadget id="calculator">-1.14</gadget>
<output>-1.14</output>

<gadget id="calculator">2.6 * 1.2</gadget>
<output>3.12</output>

<gadget id="calculator">(-1.14) - 3.12</gadget>
<output>-4.26</output>

<gadget id="calculator">(-4.26) / 2</gadget>
<output>-2.13</output>
<result>-2.13</result>

Choices:
A. - 0.71
B. - 2.13
C. 1.07
D. 1.71
E. 2.71

divide(subtract(negate(multiply(1.9, 0.6)), multiply(2.6, 1.2)), 2.0)

Explanation: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 2.0 = - 2.13 answer b"


Question: the probability that a number selected at random from the first 50 natural numbers is a composite number is

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

<gadget id="calculator">18 - 1</gadget>
<output>17</output>

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

<gadget id="calculator">34 / 50</gadget>
<output>17/25 = around 0.68</output>
<result>17/25 = around 0.68</result>

Choices:
A. 17 / 26
B. 17 / 25
C. 17 / 20
D. 17 / 22
E. 17 / 21

divide(multiply(subtract(multiply(const_6, const_3), const_1), const_2), 50)

Explanation: the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . nswer : b


Question: a retailer buys 80 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?

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

<gadget id="calculator">1 - (1/100)</gadget>
<output>99/100 = around 0.99</output>

<gadget id="calculator">36 / 80</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(99/100) - (9/20)</gadget>
<output>27/50 = around 0.54</output>

<gadget id="calculator">(27/50) / (9/20)</gadget>
<output>6/5 = around 1.2</output>

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

Choices:
A. 110
B. 115
C. 112
D. 118
E. 120

multiply(const_100, divide(subtract(subtract(1, divide(1, const_100)), divide(36, 80)), divide(36, 80)))

Explanation: "let the market price of each pen be $ 1 then , cost price of 80 pens = $ 36 selling price of 80 pens = 99 % of $ 80 = $ 79.20 profit % = ( ( 43.20 * 100 ) / 36 ) % = 120 % answer e ) 120"


Question: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 66 ?

<gadget id="calculator">66 - 2</gadget>
<output>64</output>

<gadget id="calculator">64 / 4</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 11
B. 12
C. 13
D. 16
E. 17

Explanation: "four wheeler = 16 * 4 = 64 ( max ) 2 wheel = 1 so no of 4 wheeler = 16 answer : d"


Question: a train running at the speed of 27 km / hr crosses a post in 20 seconds . what is the length of the train ?

<gadget id="calculator">27 * 1_000</gadget>
<output>27_000</output>

<gadget id="calculator">27_000 / 3_600</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">(15/2) * 20</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 200
B. 150
C. 300
D. 175
E. 250

multiply(divide(multiply(27, const_1000), const_3600), 20)

Explanation: "speed = ( 27 x 5 / 18 ) = 7.5 m / sec . length of the train = ( speed x time ) . length of the train = 7.5 x 20 m = 150 m . answer : b"


Question: what is the rate percent when the simple interest on rs . 800 amount to rs . 128 in 4 years ?

<gadget id="calculator">100 * 128</gadget>
<output>12_800</output>

<gadget id="calculator">800 * 4</gadget>
<output>3_200</output>

<gadget id="calculator">12_800 / 3_200</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 5 %
B. 3 %
C. 4 %
D. 9 %
E. 1 %

divide(multiply(const_100, 128), multiply(800, 4))

Explanation: "128 = ( 800 * 4 * r ) / 100 r = 4 % answer : c"


Question: an error 1 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :

<gadget id="calculator">100 + 1</gadget>
<output>101</output>

<gadget id="calculator">101 ** 2</gadget>
<output>10_201</output>

<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>

<gadget id="calculator">10_201 - 10_000</gadget>
<output>201</output>

<gadget id="calculator">201 * 100</gadget>
<output>20_100</output>

<gadget id="calculator">20_100 / 10_000</gadget>
<output>201/100 = around 2.01</output>
<result>201/100 = around 2.01</result>

Choices:
A. 2.01
B. 30.1
C. 3.01
D. 25.01
E. 4.05

divide(multiply(subtract(square_area(add(const_100, 1)), square_area(const_100)), const_100), square_area(const_100))

Explanation: "explanation : 100 cm is read as 101 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 101 × 101 ) cm 2 = 10609 ( a 2 - a 1 ) = 10201 - 10000 = 201 = > 201 / 10000 * 100 = 2.01 answer : a"


Question: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 60 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .

<gadget id="calculator">90 * 5</gadget>
<output>450</output>

<gadget id="calculator">5 * 60</gadget>
<output>300</output>

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

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

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

Choices:
A. 22
B. 27
C. 15
D. 99
E. 21

divide(subtract(multiply(90, 5), multiply(5, 60)), subtract(90, 80))

Explanation: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 60 ) = 90 ( x - 5 ) 150 = 10 x = > x = 15 . answer : c"


Question: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio w of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?

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

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

<gadget id="calculator">2 / (4/3)</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>

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

divide(const_2, add(const_1, divide(const_1, const_3)))

Explanation: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio w of ann ' s time to bob ' s time is 3 : 2 . answer : b ."


Question: find the value of 72515 x 9999 = m ?

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>

<gadget id="calculator">9_995 * 72_515</gadget>
<output>724_787_425</output>
<result>724_787_425</result>

Choices:
A. 345434667
B. 246465757
C. 465767867
D. 725077485
E. 645354643

Explanation: "72515 x 9999 = 72515 x ( 10000 - 1 ) = 72515 x 10000 - 72515 x 1 = 725150000 - 72515 = 725077485 d"


Question: a can give b 50 meters start and c 200 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 - 200</gadget>
<output>800</output>

<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>

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

<gadget id="calculator">800_000 / 950</gadget>
<output>16_000/19 = around 842.105263</output>

<gadget id="calculator">1_000 - (16_000/19)</gadget>
<output>3_000/19 = around 157.894737</output>
<result>3_000/19 = around 157.894737</result>

Choices:
A. 157.89
B. 157.13
C. 157.22
D. 111.0
E. 111.12

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 50)))

Explanation: "a runs 1000 m while b runs 950 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 950 = 842.10 m . b can give c = 1000 - 842.10 = 157.89 m . answer : a"


Question: the present population of a town is 1240 . population increase rate is 4 % p . a . find the population of town after 1 years ?

<gadget id="calculator">1_240 * 4</gadget>
<output>4_960</output>

<gadget id="calculator">4_960 / 100</gadget>
<output>248/5 = around 49.6</output>

<gadget id="calculator">1_240 + (248/5)</gadget>
<output>6_448/5 = around 1_289.6</output>
<result>6_448/5 = around 1_289.6</result>

Choices:
A. 990
B. 1215
C. 1345
D. 1142
E. 1290

add(1240, divide(multiply(1240, 4), const_100))

Explanation: "p = 1240 r = 4 % required population of town = p * ( 1 + r / 100 ) ^ t = 1240 * ( 1 + 4 / 100 ) = 1240 * ( 26 / 25 ) = 1290 ( approximately ) answer is e"


Question: sandy bought 65 books for $ 1080 from one shop and 55 books for $ 840 from another shop . what is the average price that sandy paid per book ?

<gadget id="calculator">1_080 + 840</gadget>
<output>1_920</output>

<gadget id="calculator">65 + 55</gadget>
<output>120</output>

<gadget id="calculator">1_920 / 120</gadget>
<output>16</output>
<result>16</result>

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

Explanation: "average price per book = ( 1080 + 840 ) / ( 65 + 55 ) = 1920 / 120 = $ 16 the answer is b ."


Question: a merchant marks goods up by 80 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 35 % . what % discount did the merchant offer ?

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

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

<gadget id="calculator">(9/5) - 1</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">(4/5) - (7/20)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(9/20) / (9/5)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 20 %
B. 25 %
C. 30 %
D. 35 %
E. 40 %

multiply(divide(subtract(subtract(add(const_1, divide(80, const_100)), const_1), divide(35, const_100)), add(const_1, divide(80, const_100))), const_100)

Explanation: "let p be the original price of the goods and let x be the rate after the markup . ( 1.8 p ) * x = 1.35 p x = 1.35 / 1.8 = 0.75 which is a discount of 25 % . the answer is b ."


Question: the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm . what was the actual average height of the students in the class ?

<gadget id="calculator">20 * 175</gadget>
<output>3_500</output>

<gadget id="calculator">151 - 136</gadget>
<output>15</output>

<gadget id="calculator">3_500 - 15</gadget>
<output>3_485</output>

<gadget id="calculator">3_485 / 20</gadget>
<output>697/4 = around 174.25</output>
<result>697/4 = around 174.25</result>

Choices:
A. 174.75 cm
B. 174.25 cm
C. 173.75 cm
D. 173.25 cm
E. 172.75 cm

divide(subtract(multiply(20, 175), subtract(151, 136)), 20)

Explanation: the total height was 15 cm too much . the average height should be reduced by 15 cm / 20 = 0.75 cm the answer is b .


Question: the cost price of a radio is rs . 3300 and it was sold for rs . 1230 , find the loss % ?

<gadget id="calculator">3_300 - 1_230</gadget>
<output>2_070</output>

<gadget id="calculator">2_070 / 3_300</gadget>
<output>69/110 = around 0.627273</output>

<gadget id="calculator">(69/110) * 100</gadget>
<output>690/11 = around 62.727273</output>
<result>690/11 = around 62.727273</result>

Choices:
A. 62.7 %
B. 65 %
C. 88 %
D. 65 %
E. 62 %

multiply(divide(subtract(3300, 1230), 3300), const_100)

Explanation: "3300 - - - - 2070 100 - - - - ? = > 62.7 % answer : a"


Question: at what rate percent per annum will the simple interest on a sum of money be 3 / 5 of the amount in 10 years ?

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

<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>

<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6 %
B. 7 %
C. 9 %
D. 3 %
E. 1 %

divide(multiply(divide(3, 5), const_100), 10)

Explanation: "let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 3 x ) / ( x * 5 * 10 ) = 6 % answer : a"


Question: working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 2 days ?

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

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

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

Choices:
A. 11
B. 13
C. 15
D. 18
E. 20

Explanation: "the rate of 5 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 5 * ( x / 4 ) = x / 20 units per day ; now , again as { time } * { combined rate } = { job done } then 2 * ( m * x / 20 ) = 2 x - - > m = 20 . answer : e ."


Question: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many litres of tomato puree will be obtained from 20 litres of tomato juice ?

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

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

<gadget id="calculator">(1/10) * 20</gadget>
<output>2</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">2 / (4/5)</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>

Choices:
A. 2 litres
B. 2.4 litres
C. 2.5 litres
D. 6 litres
E. 4 litres

divide(multiply(divide(subtract(const_100, 90), const_100), 20), divide(subtract(const_100, 20), const_100))

Explanation: "tomato juice has 90 % water and 10 % tomato tomato puree has 20 % water and 80 % tomato so 20 liter of tomato juice has 20 * 90 / 100 = 18 liters of water and 2 liters of tomato . as tomato puree has 80 % content of tomato , so 2 liters of tomato from 20 liter juice corresponds to 80 % so tomato purees that can be obtained = 100 * 2 / 80 = 2.5 answer : c"


Question: a seller of used cars has 12 cars to sell and each of his clients selected 4 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?

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

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

Choices:
A. 9
B. 10
C. 12
D. 14
E. 16

Explanation: "ifno caris selected more than once then the number of clients = 12 / 4 = 3 but since every car is being selected three times so no . of clients must be thrice as well = 3 * 3 = 9 answer : option a"


Question: set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 62 and 110 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?

<gadget id="calculator">62 - 2</gadget>
<output>60</output>

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

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

<gadget id="calculator">24 + 1</gadget>
<output>25</output>

<gadget id="calculator">60 * 25</gadget>
<output>1_500</output>
<result>1_500</result>

Choices:
A. 1500
B. 3100
C. 4400
D. 6200
E. 7400

multiply(subtract(62, 2), add(divide(subtract(50, 2), const_2), const_1))

Explanation: "each term in set b is 60 more than the corresponding term in set a . the difference of the sums = 25 * 60 = 1500 . the answer is a ."


Question: the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , then the value of x is :

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

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

<gadget id="calculator">80 / 5</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 15
B. 16
C. 18
D. 25
E. 27

divide(multiply(20, const_4), add(const_4, const_1))

Explanation: "explanation : let the cost price of 1 article be z . so , the cost price of 20 article = 20 z - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 ) selling price of 20 articles = 20 z + 25 % of 20 z = 25 z = > selling price of 1 article = 25 z / 20 = ( 5 / 4 ) * z = > selling price of x articles = ( 5 / 4 ) * z * x - - - - - - - - - - - - - - - - - - - - - - - - - ( 2 ) given that selling price ( s . p . ) of x articles = cost price ( c . p . ) of 20 articles = > ( 5 / 4 ) * z * x = 20 z = > x = 16 answer : b"


Question: the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one fourth of the males and 3 / 4 th of the females in the class ?

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

<gadget id="calculator">360 / 5</gadget>
<output>72</output>

<gadget id="calculator">72 * 3</gadget>
<output>216</output>

<gadget id="calculator">216 * 3</gadget>
<output>648</output>

<gadget id="calculator">648 / 4</gadget>
<output>162</output>

<gadget id="calculator">72 * 2</gadget>
<output>144</output>

<gadget id="calculator">144 / 4</gadget>
<output>36</output>

<gadget id="calculator">162 + 36</gadget>
<output>198</output>
<result>198</result>

Choices:
A. 160 degree
B. 198 degree
C. 191 degree
D. 192 degree
E. 204 degree

add(divide(multiply(multiply(divide(const_360, add(2, 3)), 3), 3), 4), divide(multiply(divide(const_360, add(2, 3)), 2), const_4))

Explanation: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 / 4 of m = 2 x / 4 and 3 / 4 of f = 9 / 4 x . . total preferring that carrer = x / 2 + 9 x / 4 = 11 x / 4 now 5 x = 360 , so x = 360 / 5 = 72 . . so 72 * 11 / 4 = 198 ans 198 b


Question: at what price must an article costing rs . 47.50 be marked in order that after deducting 20 % from the list price . it may be sold at a profit of 25 % on the cost price ?

<gadget id="calculator">47.5 * 25</gadget>
<output>1_187.5</output>

<gadget id="calculator">1_187.5 / 100</gadget>
<output>11.875</output>

<gadget id="calculator">47.5 + 11.875</gadget>
<output>59.375</output>

<gadget id="calculator">59.375 * 100</gadget>
<output>5_937.5</output>

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

<gadget id="calculator">5_937.5 / 80</gadget>
<output>74.21875</output>
<result>74.21875</result>

Choices:
A. 62.5
B. 62.3
C. 62.7
D. 74.2
E. 62.9

divide(multiply(add(47.5, divide(multiply(47.5, 25), const_100)), const_100), subtract(const_100, 20))

Explanation: cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2 answer : d


Question: a mail handler needs 3 hours to sort the mail . his assistant takes 6 hours to sort the mail . how many hours will it take for both of them working together to sort the mail ?

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

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

<gadget id="calculator">(1/3) + (1/6)</gadget>
<output>1/2 = around 0.5</output>

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

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

inverse(add(divide(const_1, 3), divide(const_1, 6)))

Explanation: work hrs = ab / ( a + b ) = 18 / 9 = 2 answer is b


Question: a bag contains 7 black and 8 white balls . if two balls are drawn simultaneously , what is the probability that both are of the same color is ?

<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>

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

<gadget id="calculator">factorial(6)</gadget>
<output>720</output>

<gadget id="calculator">40_320 / 720</gadget>
<output>56</output>

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

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

<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>

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

<gadget id="calculator">factorial(5)</gadget>
<output>120</output>

<gadget id="calculator">5_040 / 120</gadget>
<output>42</output>

<gadget id="calculator">42 / 2</gadget>
<output>21</output>

<gadget id="calculator">28 + 21</gadget>
<output>49</output>

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

<gadget id="calculator">factorial(15)</gadget>
<output>1_307_674_368_000</output>

<gadget id="calculator">15 - 2</gadget>
<output>13</output>

<gadget id="calculator">factorial(13)</gadget>
<output>6_227_020_800</output>

<gadget id="calculator">1_307_674_368_000 / 6_227_020_800</gadget>
<output>210</output>

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

<gadget id="calculator">49 / 105</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>

Choices:
A. 1 / 2
B. 1 / 3
C. 2 / 3
D. 3 / 5
E. 7 / 15

divide(add(divide(divide(factorial(8), factorial(subtract(8, const_2))), factorial(const_2)), divide(divide(factorial(7), factorial(subtract(7, const_2))), factorial(const_2))), divide(divide(factorial(add(7, 8)), factorial(subtract(add(7, 8), const_2))), factorial(const_2)))

Explanation: drawing two balls of same color from seven black balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer is e


Question: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 240 responses are needed , what is the minimum number of questionnaires that should be mailed ?

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

<gadget id="calculator">240 / (3/5)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 400
B. 500
C. 600
D. 700
E. 800

Explanation: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 240 x = 400 the answer is a ."


Question: a does half as much work as b in 3 - fourth of the time . if together they take 18 days to complete the work , how much time shall b take to do it ?

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

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

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

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

divide(multiply(18, add(3, const_2)), 3)

Explanation: explanation : let ‘ x ’ be the number of days taken by b alone to finish the whole work then , a alone will finish the whole work in 3 x / 4 × 2 days = 3 x / 2 days . then , working together , 3 x / 2 × x / 3 x / 2 + x = 18 days 3 x × x / 5 x = 18 3 x / 5 = 18 therefore , the number of days taken by b = x = 18 × 5 / 3 = 30 days . answer : option a


Question: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 56 , find the sum of money ?

<gadget id="calculator">56 / 40</gadget>
<output>7/5 = around 1.4</output>

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

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

<gadget id="calculator">(7/5) * 205</gadget>
<output>287</output>
<result>287</result>

Choices:
A. 288
B. 287
C. 72
D. 205
E. 267

multiply(divide(56, 40), add(add(const_100, 65), 40))

Explanation: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 56 41 - - - - ? = > rs . 287 answer : b"


Question: in what time will a train 80 m long cross an electric pole , it its speed be 144 km / hr ?

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

<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>

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

Choices:
A. 2.0 sec
B. 2.8 sec
C. 7.5 sec
D. 2.3 sec
E. 1.5 sec

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 80 / 40 = 2.0 sec . answer : a"


Question: john purchased 1375 large bottles at $ 1.75 per bottle and 690 small bottles at $ 1.35 per bottle . what was the approximate average price paid per bottle ?

<gadget id="calculator">1_375 * 1.75</gadget>
<output>2_406.25</output>

<gadget id="calculator">690 * 1.35</gadget>
<output>931.5</output>

<gadget id="calculator">2_406.25 + 931.5</gadget>
<output>3_337.75</output>

<gadget id="calculator">1_375 + 690</gadget>
<output>2_065</output>

<gadget id="calculator">3_337.75 / 2_065</gadget>
<output>1.616344</output>
<result>1.616344</result>

Choices:
A. $ 1.62
B. $ 1.64
C. $ 1.68
D. $ 1.72
E. $ 1.76

Explanation: "( 1375 * 1.75 + 690 * 1.35 ) / ( 1375 + 690 ) = ~ 1.62 option ( a )"


Question: an investor deposited $ 5,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?

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

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

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

<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>

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

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

<gadget id="calculator">(1/50) + 1</gadget>
<output>51/50 = around 1.02</output>

<gadget id="calculator">(51/50) ** 2</gadget>
<output>2_601/2_500 = around 1.0404</output>

<gadget id="calculator">5_000 * (2_601/2_500)</gadget>
<output>5_202</output>
<result>5_202</result>

Choices:
A. $ 5050
B. $ 5101
C. $ 5202
D. $ 5303
E. $ 5404

multiply(multiply(multiply(add(const_2, const_3), const_100), multiply(add(const_2, const_3), const_2)), power(add(divide(divide(8, const_4), const_100), const_1), const_2))

Explanation: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 5,000 ) = $ 5202 the answer is c ."


Question: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 11 . what could be the ratio of cats to dogs in the pet store ?

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

<gadget id="calculator">44 + 11</gadget>
<output>55</output>

<gadget id="calculator">44 / 55</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>

Choices:
A. 1 : 3
B. 1 : 4
C. 1 : 5
D. 44 : 55
E. 4 : 6

divide(multiply(11, const_4), add(multiply(11, const_4), 11))

Explanation: say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 11 - - > x ( a - b ) = 11 . since 11 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 11 . the above implies that either x = 1 and ( a - b ) = 11 or x = 11 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11 . for the original question only option which fits is e , 4 : 5 . cats = 11 * 4 = 44 and dogs = 11 * 5 = 55 . answer : d .


Question: john makes $ 60 a week from his job . he earns a raise and now makes $ 90 a week . what is the % increase ?

<gadget id="calculator">90 - 60</gadget>
<output>30</output>

<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 16 %
B. 50 %
C. 17 %
D. 17.61 %
E. 17.56 %

multiply(divide(subtract(90, 60), 60), const_100)

Explanation: "increase = ( 30 / 60 ) * 100 = ( 3 / 6 ) * 100 = 50 % . b"


Question: x can finish a work in 21 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?

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

<gadget id="calculator">10 * (1/15)</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">1 / 21</gadget>
<output>1/21 = around 0.047619</output>

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

Choices:
A. 3
B. 5
C. 7
D. 8
E. 9

divide(subtract(const_1, multiply(10, divide(const_1, 15))), divide(const_1, 21))

Explanation: "work done by x in 1 day = 1 / 21 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 21 ) = 7 c"


Question: a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 50 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .

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

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

<gadget id="calculator">225 / (3/2)</gadget>
<output>150</output>

<gadget id="calculator">25 + 100</gadget>
<output>125</output>

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">150 / (5/4)</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 237
B. 126
C. 971
D. 611
E. 120

divide(divide(225, divide(add(const_100, 50), const_100)), divide(add(25, const_100), const_100))

Explanation: explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 50 % profit = 125 x ( 1 + 50 / 100 ) = 187.5 cp - - - sp 100 - - - 187.5 x - - - 225 cp = 225 x 100 / 187.5 = 120 answer : e


Question: the average marks of a class of 12 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?

<gadget id="calculator">12 * 40</gadget>
<output>480</output>

<gadget id="calculator">28 * 60</gadget>
<output>1_680</output>

<gadget id="calculator">480 + 1_680</gadget>
<output>2_160</output>

<gadget id="calculator">12 + 28</gadget>
<output>40</output>

<gadget id="calculator">2_160 / 40</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 52.2
B. 59.5
C. 52.8
D. 52.5
E. 54.0

divide(add(multiply(12, 40), multiply(28, 60)), add(12, 28))

Explanation: "sum of the marks for the class of 12 students = 12 * 40 = 480 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 40 students = 480 + 1680 = 2160 average marks of all the students = 2160 / 40 = 54 answer : e"


Question: if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 20 percent grape juice then what percent of the resulting mixture is grape juice ?

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

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

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

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

<gadget id="calculator">18 / 50</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) * 100</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 14 %
B. 25 %
C. 28 %
D. 36 %
E. 50 %

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

Explanation: official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.20 = 8 gallons of grape juice . 40 × 0.80 = 32 gallons of other components . if we add 10 gallons of grape juice , we will end up with 18 gallons of grape juice and 32 gallons of other components , and we will have a total of 50 gallons of the mixture . so 18 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 18 / 50 = 36 / 100 = 36 % . the correct answer is choice ( d )


Question: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 5 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?

<gadget id="calculator">15 * 21</gadget>
<output>315</output>

<gadget id="calculator">315 * 8</gadget>
<output>2_520</output>

<gadget id="calculator">21 * 5</gadget>
<output>105</output>

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

<gadget id="calculator">105 * (2/3)</gadget>
<output>70</output>

<gadget id="calculator">2_520 / 70</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 30
B. 20
C. 16
D. 26
E. 36

divide(multiply(multiply(15, 21), 8), multiply(multiply(21, 5), divide(2, 3)))

Explanation: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 6 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 5 * ( 2 / 3 ) ) days = > 36 days answer : e"


Question: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio e of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?

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

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

<gadget id="calculator">2 / (4/3)</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>

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

divide(const_2, add(const_1, divide(const_1, const_3)))

Explanation: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio e of ann ' s time to bob ' s time is 3 : 2 . answer : b ."


Question: as a treat for her two crying children , a mother runs to the freezer in which she has 4 cherry ice pops , 3 orange ice pops , and 4 lemon - lime ice pops . if she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one invariably being jealous of the other and getting even more upset , what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?

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

<gadget id="calculator">100 - 1</gadget>
<output>99</output>

<gadget id="calculator">1 / 99</gadget>
<output>1/99 = around 0.010101</output>
<result>1/99 = around 0.010101</result>

Choices:
A. 1 / 99
B. 1 / 6
C. 5 / 18
D. 13 / 18
E. 5 / 6

divide(subtract(4, 3), subtract(const_100, subtract(4, 3)))

Explanation: probability of not getting the same flavor - > fouvarable - > cherry - orange [ 4 c 1 * 3 c 1 [ or simply 4 * 3 ] or cherry - lemon [ 4 * 4 ] or orange - lemon [ 3 * 4 ] prob = ( 4 * 3 + 4 * 4 + 3 * 4 ) / 9 c 2 = 40 / 3960 = 1 / 99 answer - > a


Question: a and b together can complete a work in 12 days . a alone complete it in 20 days . if b does the work only for half a day daily , then in how many days a and b together will complete the work ?

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

Choices:
A. 110 days
B. 11 days
C. 15 days
D. 20 days
E. 17 days

Explanation: b ' s one day work = ( 1 / 12 - 1 / 20 ) = 1 / 30 . now , ( a + b ) ' s one day work = ( 1 / 20 + 1 / 60 ) = 1 / 15 . [ ∵ b work for half day only ] . so , a and b together will complete the work in 15 days . correct answer : ` ` c ' ' .


Question: in a fuel station the service costs $ 1.65 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?

<gadget id="calculator">0.65 * 55</gadget>
<output>35.75</output>

<gadget id="calculator">35.75 * 12</gadget>
<output>429</output>
<result>429</result>

Choices:
A. 320 $
B. 380 $
C. 420 $
D. 448.8 $
E. 480 $

Explanation: "total cost = ( 1.65 * 12 ) + ( 0.65 * 12 * 55 ) = 19.8 + 429 = > 448.8 hence answer will be ( d )"


Question: a certain rectangular crate measures 6 feet by 8 feet by 10 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?

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

<gadget id="calculator">pi * (4 ** 2) * 6</gadget>
<output>96*pi = around 301.592895</output>

<gadget id="calculator">pi * 6</gadget>
<output>6*pi = around 18.849556</output>

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

<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<result>4</result>

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

sqrt(divide(volume_cylinder(divide(8, const_2), 6), multiply(const_pi, 6)))

Explanation: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 8 x 10 i . e . of radius 8 / 2 = 4 b"


Question: the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 950 per sq . metre .

<gadget id="calculator">5.5 * 4</gadget>
<output>22</output>

<gadget id="calculator">950 * 22</gadget>
<output>20_900</output>
<result>20_900</result>

Choices:
A. s . 20,550
B. s . 15,600
C. s . 20,900
D. s . 17,600
E. s . 17,900

Explanation: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 950 ã — 22 ) = rs . 20900 answer : option c"


Question: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 136 m length ?

<gadget id="calculator">110 + 136</gadget>
<output>246</output>

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

<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>

<gadget id="calculator">246 / 20</gadget>
<output>123/10 = around 12.3</output>
<result>123/10 = around 12.3</result>

Choices:
A. 82.1 sec .
B. 12.3 sec
C. 19.1 sec .
D. 17.1 sec .
E. 42.1 sec .

Explanation: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 136 = 246 m . required time = 246 / 20 = 12.3 sec . answer : b"


Question: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability that jane will be on the same committee as albert ?

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

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

<gadget id="calculator">binomial(6, 3)</gadget>
<output>20</output>

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

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

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

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

Choices:
A. 12 %
B. 20 %
C. 33 %
D. 40 %
E. 50 %

multiply(divide(multiply(choose(const_4, const_1), const_2), choose(6, 3)), multiply(multiply(const_5, const_5), const_4))

Explanation: total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability = ( 8 / 20 ) * 100 = 40 % . ans : : d


Question: a group of 7 teenagers recently visited the japanese restaurant . the total bill for the meal , including 20 % gratuity , came to $ 840 . on average , how much did the meal of each individual cost before gratuity ?

<gadget id="calculator">840 / 20</gadget>
<output>42</output>

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

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

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

Choices:
A. $ 160
B. $ 96
C. $ 90
D. $ 10
E. $ 55

subtract(subtract(subtract(divide(840, 20), 20), const_10), const_2)

Explanation: 7 teenagers - so total 7 people the bill $ 840 includes 20 % gratuity . . . so the actual cost of dinner was $ 700 now , the cost per person will be $ 700 / 7 which is $ 10 option d


Question: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

<gadget id="calculator">75 - 68</gadget>
<output>7</output>

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

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

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

Choices:
A. 20
B. 30
C. 35
D. 40
E. 55

divide(subtract(75, 68), subtract(const_1, divide(65, const_100)))

Explanation: "total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 65 % = 35 % of books that were loaned out are not returned . now , there are 68 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.35 = 7 - - > { loaned out } = 20 . answer : a ."


Question: if 7 ^ q is a factor of the product of the integers from 1 to 100 , inclusive , what is the largest value of q ?

<gadget id="calculator">100 / 7</gadget>
<output>100/7 = around 14.285714</output>

<gadget id="calculator">(100/7) / 7</gadget>
<output>100/49 = around 2.040816</output>

<gadget id="calculator">(100/7) + (100/49)</gadget>
<output>800/49 = around 16.326531</output>
<result>800/49 = around 16.326531</result>

Choices:
A. 12
B. 13
C. 14
D. 15
E. 16

add(divide(100, 7), divide(divide(100, 7), 7))

Explanation: so the question just means that we have to find all the multiples q of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e


Question: susan drove an average speed of 30 miles per hour for the first 60 miles of a tripthen at a average speed of 60 miles / hr for the remaining 30 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip

<gadget id="calculator">60 + 30</gadget>
<output>90</output>

<gadget id="calculator">60 / 30</gadget>
<output>2</output>

<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">90 / (5/2)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 35
B. 36
C. 45
D. 50
E. 55

Explanation: "avg . speed = total distance / total time total distance = 90 miles total time = 60 / 30 + 30 / 60 = 5 / 2 avg . speed = 36 answer - b"


Question: a 415 m long train is running at 63 km / hr . in how much time will it cross a tunnel 285 m long ?

<gadget id="calculator">415 + 285</gadget>
<output>700</output>

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

<gadget id="calculator">63 * (5/18)</gadget>
<output>35/2 = around 17.5</output>

<gadget id="calculator">700 / (35/2)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 25
B. 35
C. 45
D. 60
E. 40

Explanation: "speed of the train = ( 63 * 5 / 18 ) m / sec = 35 / 2 m / sec . distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the tunnel = 415 + 285 = 700 m time = ( 700 / 35 / 2 ) = 40 sec answer : e"


Question: the bankers discount of a certain sum of money is rs . 288 and the true discount on the same sum for the same time is rs . 240 . the sum due is :

<gadget id="calculator">240 * 288</gadget>
<output>69_120</output>

<gadget id="calculator">288 - 240</gadget>
<output>48</output>

<gadget id="calculator">69_120 / 48</gadget>
<output>1_440</output>
<result>1_440</result>

Choices:
A. 1400
B. 1420
C. 1440
D. 1460
E. 1480

divide(multiply(240, 288), subtract(288, 240))

Explanation: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 288 * 240 ) / 288 - 240 ; 1440 answer : c"


Question: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 32 % . what would have been the percentage of profit earned if no discount was offered ?

<gadget id="calculator">100 + 32</gadget>
<output>132</output>

<gadget id="calculator">132 * 100</gadget>
<output>13_200</output>

<gadget id="calculator">100 - 4</gadget>
<output>96</output>

<gadget id="calculator">13_200 / 96</gadget>
<output>275/2 = around 137.5</output>

<gadget id="calculator">(275/2) - 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>

Choices:
A. 24.5
B. 28.5
C. 30.5
D. 32.5
E. 37.5

subtract(divide(multiply(add(const_100, 32), const_100), subtract(const_100, 4)), const_100)

Explanation: let c . p . be rs . 100 . then , s . p . = rs . 132 let marked price be rs . x . then , 96 / 100 x = 132 x = 13200 / 96 = rs . 137.5 now , s . p . = rs . 137.5 , c . p . = rs . 100 profit % = 37.5 % . answer : e


Question: the volume of the sphere qq is ( dfrac { 37 } { 64 } % ) less than the volume of sphere pp and the volume of sphere rr is ( dfrac { 19 } { 27 } % ) less than that of sphere qq . by what is the surface areaof sphere rr less than the surfacearea of sphere pp ?

Choices:
A. 50 %
B. 60 %
C. 75 %
D. 80 %
E. 89 %

subtract(const_100, multiply(multiply(multiply(divide(37, 64), divide(19, 27)), divide(37, 64)), const_100))

Explanation: let the volume of sphere pp be 64 parts . therefore volume of sphere qq = 64 − 3764 % = 64 − 3764 % of 6464 = 64 − 37 = 27 = 64 − 37 = 27 parts . the volume of rr = 27 − 1927 × 27 = 27 − 1927 × 27 = 27 − 19 = 8 = 27 − 19 = 8 parts . volume ratio : = p : q : r = 64 : 27 : 8 = p : q : r = 64 : 27 : 8 radius ratio : = p : q : r = 4 : 3 : 2 = p : q : r = 4 : 3 : 2 the surface area will be 16 : 9 : 516 : 9 : 5 surface area of rr is less than the surface area of sphere pp 16 k − 4 k = 12 k 16 k − 4 k = 12 k now , = 12 k 16 k × 100 = 12 k 16 k × 100 = 75 % = 75 % thus surface area of sphere rr is less than the surface area of sphere p by 75 % c


Question: what will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of rs . 10 per square meter ?

<gadget id="calculator">340 + 4</gadget>
<output>344</output>

<gadget id="calculator">344 * 10</gadget>
<output>3_440</output>
<result>3_440</result>

Choices:
A. rs . 3430
B. rs . 3440
C. rs . 3450
D. rs . 3460
E. rs . 3490

Explanation: explanation : in this question , we are having perimeter . we know perimeter = 2 ( l + b ) , right so , 2 ( l + b ) = 340 as we have to make 1 meter boundary around this , so area of boundary = ( ( l + 2 ) + ( b + 2 ) - lb ) = 2 ( l + b ) + 4 = 340 + 4 = 344 so required cost will be = 344 * 10 = 3440 answer : option b


Question: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 18 days . in how many days b alone can do the work ?

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

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

<gadget id="calculator">5 * (1/15)</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">(1/18) * (2/3)</gadget>
<output>1/27 = around 0.037037</output>

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

Choices:
A. 5 days
B. 7 days
C. 27 days
D. 9 days
E. 10 days

inverse(multiply(inverse(18), subtract(const_1, multiply(5, inverse(15)))))

Explanation: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 18 x = 27 days answer : option c"


Question: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 25 and 24 . the larger of the two numbers is

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

Choices:
A. 276
B. 799
C. 712
D. 750
E. none

Explanation: "solution clearly , the numbers are ( 30 x 25 ) and ( 30 x 24 ) . larger number = ( 30 x 25 ) = 750 . answer d"


Question: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 15 % profit ?

<gadget id="calculator">30 * 11.5</gadget>
<output>345</output>

<gadget id="calculator">20 * 14.25</gadget>
<output>285</output>

<gadget id="calculator">345 + 285</gadget>
<output>630</output>

<gadget id="calculator">630 / 100</gadget>
<output>63/10 = around 6.3</output>

<gadget id="calculator">(63/10) * 15</gadget>
<output>189/2 = around 94.5</output>

<gadget id="calculator">630 + (189/2)</gadget>
<output>1_449/2 = around 724.5</output>

<gadget id="calculator">30 + 20</gadget>
<output>50</output>

<gadget id="calculator">(1_449/2) / 50</gadget>
<output>1_449/100 = around 14.49</output>
<result>1_449/100 = around 14.49</result>

Choices:
A. 14.49
B. 16.33
C. 16.35
D. 16.3
E. 16.32

Explanation: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 115 % of rs . 630 = 115 / 100 * 630 = rs . 724.5 s . p . per kg = 724.5 / 50 = 14.49 a"


Question: one pipe can fill a tank four times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in :

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

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

Choices:
A. 180 min
B. 144 min .
C. 126 min
D. 114 min
E. 124 min

Explanation: explanation : let time taken by the faster pipe to fill the tank = x minutes . then , time taken by the slower pipe to fill the tank = 4 x minutes . time taken by both pipes together to fill the tank = x x 4 x / x + 4 x = 4 x / 5 4 x / 5 = 36 ⇒ x = 45 time taken by the slower pipe to fill the tank = 4 x = 180 minutes . answer : option a


Question: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 8 % . what is the approximate interest he pays annually ?

Choices:
A. 1500
B. 1750
C. 2000
D. 3500
E. 2500

subtract(multiply(multiply(const_100, const_100), power(add(const_1, divide(8, const_100)), const_4)), multiply(const_100, const_100))

Explanation: "an easy way too attempt this is by approximation : for the first quarter , he pays 8 % of 10,000 which is $ 800 . so for the four quarters in the year , he will approximately play 800 * 4 = 3200 over the entire year . because of compound interest it will be more than 3200 . approx . option d is correct . answer : d"


Question: a patient is given exactly 750 milliliters of a mixture of two medications daily . medication a contains 40 % pain killer and medication b contains 20 % pain killer . if the patient receives exactly 215 milliliters of pain killer daily , how many milliliters of medication b are in the mixture ?

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 750</gadget>
<output>300</output>

<gadget id="calculator">300 - 215</gadget>
<output>85</output>

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

<gadget id="calculator">(2/5) - (1/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">85 / (1/5)</gadget>
<output>425</output>
<result>425</result>

Choices:
A. 150
B. 225
C. 325
D. 425
E. 550

divide(subtract(multiply(divide(40, const_100), 750), 215), subtract(divide(40, const_100), divide(20, const_100)))

Explanation: let there be a milliliters of medication a and b milliliters of medication b a + b = 750 - - 1 medication a contains 40 % pain killer and medication b contains 20 % pain killer . ( 40 / 100 ) * a + ( 20 / 100 ) * b = 215 = > ( 2 / 5 ) * a + ( 1 / 5 ) * b = 215 multiplying by 5 , we get 2 a + b = 1075 - - 2 equation 2 - equation 1 , we get a = 325 b = 425 answer d


Question: let s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . find the sum of all elements in s ?

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

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

<gadget id="calculator">500 + 1_000</gadget>
<output>1_500</output>

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

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

<gadget id="calculator">80 + 4</gadget>
<output>84</output>

<gadget id="calculator">1_500 + 84</gadget>
<output>1_584</output>
<result>1_584</result>

Choices:
A. 1584
B. 7640
C. 5640
D. 7240
E. 6780

add(add(multiply(add(1, const_4), const_100), const_1000), add(multiply(multiply(const_2, const_4), const_10), const_4))

Explanation: s is a set of all natural numbers less than 120 such that hcf of any element in s and 120 is 1 . such numbers are , s = { 1 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 } sum of s = 1584 . answer : a


Question: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 5 km ?

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

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

Choices:
A. 2.0
B. 2.5
C. 3.0
D. 3.5
E. 4.0

Explanation: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 5 / 2 = 2.5 hours . the answer is b ."


Question: if a tire rotates at 400 revolutions per minute when the car is traveling 48 km / h , what is the circumference of the tire ?

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

<gadget id="calculator">6 * 10</gadget>
<output>60</output>

<gadget id="calculator">60 * 400</gadget>
<output>24_000</output>

<gadget id="calculator">48 / 24_000</gadget>
<output>1/500 = around 0.002</output>

<gadget id="calculator">(1/500) * 1_000</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 7 meters
B. 9 meters
C. 8 meters
D. 2 meters
E. 3 meters

multiply(divide(48, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)

Explanation: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 48,000 m : c is the circumference c = 2 meters correct answer d"


Question: a snooker tournament charges $ 45.00 for vip seats and $ 20.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?

<gadget id="calculator">7_500 / 20</gadget>
<output>375</output>

<gadget id="calculator">375 - 320</gadget>
<output>55</output>

<gadget id="calculator">45 / 20</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">(9/4) - 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">55 / (5/4)</gadget>
<output>44</output>

<gadget id="calculator">320 - 44</gadget>
<output>276</output>
<result>276</result>

Choices:
A. 200
B. 276
C. 230
D. 240
E. 250

subtract(320, divide(subtract(divide(7500, 20), 320), subtract(divide(45, 20), const_1)))

Explanation: let no of sits in vip enclosure is x then x * 45 + 20 ( 320 - x ) = 7500 or 25 x = 7500 - 6400 , x = 1100 / 25 = 44 vip = 44 general 320 - 44 = 276 b


Question: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1160 ?

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

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

<gadget id="calculator">18 / 5</gadget>
<output>18/5 = around 3.6</output>

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

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">(9/50) + 1</gadget>
<output>59/50 = around 1.18</output>

<gadget id="calculator">1_160 / (59/50)</gadget>
<output>58_000/59 = around 983.050847</output>
<result>58_000/59 = around 983.050847</result>

Choices:
A. rs . 1000
B. rs . 1100
C. rs . 1010
D. rs . 10000
E. none of these

divide(1160, add(divide(multiply(divide(add(multiply(3, 5), 3), 5), 5), const_100), const_1))

Explanation: "explanation : 1160 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1000 answer : option a"


Question: 4 balls of different colors are to be placed in 3 different boxes such that any box contains at least 1 ball . what is the maximum number of different ways in which this can be done ?

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

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

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

<gadget id="calculator">24 * 6</gadget>
<output>144</output>

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

<gadget id="calculator">144 + 36</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 60
B. 90
C. 120
D. 150
E. 180

add(multiply(multiply(multiply(4, 3), const_2), multiply(3, const_2)), multiply(multiply(3, const_2), multiply(3, const_2)))

Explanation: since the balls are all of different colors , let ' s permute them and then decide how many balls we put in each box . for example , arrange in a row the balls , then decide : two balls go into the first box , next two in the second box , and the last ball goes to the third box . since in each box there must be at least one ball , we have the possibilities of ( 2 , 2,1 ) , ( 2 , 1,2 ) , ( 1 , 2,2 ) or ( 3 , 1,1 ) , ( 1 , 3,1 ) , ( 1 , 1,3 ) balls in the three boxes . for the 2 , 2,1 type arrangements , we have [ 6 ! / ( 2 ! 2 ! 1 ! ) ] * 3 = 100 possibilities . inside a box , it does n ' t matter the order of the balls . for the 3 , 1,1 type arrangements , we have [ 6 ! / ( 3 ! 1 ! 1 ! ) ] * 3 = 80 possibilities . total of 100 + 80 = 180 possibilities . answer e .


Question: the length of the bridge , which a train 140 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?

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

<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>

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

<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>

<gadget id="calculator">375 - 140</gadget>
<output>235</output>
<result>235</result>

Choices:
A. 255
B. 267
C. 235
D. 277
E. 211

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 140)

Explanation: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 140 + x ) / 30 = 25 / 2 = > 2 ( 140 + x ) = 750 = > x = 235 m . answer : c"


Question: the average height of 35 boys in a class was calculated as 185 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 * 185</gadget>
<output>6_475</output>

<gadget id="calculator">6_475 - 166</gadget>
<output>6_309</output>

<gadget id="calculator">6_309 + 106</gadget>
<output>6_415</output>

<gadget id="calculator">6_415 / 35</gadget>
<output>1_283/7 = around 183.285714</output>

<gadget id="calculator">floor(1_283/7)</gadget>
<output>183</output>
<result>183</result>

Choices:
A. 187.89 cm
B. 183.29 cm
C. 123.98 cm
D. 149.98 cm
E. 146.89 cm

floor(divide(add(subtract(multiply(35, 185), 166), 106), 35))

Explanation: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 180 * 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 = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"


Question: whats the reminder when 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 is divided by 16

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

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

<gadget id="calculator">9 * 100</gadget>
<output>900</output>

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

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

<gadget id="calculator">500 * 10</gadget>
<output>5_000</output>

<gadget id="calculator">900 + 5_000</gadget>
<output>5_900</output>

<gadget id="calculator">12 + 5</gadget>
<output>17</output>

<gadget id="calculator">17 * 5</gadget>
<output>85</output>

<gadget id="calculator">5_900 + 85</gadget>
<output>5_985</output>

<gadget id="calculator">5_985 % 16</gadget>
<output>1</output>

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

Choices:
A. 1
B. 7 .
C. 2 .
D. 3
E. 9

add(multiply(const_4, const_2), reminder(add(add(multiply(subtract(const_10, const_1), const_100), multiply(multiply(add(const_3, const_2), const_100), const_10)), multiply(add(const_12, add(const_3, const_2)), add(const_3, const_2))), 16))

Explanation: a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 = 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 450,000 + 4,889 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 16 . 4889 / 16 gives remainder 9 . answer ( e )


Question: you enter a weight loss challenge game and manage to lose 12 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">1 - (3/25)</gadget>
<output>22/25 = around 0.88</output>

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

<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>

<gadget id="calculator">(22/25) * (51/50)</gadget>
<output>561/625 = around 0.8976</output>

<gadget id="calculator">1 - (561/625)</gadget>
<output>64/625 = around 0.1024</output>

<gadget id="calculator">(64/625) * 100</gadget>
<output>256/25 = around 10.24</output>
<result>256/25 = around 10.24</result>

Choices:
A. 10.24 %
B. 9.22 %
C. 9 %
D. 14 %
E. 12 %

multiply(subtract(const_1, multiply(subtract(const_1, divide(12, const_100)), add(const_1, divide(2, const_100)))), const_100)

Explanation: "( 100 % - 12 % ) * ( 100 % + 2 % ) = 0.88 * 1.02 = 10.24 % the weigh in records your weight loss at 10.24 % ! the answer is a"


Question: if 20 men can build a water fountain 56 metres long in 14 days , what length of a similar water fountain can be built by 35 men in 3 days ?

<gadget id="calculator">20 * 14</gadget>
<output>280</output>

<gadget id="calculator">56 / 280</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">35 * 3</gadget>
<output>105</output>

<gadget id="calculator">(1/5) * 105</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 21 m
B. 24 m
C. 27 m
D. 29 m
E. 30 m

multiply(divide(56, multiply(20, 14)), multiply(35, 3))

Explanation: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 14 : 3 : : 56 : x therefore ( 20 x 14 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 280 = 49 hence , the required length is 21 m . answer : a"


Question: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , r will receive

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

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

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

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

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

<gadget id="calculator">4_650 * (6/31)</gadget>
<output>900</output>
<result>900</result>

Choices:
A. 600
B. 700
C. 800
D. 900
E. none of these

multiply(4650, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 * ( 6 / 31 ) = 150 * 6 = 900 . answer : option d"


Question: the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years , the age of the 15 th student is

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

<gadget id="calculator">8 * 14</gadget>
<output>112</output>

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

<gadget id="calculator">112 + 96</gadget>
<output>208</output>

<gadget id="calculator">225 - 208</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 17
B. 12
C. 13
D. 14
E. 15

subtract(multiply(15, 15), add(multiply(8, 14), multiply(6, 16)))

Explanation: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 8 + 16 * 6 ) ] = 17 years . answer : a"


Question: a committee is reviewing a total of 40 x black - and - white films and 10 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) + 10</gadget>
<output>52/5 = around 10.4</output>

<gadget id="calculator">10 / (52/5)</gadget>
<output>25/26 = around 0.961538</output>
<result>25/26 = around 0.961538</result>

Choices:
A. 50 / 52
B. 55 / 52
C. 60 / 52
D. 40 / 52
E. 30 / 52

divide(10, add(divide(40, const_100), 10))

Explanation: "say x = y = 10 . in this case we would have : 40 x = 400 black - and - white films ; 10 y = 100 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 100 color films , thus total of 104 films were selected . color films thus compose 100 / 104 = 50 / 52 of the selected films . answer : a"


Question: if the cost price of 24 chocolates is equal to the selling price of 16 chocolates , the gain percent is :

<gadget id="calculator">24 - 16</gadget>
<output>8</output>

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

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

Choices:
A. 24 %
B. 8 %
C. 50 %
D. 40 %
E. none of these

divide(const_100, divide(16, subtract(24, 16)))

Explanation: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 16 chocolates = rs . 16 ; s . p . of 16 chocolates = rs . 24 . . ' . gain % = 8 * 100 / 16 = 50 % answer : c"


Question: a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . find out the number of days for which the remaining food will last .

<gadget id="calculator">25 + 10</gadget>
<output>35</output>

<gadget id="calculator">150 * 35</gadget>
<output>5_250</output>

<gadget id="calculator">150 - 25</gadget>
<output>125</output>

<gadget id="calculator">5_250 / 125</gadget>
<output>42</output>
<result>42</result>

Choices:
A. 44
B. 42
C. 40
D. 38
E. 36

divide(multiply(150, add(25, 10)), subtract(150, 25))

Explanation: explanation : given that fort had provision of food for 150 men for 45 days hence , after 10 days , the remaining food is sufficient for 150 men for 35 days remaining men after 10 days = 150 - 25 = 125 assume that after 10 days , the remaining food is sufficient for 125 men for x days more men , less days ( indirect proportion ) ( men ) 150 : 125 : : x : 35 ⇒ 150 × 35 = 125 x ⇒ 6 × 35 = 5 x ⇒ x = 6 × 7 = 42 i . e . , the remaining food is sufficient for 125 men for 42 days answer : option b


Question: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 14 and 15 . the larger of the two numbers is :

<gadget id="calculator">23 * 15</gadget>
<output>345</output>
<result>345</result>

Choices:
A. 338
B. 278
C. 345
D. 231
E. 121

Explanation: "clearly , the numbers are ( 23 * 14 ) and ( 23 * 15 ) . larger number = ( 23 * 15 ) = 345 . answer : c"


Question: during a given week a programmer spends 1 / 4 of his time preparing flow chart , 3 / 8 of his time coding and the rest of the time in debugging the programs . if he works 48 hours during the week , how many hours did he spend debugging the program .

<gadget id="calculator">48 * 3</gadget>
<output>144</output>

<gadget id="calculator">144 / 8</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 15 hrs
B. 16 hrs
C. 18 hrs
D. 19 hrs
E. 17 hrs

Explanation: programmer takes 1 / 4 * 48 = 12 hrs a week to make flowchrt same way . . . . . 18 hrs a week for codin . . . so . . . . for debugging = 48 - ( 12 + 18 ) = 18 hrs answer : c


Question: there is enough provisions for 600 men in an army camp for 25 days . if there were 250 men less , how long will the provision last ?

<gadget id="calculator">600 * 25</gadget>
<output>15_000</output>

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

Choices:
A. 10 days
B. 40 days
C. 50 days
D. 60 days
E. 80 days

Explanation: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 250 * d 2 d 2 = 600 * 25 / 250 = 60 days . answer : d"


Question: in what time will a train 200 m long cross an electric pole , it its speed be 144 km / hr ?

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

<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>

<gadget id="calculator">200 / 40</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 2.5 sec
B. 1.9 sec
C. 8.9 sec
D. 6.9 sec
E. 5 sec

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 200 / 40 = 5 sec . answer : e"


Question: in a group of 100 cars , 49 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?

<gadget id="calculator">100 - 51</gadget>
<output>49</output>
<result>49</result>

Choices:
A. 49
B. 47
C. 48
D. 51
E. 53

Explanation: lets assume ac = 51 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 2 tocars with ac and racing stripes . hence ac = 51 - 2 = 49 . the answer is a


Question: last year a certain bond price with a face value of 5000 yielded 10 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?

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

<gadget id="calculator">5_000 * (1/10)</gadget>
<output>500</output>

<gadget id="calculator">6.5 / 100</gadget>
<output>0.065</output>

<gadget id="calculator">500 / 0.065</gadget>
<output>7_692.307692</output>
<result>7_692.307692</result>

Choices:
A. 7692
B. 5325
C. 5351
D. 6000
E. 6154

divide(multiply(5000, divide(10, const_100)), divide(6.5, const_100))

Explanation: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.1 * 5000 / 0.065 - - > selling price = ~ 7692 answer : a ."


Question: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people c who purchased only book a ?

<gadget id="calculator">500 / 2</gadget>
<output>250</output>

<gadget id="calculator">500 + 250</gadget>
<output>750</output>

<gadget id="calculator">750 * 2</gadget>
<output>1_500</output>

<gadget id="calculator">1_500 - 500</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 250
B. 500
C. 750
D. 1000
E. 1500

subtract(multiply(add(500, divide(500, const_2)), const_2), 500)

Explanation: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , c = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"


Question: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 6 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?

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

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

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

Choices:
A. 23 / 30
B. 11 / 15
C. 7 / 10
D. 1 / 6
E. 2 / 15

divide(add(10, 5), multiply(10, const_2))

Explanation: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 6 ( equiped with cable tv ) i . e . 1 / 6 ( 1 / 5 ) = 1 / 30 therefore only video cassette recorder = 1 / 10 - 1 / 30 = 1 / 15 total = 1 / 5 + 1 / 15 + neither cable tv nor videocassette recorders 1 = 4 / 15 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 4 / 15 = 11 / 15 hence b ."


Question: walking at 3 / 4 of her normal speed , a worker is 8 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is

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

Choices:
A. 20
B. 24
C. 28
D. 32
E. 36

Explanation: "let v be her normal speed and let t be her normal time . d = ( 3 / 4 ) v * ( t + 8 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 3 / 4 ) v * ( t + 8 ) t / 4 = 6 t = 24 the answer is b ."


Question: the total age of a and b is 14 years more than the total age of b and c . c is how many years younger than a ?

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

Choices:
A. 14
B. 27
C. 21
D. 18
E. 11

Explanation: "( a + b ) - ( b + c ) = 14 a - c = 14 . c is younger than a by 14 years . answer : a"


Question: in a party every person shakes hands with every other person . if there were a total of 171 handshakes in the party then what is the number of persons present in the party ?

<gadget id="calculator">171 * 2</gadget>
<output>342</output>

<gadget id="calculator">342 * 4</gadget>
<output>1_368</output>

<gadget id="calculator">1_368 + 1</gadget>
<output>1_369</output>

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

<gadget id="calculator">37 + 1</gadget>
<output>38</output>

<gadget id="calculator">38 / 2</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 15
B. 16
C. 17
D. 18
E. 19

divide(add(sqrt(add(multiply(multiply(171, const_2), const_4), const_1)), const_1), const_2)

Explanation: explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 171 n ( n - 1 ) / 2 = 171 â ˆ ´ n = 19 answer : option e


Question: a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is

<gadget id="calculator">20 * 6.5</gadget>
<output>130</output>
<result>130</result>

Choices:
A. 65 km
B. 100 km
C. 120 km
D. 130 km
E. 140 km

Explanation: explanation : let the journey be x km then , 3 x / 5 + 7 x / 20 + 6.5 = x 12 x + 7 x + 130 = 20 x x = 130 km answer : option d


Question: two trains of length 100 meters and 200 meters are 450 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 72 km / h . after how many seconds will the trains meet ?

<gadget id="calculator">90 + 72</gadget>
<output>162</output>

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

<gadget id="calculator">162 * (5/18)</gadget>
<output>45</output>

<gadget id="calculator">450 / 45</gadget>
<output>10</output>
<result>10</result>

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

Explanation: "the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 450 / 45 = 10 seconds the answer is c ."


Question: a train is 360 meter long is running at a speed of 52 km / hour . in what time will it pass a bridge of 140 meter length .

<gadget id="calculator">360 + 140</gadget>
<output>500</output>

<gadget id="calculator">52 * 1_000</gadget>
<output>52_000</output>

<gadget id="calculator">52_000 / 3_600</gadget>
<output>130/9 = around 14.444444</output>

<gadget id="calculator">500 / (130/9)</gadget>
<output>450/13 = around 34.615385</output>
<result>450/13 = around 34.615385</result>

Choices:
A. 24.62 seconds
B. 34.62 seconds
C. 44.62 seconds
D. 54.62 seconds
E. none of these

divide(add(360, 140), divide(multiply(52, const_1000), const_3600))

Explanation: "explanation : speed = 52 km / hr = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 130 / 9 = 34.62 seconds answer : b"


Question: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 540 ?

<gadget id="calculator">540 - 2</gadget>
<output>538</output>

<gadget id="calculator">538 / 2</gadget>
<output>269</output>
<result>269</result>

Choices:
A. 249
B. 498
C. 676
D. 269
E. 1,002

Explanation: "slope of 2 and a y - intercept of 2 y - coordinate is 540 y = 2 x + 2 538 = 2 x x = 269 answer : d . 269"


Question: in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 24 per kg so that cost of mixture is rs . 18 per kg ?

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

<gadget id="calculator">16 - 24</gadget>
<output>-8</output>

<gadget id="calculator">(-6) / (-8)</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">(3/4) / (1/4)</gadget>
<output>3</output>
<result>3</result>

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

divide(divide(subtract(18, 24), subtract(16, 24)), subtract(const_1, divide(subtract(18, 24), subtract(16, 24))))

Explanation: "( 18 - 24 ) / ( 16 - 18 ) = 6 / 2 = 3 : 1 answer : c"


Question: in a class of 25 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?

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

<gadget id="calculator">25 - 6</gadget>
<output>19</output>

<gadget id="calculator">45 * 19</gadget>
<output>855</output>

<gadget id="calculator">95 * 3</gadget>
<output>285</output>

<gadget id="calculator">855 + 285</gadget>
<output>1_140</output>

<gadget id="calculator">1_140 / 25</gadget>
<output>228/5 = around 45.6</output>
<result>228/5 = around 45.6</result>

Choices:
A. 47
B. 45.6
C. 44
D. 48
E. 49

divide(add(multiply(45, subtract(25, add(3, 3))), multiply(95, 3)), 25)

Explanation: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 19 * 45 = 1140 average marks of whole class = 1140 / 25 = 45.6 answer : option b"


Question: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 3 percent and the mobile phone at a profit of 10 percent . overall he make a .

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

<gadget id="calculator">1 - (3/100)</gadget>
<output>97/100 = around 0.97</output>

<gadget id="calculator">15_000 * (97/100)</gadget>
<output>14_550</output>

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

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">8_000 * (11/10)</gadget>
<output>8_800</output>

<gadget id="calculator">14_550 + 8_800</gadget>
<output>23_350</output>

<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>

<gadget id="calculator">23_350 - 23_000</gadget>
<output>350</output>
<result>350</result>

Choices:
A. 228
B. 350
C. 27
D. 200
E. 881

subtract(add(multiply(15000, subtract(const_1, divide(3, const_100))), multiply(8000, add(const_1, divide(10, const_100)))), add(15000, 8000))

Explanation: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 3 / 100 ) = 15000 - 450 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 450 + 800 = rs . 350 as this is positive , an overall profit of rs . 350 was made . answer : b"


Question: a man , a woman and a boy can together complete a piece of work in 3 days . if a woman alone can do it in 6 days and a boy alone in 18 days , how long will a man take to complete the work ?

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

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

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(1/6) + (1/18)</gadget>
<output>2/9 = around 0.222222</output>

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

<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>

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

Explanation: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 wo man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 man alone can finish the work in 9 days . answer : option d"


Question: a train running at the speed of 70 km / hr crosses a pole in 9 sec . what is the length of the train ?

<gadget id="calculator">70 * 1_000</gadget>
<output>70_000</output>

<gadget id="calculator">70_000 / 3_600</gadget>
<output>175/9 = around 19.444444</output>

<gadget id="calculator">(175/9) * 9</gadget>
<output>175</output>
<result>175</result>

Choices:
A. 227 m
B. 150 m
C. 167 m
D. 175 m
E. 187 m

multiply(divide(multiply(70, const_1000), const_3600), 9)

Explanation: "speed = 70 * 5 / 18 = 175 / 9 m / sec length of the train = speed * time = 175 / 9 * 9 = 175 m answer : d"


Question: on my sister ' s birthday , she was 126 cm in height , having grown 5 % since the year before . how tall was she the previous year ?

<gadget id="calculator">126 * 5</gadget>
<output>630</output>

<gadget id="calculator">630 / 100</gadget>
<output>63/10 = around 6.3</output>

<gadget id="calculator">126 - (63/10)</gadget>
<output>1_197/10 = around 119.7</output>
<result>1_197/10 = around 119.7</result>

Choices:
A. 124 cm
B. 120 cm
C. 116 cm
D. 112 cm
E. 110 cm

subtract(126, divide(multiply(126, 5), const_100))

Explanation: let the previous year ' s height be x . 1.05 x = 126 x = 120 the answer is b .


Question: for a certain art exhibit , a museum sold admission tickets to a group of 50 people every 5 minutes from 9 : 00 in the morning to 5 : 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 + 5</gadget>
<output>17</output>

<gadget id="calculator">17 - 9</gadget>
<output>8</output>

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

<gadget id="calculator">9 * 12</gadget>
<output>108</output>

<gadget id="calculator">108 * 50</gadget>
<output>5_400</output>

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

<gadget id="calculator">5_400 / 4</gadget>
<output>1_350</output>

<gadget id="calculator">1_350 * 3</gadget>
<output>4_050</output>

<gadget id="calculator">4_050 * 10</gadget>
<output>40_500</output>

<gadget id="calculator">1_350 * 6</gadget>
<output>8_100</output>

<gadget id="calculator">40_500 + 8_100</gadget>
<output>48_600</output>
<result>48_600</result>

Choices:
A. $ 24960
B. $ 25920
C. $ 28080
D. $ 38500
E. $ 48600

add(multiply(multiply(divide(multiply(multiply(add(subtract(add(const_12, 5), 9), const_1), const_12), 50), add(3, const_1)), 3), 10), multiply(divide(multiply(multiply(add(subtract(add(const_12, 5), 9), const_1), const_12), 50), add(3, const_1)), 6))

Explanation: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 50 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 50 - - > x = 27 * 50 and 3 x = 3 * ( 27 * 50 ) = 27 * 150 . therefore , the total revenue from ticket sales that day was 27 * 50 * 6 + 27 * 150 * 10 = $ 48,600 . answer : e ."


Question: sum of 3 numbers 264 , if the first number be twice then second and third number be one third of the first , then the second number is

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

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

<gadget id="calculator">3 + (2/3)</gadget>
<output>11/3 = around 3.666667</output>

<gadget id="calculator">264 / (11/3)</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 70
B. 71
C. 72
D. 73
E. 74

divide(264, add(add(const_2, const_1), divide(const_2, const_3)))

Explanation: explanation : let the second number is x , then first is 2 x , and third is 1 / 3 ( 2 x ) = > 2 x + x + 2 x / 3 = 264 < = > 11 x / 3 = 264 = > x = 72 answer : option c


Question: a train moves with a speed of 216 kmph . its speed in metres per second is

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

<gadget id="calculator">216 * (5/18)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 10.8
B. 18
C. 30
D. 38.8
E. 60

Explanation: solution speed = 216 kmph = ( 216 x 5 / 18 ) m / sec = 60 m / sec . answer e


Question: find the least number must be subtracted from 105829 so that remaining no . is divisible by 21 ?

<gadget id="calculator">105_829 / 21</gadget>
<output>105_829/21 = around 5_039.47619</output>

<gadget id="calculator">floor(105_829/21)</gadget>
<output>5_039</output>

<gadget id="calculator">5_039 * 21</gadget>
<output>105_819</output>

<gadget id="calculator">105_829 - 105_819</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 7
B. 10
C. 20
D. 32
E. 35

subtract(105829, multiply(floor(divide(105829, 21)), 21))

Explanation: "on dividing 105829 by 21 we get the remainder 10 , so 10 should be subtracted answer is b"


Question: the average age of 50 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .

<gadget id="calculator">50 * 14</gadget>
<output>700</output>

<gadget id="calculator">700 + 15</gadget>
<output>715</output>

<gadget id="calculator">715 + 50</gadget>
<output>765</output>

<gadget id="calculator">765 - 700</gadget>
<output>65</output>
<result>65</result>

Choices:
A. 30
B. 65
C. 60
D. 55
E. 56

subtract(add(add(multiply(50, 14), 15), 50), multiply(50, 14))

Explanation: "explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 50 ) = 65 years answer : b"


Question: the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 60 less . what was the total cost cost of the vacation ?

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

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

<gadget id="calculator">60 / 1</gadget>
<output>60</output>

<gadget id="calculator">12 * 60</gadget>
<output>720</output>
<result>720</result>

Choices:
A. $ 200
B. $ 300
C. $ 400
D. $ 720
E. $ 600

multiply(multiply(4, 3), divide(60, subtract(4, 3)))

Explanation: "c for cost . p price per person . c = 3 * p c = 4 * p - 240 substituting the value of p from the first equation onto the second we get p = 240 . plugging in the value of p in the first equation , we get c = 720 . which leads us to answer choice d"


Question: twice the larger of two numbers is 3 more than 5 times the smaller , and the sum of 4 times the larger and 3 times the smaller is 71 . what are the numbers ?

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

<gadget id="calculator">25 + 3</gadget>
<output>28</output>

<gadget id="calculator">28 + 1</gadget>
<output>29</output>

<gadget id="calculator">29 / 2</gadget>
<output>29/2 = around 14.5</output>
<result>29/2 = around 14.5</result>

Choices:
A. 21 , 12
B. 9 , 0
C. 15 , 6
D. 10 , 1
E. 14 , 5

divide(add(add(multiply(5, 5), 3), const_1), const_2)

Explanation: the larger number : x the smaller number : y twice the larger : 2 x three more than five times the smaller : 5 y + 3 relationship between ( ` ` is ' ' ) : 2 x = 5 y + 3 four times the larger : 4 x three times the smaller : 3 y relationship between ( ` ` sum of ' ' ) : 4 x + 3 y = 71 now i have two equations in two variables : 2 x = 5 y + 3 4 x + 3 y = 71 i will solve , say , the first equation for x : x = ( 5 / 2 ) y + ( 3 / 2 ) then i ' ll plug the right - hand side of this into the second equation in place of the ` ` x ' ' : 4 [ ( 5 / 2 ) y + ( 3 / 2 ) ] + 3 y = 71 10 y + 6 + 3 y = 71 13 y + 6 = 71 13 y = 65 y = 65 / 13 = 5 now that i have the value for y , i can solve for x : x = ( 5 / 2 ) y + ( 3 / 2 ) x = ( 5 / 2 ) ( 5 ) + ( 3 / 2 ) x = ( 25 / 2 ) + ( 3 / 2 ) x = 28 / 2 = 14 answer : e


Question: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is ?

<gadget id="calculator">72 / 2</gadget>
<output>36</output>

<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>

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

Choices:
A. 6
B. 12
C. 24
D. 36
E. 48

Explanation: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"


Question: 800 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?

<gadget id="calculator">20 * 800</gadget>
<output>16_000</output>

<gadget id="calculator">800 + 200</gadget>
<output>1_000</output>

<gadget id="calculator">16_000 / 1_000</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 10
B. 8
C. 16
D. 11
E. 15

Explanation: "800 * 20 = 1200 * x x = 16 . answer : c"