Question: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24 % of the original number . what percent of the red candies remain ?

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

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

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

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

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

<gadget id="calculator">24 - 15</gadget>
<output>9</output>

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

<gadget id="calculator">(9/2) / 20</gadget>
<output>9/40 = around 0.225</output>

<gadget id="calculator">(9/40) * 100</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>

Choices:
A. 12.5 %
B. 16.7 %
C. 22.5 %
D. 27.5 %
E. 33.3 %

multiply(divide(divide(subtract(24, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)

Explanation: let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.2 x red + yellow = 0.45 x red = 0.225 x , since red = yellow . the answer is c .


Question: on selling 9 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :

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

<gadget id="calculator">720 / 4</gadget>
<output>180</output>
<result>180</result>

Choices:
A. s . 145
B. s . 150
C. s . 155
D. s . 160
E. s . 180

Explanation: "( c . p . of 9 balls ) - ( s . p . of 9 balls ) = ( c . p . of 5 balls ) c . p . of 4 balls = s . p . of 9 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 4 = rs . 180 . answer : option e"


Question: boy sells a book for rs . 630 he gets a loss of 10 % , to gain 10 % , what should be the sp ?

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

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

<gadget id="calculator">630 / (9/10)</gadget>
<output>700</output>

<gadget id="calculator">700 * (1/10)</gadget>
<output>70</output>

<gadget id="calculator">700 + 70</gadget>
<output>770</output>
<result>770</result>

Choices:
A. 430
B. 450
C. 550
D. 770
E. 660

add(divide(630, subtract(const_1, divide(10, const_100))), multiply(divide(630, subtract(const_1, divide(10, const_100))), divide(10, const_100)))

Explanation: "cost price = 630 / 90 x 100 = 700 to gain 10 % = 700 x 10 / 100 = 70 sp = cp + gain = 700 + 70 = 770 answer : d"


Question: a train 310 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?

<gadget id="calculator">310 / 1_000</gadget>
<output>31/100 = around 0.31</output>

<gadget id="calculator">60 + 6</gadget>
<output>66</output>

<gadget id="calculator">(31/100) / 66</gadget>
<output>31/6_600 = around 0.004697</output>

<gadget id="calculator">3_600 * (31/6_600)</gadget>
<output>186/11 = around 16.909091</output>
<result>186/11 = around 16.909091</result>

Choices:
A. 4
B. 6
C. 5
D. 17
E. 13

multiply(const_3600, divide(divide(310, const_1000), add(60, 6)))

Explanation: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 310 * 3 / 55 ] sec = 17 sec answer : d"


Question: how many odd factors does 210 have ?

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

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

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

Choices:
A. 3
B. 4
C. 5
D. 6
E. 8

add(add(add(const_4, const_2), const_1), const_1)

Explanation: start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , 3 , 5 , 7 , 15 , 21 , 35 , and 105 } answer : e .


Question: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?

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

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

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

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

<gadget id="calculator">24 * 10</gadget>
<output>240</output>

<gadget id="calculator">240 + 350</gadget>
<output>590</output>

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

<gadget id="calculator">7 * 32</gadget>
<output>224</output>

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

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

<gadget id="calculator">(5/4) * 3</gadget>
<output>15/4 = around 3.75</output>

<gadget id="calculator">(15/4) * 32</gadget>
<output>120</output>

<gadget id="calculator">224 + 120</gadget>
<output>344</output>

<gadget id="calculator">590 / 344</gadget>
<output>295/172 = around 1.715116</output>

<gadget id="calculator">(295/172) * (5/4)</gadget>
<output>1_475/688 = around 2.143895</output>
<result>1_475/688 = around 2.143895</result>

Choices:
A. $ 1.50
B. $ 1.88
C. $ 2.14
D. $ 2.50
E. $ 3.25

multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 350), add(multiply(subtract(multiply(add(const_4, 1), const_2), 3), 32), multiply(multiply(divide(add(const_100, 25), const_100), 3), 32))), divide(add(const_100, 25), const_100))

Explanation: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 350 - - > x = 1.715 . 1.25 x = ~ 2.14 . answer : c ."


Question: a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?

<gadget id="calculator">480 * 10</gadget>
<output>4_800</output>

<gadget id="calculator">4_800 / 60</gadget>
<output>80</output>

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

Choices:
A. 50
B. 60
C. 90
D. 48
E. 67

add(divide(multiply(480, 10), const_60), 10)

Explanation: c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 .


Question: find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?

<gadget id="calculator">10_000 / 3</gadget>
<output>10_000/3 = around 3_333.333333</output>

<gadget id="calculator">floor(10_000/3)</gadget>
<output>3_333</output>

<gadget id="calculator">3_333 + 1</gadget>
<output>3_334</output>
<result>3_334</result>

Choices:
A. 2468
B. 2789
C. 2987
D. 3334
E. 3568

Explanation: if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common difference = 3 ) . count of such numbers = 9999 3 = 3333 99993 = 3333 but zero is also divisible by 3 . this makes our total count 3334 d


Question: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 6 days ?

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

<gadget id="calculator">1 / 45</gadget>
<output>1/45 = around 0.022222</output>

<gadget id="calculator">(1/30) + (1/45)</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">6 * (1/18)</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>

Choices:
A. 2 / 5
B. 1 / 6
C. 1 / 3
D. 1 / 9
E. 2 / 6

multiply(6, add(divide(const_1, 30), divide(const_1, 45)))

Explanation: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 6 days = 6 ( 1 / 18 ) = 1 / 3 . answer c"


Question: in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate .

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>

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

Choices:
A. 144
B. 288
C. 12
D. 576
E. none

Explanation: "solution : let the arrangement be , b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 4 ! ways . required number of ways , = 4 ! * 4 ! = 576 . answer : option d"


Question: kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?

<gadget id="calculator">19_000 * 50</gadget>
<output>950_000</output>

<gadget id="calculator">950_000 / 100</gadget>
<output>9_500</output>

<gadget id="calculator">9_500 * 80</gadget>
<output>760_000</output>

<gadget id="calculator">760_000 / 100</gadget>
<output>7_600</output>

<gadget id="calculator">7_600 / 2</gadget>
<output>3_800</output>
<result>3_800</result>

Choices:
A. rs . 2000
B. rs . 600
C. rs . 8000
D. rs . 3800
E. rs . 1200

divide(divide(multiply(divide(multiply(19000, 50), const_100), 80), const_100), const_2)

Explanation: explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 – rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d


Question: a man can row upstream at 40 kmph and downstream at 52 kmph , and then find the speed of the man in still water ?

<gadget id="calculator">40 + 52</gadget>
<output>92</output>

<gadget id="calculator">92 / 2</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 27
B. 40
C. 42
D. 46
E. 24

Explanation: "us = 40 ds = 52 m = ( 40 + 52 ) / 2 = 46 answer : d"


Question: a can do a piece of work in 10 days and b alone can do it in 20 days . how much time will both take to finish the work ?

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

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

<gadget id="calculator">(1/10) + (1/20)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 / (3/20)</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>

Choices:
A. 5.333
B. 6
C. 6.666
D. 8.333
E. 9

divide(const_1, add(divide(const_1, 10), divide(const_1, 20)))

Explanation: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 10 x 20 / ( 10 + 20 ) = 200 / 30 = 6.666 days answer : c"


Question: a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,600 to 3,000 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?

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

<gadget id="calculator">200 * 1_000</gadget>
<output>200_000</output>

<gadget id="calculator">1_000 + 100</gadget>
<output>1_100</output>

<gadget id="calculator">1_100 + 100</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 + 100</gadget>
<output>1_300</output>

<gadget id="calculator">1_300 + 100</gadget>
<output>1_400</output>

<gadget id="calculator">1_400 + 100</gadget>
<output>1_500</output>

<gadget id="calculator">1_500 + 100</gadget>
<output>1_600</output>

<gadget id="calculator">200_000 / 1_600</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 110
B. 128
C. 115
D. 130
E. 120

divide(multiply(multiply(100, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100))

Explanation: "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 100 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 120 total weight will be = 120 * 1600 = 192000 pounds , which is lesser than the maximum weight allowed . ans : e"


Question: the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is

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

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

<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>

Choices:
A. 1.2
B. 1.4
C. 2.25
D. 3.21
E. none

divide(multiply(multiply(10, 4), 3), const_100)

Explanation: "sol . s . i . = rs . [ 10 * 3 / 100 * 4 ] = rs . 1.20 answer a"


Question: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25 % of the original number . what percent of the red candies remain ?

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

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

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

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

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

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

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

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

Choices:
A. 10 %
B. 15 %
C. 25 %
D. 35 %
E. 40 %

multiply(divide(divide(subtract(25, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)

Explanation: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.25 x red + yellow = 0.5 x red = 0.25 x , since red = yellow . the answer is c ."


Question: if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is

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

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

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

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

Choices:
A. - 32
B. - 30
C. 34
D. - 24
E. - 10

Explanation: answer : c


Question: the maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

<gadget id="calculator">gcd(1_234, 874)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 91
B. 2
C. 1001
D. 1911
E. none of these

Explanation: "explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b"


Question: a boatman selling a boat along river flow . if he sell boat in steal water at 3 m / sec and flow of river is 2 m / sec . how much time he will take to sell 100 m .

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

<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 30
B. 10
C. 15
D. 20
E. 25

Explanation: net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d


Question: a man can row his boat with the stream at 12 km / h and against the stream in 8 km / h . the man ' s rate is ?

<gadget id="calculator">12 - 8</gadget>
<output>4</output>

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

Choices:
A. 2 kmph
B. 6 kmph
C. 7 kmph
D. 4 kmph
E. 9 kmph

Explanation: explanation : ds = 12 us = 8 s = ? s = ( 12 - 8 ) / 2 = 2 kmph answer : a


Question: a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?

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

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

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

<gadget id="calculator">(3/10) * 6</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">(1/2) + (9/5)</gadget>
<output>23/10 = around 2.3</output>

<gadget id="calculator">(23/10) / 10</gadget>
<output>23/100 = around 0.23</output>

<gadget id="calculator">(23/100) * 100</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 23 % .
B. 71 % .
C. 49 % .
D. 29 % .
E. 51 % .

multiply(divide(add(multiply(divide(25, const_100), 2), multiply(divide(30, const_100), 6)), 10), const_100)

Explanation: "25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a"


Question: jack and jill work at a hospital with 4 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?

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

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

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>

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

<gadget id="calculator">720 / 48</gadget>
<output>15</output>

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

Choices:
A. 1 / 3
B. 1 / 4
C. 1 / 15
D. 3 / 8
E. 2 / 3

Explanation: "total number of ways to choose 2 out of 6 workers = 6 ! / 2 ! 4 ! = 15 number of ways to choose both jack and jill = 1 probability = 1 / 15 c should be the answer"


Question: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?

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

<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>

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

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

<gadget id="calculator">1 + (7/20)</gadget>
<output>27/20 = around 1.35</output>

<gadget id="calculator">140 * (27/20)</gadget>
<output>189</output>

<gadget id="calculator">189 / 100</gadget>
<output>189/100 = around 1.89</output>

<gadget id="calculator">(189/100) - 1</gadget>
<output>89/100 = around 0.89</output>

<gadget id="calculator">(89/100) * 100</gadget>
<output>89</output>
<result>89</result>

Choices:
A. 65 %
B. 70 %
C. 75 %
D. 89 %
E. 95 %

multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(35, const_100))), const_100), const_1), const_100)

Explanation: "find the product of the two increases : ( 1.4 ) * ( 1.35 ) which is 1.89 and a 89 % increase . d"


Question: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?

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

<gadget id="calculator">30 - 25</gadget>
<output>5</output>

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

<gadget id="calculator">3 * 150</gadget>
<output>450</output>
<result>450</result>

Choices:
A. 250 / 3
B. 500 / 3
C. 400
D. 450
E. 600

multiply(divide(subtract(25, 10), subtract(30, 25)), 150)

Explanation: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d"


Question: a cycle is bought for rs . 750 and sold for rs . 1080 , find the gain percent ?

<gadget id="calculator">1_080 - 750</gadget>
<output>330</output>

<gadget id="calculator">330 / 750</gadget>
<output>11/25 = around 0.44</output>

<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 22
B. 44
C. 99
D. 88
E. 11

multiply(divide(subtract(1080, 750), 750), const_100)

Explanation: "750 - - - - 180 100 - - - - ? = > 44 % answer : b"


Question: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?

<gadget id="calculator">16 * 62.5</gadget>
<output>1_000</output>

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

<gadget id="calculator">15 * 65</gadget>
<output>975</output>

<gadget id="calculator">1_000 - 975</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 10
B. 25
C. 40
D. 55
E. 70

subtract(multiply(16, 62.5), multiply(subtract(16, const_1), 65.0))

Explanation: "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )"


Question: when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?

<gadget id="calculator">floor(96.12)</gadget>
<output>96</output>

<gadget id="calculator">96.12 - 96</gadget>
<output>0.12</output>

<gadget id="calculator">8 / 0.12</gadget>
<output>66.666667</output>
<result>66.666667</result>

Choices:
A. 96
B. 75
C. 66.7
D. 25
E. 12

Explanation: "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c ."


Question: a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left .

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

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

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

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

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

Choices:
A. 10 kmph
B. 20 kmph
C. 30 kmph
D. 40 kmph
E. 50 kmph

divide(divide(80, const_2), subtract(10, multiply(divide(10, 5), 3)))

Explanation: a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph


Question: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ?

<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>

<gadget id="calculator">30_000 / 1_200</gadget>
<output>25</output>

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

Choices:
A. 5
B. 6
C. 18
D. can not be determined
E. none of these

Explanation: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 300 12 r 2 = 300 r 2 = 25 r = 5 . answer : a"


Question: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 20 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?

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

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

<gadget id="calculator">20 / 1.5</gadget>
<output>13.333333</output>

<gadget id="calculator">60 / 13.333333</gadget>
<output>4.5</output>

<gadget id="calculator">10 - 4.5</gadget>
<output>5.5</output>
<result>5.5</result>

Choices:
A. 5.5
B. 15
C. 25.5
D. 30
E. 60

subtract(subtract(divide(const_60, const_2), 20), divide(const_60, divide(20, 1.5)))

Explanation: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 20 x = 5.5 minutes answer : a"


Question: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 150 cm when it touches the floor on third time . what is the value of the original height ?

<gadget id="calculator">50 / 100</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">150 / (5/2)</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 60 cm
B. 90 cm
C. 100 cm
D. 120 cm
E. 130 cm

divide(150, add(const_2, divide(50, const_100)))

Explanation: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 150 2.5 h = 150 h = 60 . a is the answer ."


Question: a furniture manufacturer has two machines , but only one can be used at a time . machine w is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine w can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?

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

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

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

<gadget id="calculator">24 / (3/2)</gadget>
<output>16</output>

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

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

<gadget id="calculator">30 / (3/2)</gadget>
<output>20</output>

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

<gadget id="calculator">(1/16) + (1/20)</gadget>
<output>9/80 = around 0.1125</output>

<gadget id="calculator">1 / (9/80)</gadget>
<output>80/9 = around 8.888889</output>
<result>80/9 = around 8.888889</result>

Choices:
A. 14
B. 13
C. 11
D. 9
E. 7

inverse(add(inverse(divide(multiply(12, const_2), add(const_1, divide(const_1, const_2)))), inverse(divide(multiply(15, const_2), add(const_1, divide(const_1, const_2))))))

Explanation: ' approximately ' could actually make such a question ambiguous . not this one though but a similar question with the answer as 9.2 days . you round off 8.89 days as 9 days and everything is fine in this question . what do you do when you get 9.2 days ? do you need 9 days or 10 days ? can you round off 9.2 as 9 even though that is what you do with numbers ? no , because in 9 days your work is not over . you do need 10 days . to finish a work machine w say you need to work full 9 days and a part of the 10 th day . if i ask you how many days do you need to complete the work , will you say 9 or 10 ? you will say 10 even if you do n ' t use the 10 th day fully = d


Question: calculate 469200 x 9999 = ?

Choices:
A. 4586970843
B. 4686970743
C. 4691100843
D. 4586870843
E. 4691530800

Explanation: "answer 469200 x 9999 = 469200 x ( 10000 - 1 ) = 4692000000 - 469200 = 4691100843 . option : e"


Question: how many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph ?

<gadget id="calculator">130 + 100</gadget>
<output>230</output>

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

<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>

<gadget id="calculator">230 / 10</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 26
B. 72
C. 25
D. 23
E. 27

Explanation: "explanation : d = 100 + 130 = 230 s = 36 * 5 / 18 = 10 mps t = 230 / 10 = 23 sec answer : option d"


Question: a is two years older than b who is twice as old as c . if the total ages of a , b and c be 27 . what is the age of b ?

<gadget id="calculator">27 - 2</gadget>
<output>25</output>

<gadget id="calculator">25 * 2</gadget>
<output>50</output>

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

<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 12 years
B. 10 years
C. 8 years
D. 14 years
E. 16 years

divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1))

Explanation: "c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b"


Question: a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 22 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 22 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?

<gadget id="calculator">22 * 410</gadget>
<output>9_020</output>

<gadget id="calculator">410 + 65</gadget>
<output>475</output>

<gadget id="calculator">52 - 22</gadget>
<output>30</output>

<gadget id="calculator">475 * 30</gadget>
<output>14_250</output>

<gadget id="calculator">9_020 + 14_250</gadget>
<output>23_270</output>

<gadget id="calculator">23_270 / 52</gadget>
<output>895/2 = around 447.5</output>
<result>895/2 = around 447.5</result>

Choices:
A. 447.5
B. 450
C. 465
D. 468
E. 475

divide(add(multiply(22, 410), multiply(add(410, 65), subtract(52, 22))), 52)

Explanation: total number of installments = 52 payment per installment for the first 22 installments = 410 payment per installment for the remaining 30 installments = 410 + 65 = 475 average = ( 22 * 410 + 30 * 475 ) / 52 = 447.50 answer a


Question: the ratio of numbers is 5 : 6 and their h . c . f is 4 . their l . c . m is :

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

<gadget id="calculator">6 * 4</gadget>
<output>24</output>

<gadget id="calculator">lcm(20, 24)</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 12
B. 16
C. 24
D. 48
E. 120

Explanation: "let the numbers be 5 x and 6 x . then their h . c . f = x . so , x = 4 . so , the numbers are 20 and 24 . l . c . m of 20 and 24 = 120 . answer : e"


Question: a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 102 . find the divisor ?

<gadget id="calculator">241 * 2</gadget>
<output>482</output>

<gadget id="calculator">482 - 102</gadget>
<output>380</output>
<result>380</result>

Choices:
A. 370
B. 365
C. 380
D. 456
E. 460

Explanation: "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 102 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 380 d * some integer = 380 checking all options only ( c ) syncs with it . answer c"


Question: the banker â € ™ s discount of a certain sum of money is rs . 90 and the true discount on the same sum for the same time is rs . 60 . the sum due is

<gadget id="calculator">90 * 60</gadget>
<output>5_400</output>

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

<gadget id="calculator">5_400 / 30</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 210
B. 180
C. 360
D. 450
E. none

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

Explanation: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 90 * 60 / 90 - 60 ] = rs . [ 90 * 60 / 30 ] = rs . 180 answer b"


Question: s is a positive integer and multiple of 2 ; p = 4 ^ s , what is the remainder when p is divided by 10 ?

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

<gadget id="calculator">16 % 10</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 10
B. 6
C. 4
D. 0
E. it can not be determined

Explanation: it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b .


Question: if the sum of two numbers is 22 and the sum of their squares is 386 , then the product of the numbers is

<gadget id="calculator">22 ** 2</gadget>
<output>484</output>

<gadget id="calculator">484 - 386</gadget>
<output>98</output>

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

Choices:
A. 40
B. 49
C. 80
D. 88
E. 90

divide(subtract(power(22, const_2), 386), const_2)

Explanation: "sol . let the numbers be x and y . then , ( x + y ) = 22 and x 2 + y 2 = 386 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 22 ) 2 - 386 = 484 - 386 = 98 xy = 49 . answer b"


Question: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 80 percent of the drive from the center , what percent of the round - trip has the technician completed ?

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

<gadget id="calculator">80 * 50</gadget>
<output>4_000</output>

<gadget id="calculator">4_000 / 100</gadget>
<output>40</output>

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

Choices:
A. 50
B. 60
C. 70
D. 80
E. 90

add(divide(const_100, const_2), divide(multiply(80, divide(const_100, const_2)), const_100))

Explanation: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 80 % of 50 % i . e 40 % . so he completed 50 + 40 = 90 % of total trip . e"


Question: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 15 - m ) then m = ?

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

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

Choices:
A. 1
B. 2
C. 3
D. 5
E. 6

Explanation: "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 15 - m ) = 4 ^ ( ( 15 - m ) / 2 ) therefore , m = ( 15 - m ) / 2 2 m = 15 - m m = 5 answer d"


Question: $ 378 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?

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

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

<gadget id="calculator">(3/2) + 2</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">378 / (7/2)</gadget>
<output>108</output>

<gadget id="calculator">108 * 2</gadget>
<output>216</output>
<result>216</result>

Choices:
A. $ 200
B. $ 208
C. $ 216
D. $ 224
E. $ 232

multiply(divide(378, add(add(divide(const_1, const_2), const_1), const_2)), const_2)

Explanation: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 378 x = 54 4 x = 216 the answer is c ."


Question: harkamal purchased 8 kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?

<gadget id="calculator">8 * 75</gadget>
<output>600</output>

<gadget id="calculator">9 * 55</gadget>
<output>495</output>

<gadget id="calculator">600 + 495</gadget>
<output>1_095</output>
<result>1_095</result>

Choices:
A. 1000
B. 1055
C. 1065
D. 1075
E. 1095

Explanation: "cost of 8 kg grapes = 75 × 8 = 600 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 600 + 495 = 1095 . e )"


Question: if the side length of square b is sqrt ( 5 ) times that of square a , the area of square b is how many times the area of square a ?

<gadget id="calculator">5 ** (1/2)</gadget>
<output>sqrt(5) = around 2.236068</output>

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

Choices:
A. 1.5
B. 2
C. 3
D. 4
E. 5

Explanation: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 5 ) x ) ^ 2 = 5 x ^ 2 . the answer is e ."


Question: a certain quantity of 50 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?

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

<gadget id="calculator">50 - 35</gadget>
<output>15</output>

<gadget id="calculator">10 / 15</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>

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

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

inverse(add(divide(subtract(35, 25), subtract(50, 35)), const_1))

Explanation: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 15 % . therefore , 15 out of 25 is 3 / 5 and e is the answer ."


Question: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?

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

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

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

<gadget id="calculator">(6/5) * (4/5)</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">1 - (24/25)</gadget>
<output>1/25 = around 0.04</output>

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

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

multiply(subtract(const_1, multiply(add(divide(20, const_100), const_1), divide(80, const_100))), const_100)

Explanation: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.2 x ) = 0.96 x . the difference is 4 % . the answer is d ."


Question: there is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save . auggie was very curious to test this theory . auggie spent all of his money in 5 stores . in each store , he spent rs . 4 more than one - half of what he had when he went in . how many rupees did auggie have when he entered the first store ?

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

<gadget id="calculator">8 + 4</gadget>
<output>12</output>

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

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

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

<gadget id="calculator">56 + 4</gadget>
<output>60</output>

<gadget id="calculator">60 * 2</gadget>
<output>120</output>

<gadget id="calculator">120 + 4</gadget>
<output>124</output>

<gadget id="calculator">124 * 2</gadget>
<output>248</output>
<result>248</result>

Choices:
A. 248
B. 120
C. 252
D. 250
E. 350

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

Explanation: amount left = 0.5 x − 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x − 4 = 8 ⇒ x = 24 for third store , amount left = 24 so 12 x − 4 = 24 ⇒ x = 56 for second store , amount left = 56 so 0.5 x − 4 = 56 ⇒ x = 120 for first store , amount left = 120 so 0.5 x − 4 = 120 ⇒ x = 248 so he entered first store with 248 . answer : a


Question: 3 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire cost of the car , then the share of each of the remaining persons increased by :

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

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

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

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

Choices:
A. 1 / 2
B. 2 / 7
C. 3 / 2
D. 4 / 7
E. none of them

divide(subtract(divide(const_1, const_2), divide(const_1, 3)), divide(const_1, 3))

Explanation: original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a .


Question: two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?

<gadget id="calculator">200 + 150</gadget>
<output>350</output>

<gadget id="calculator">350 / 1_000</gadget>
<output>7/20 = around 0.35</output>

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

<gadget id="calculator">(7/20) / 5</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">3_600 * (7/100)</gadget>
<output>252</output>
<result>252</result>

Choices:
A. 72 sec
B. 132 sec
C. 192 sec
D. 252 sec
E. none

multiply(const_3600, divide(divide(add(200, 150), const_1000), subtract(45, 40)))

Explanation: solution relative speed = ( 45 - 40 ) kmph = 5 kmph = ( 5 x 5 / 18 ) m / sec = ( 25 / 18 ) m / sec time taken = ( 350 x 18 / 25 ) sec = 252 sec . answer d


Question: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 35 . find the profit percentage ?

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

<gadget id="calculator">35 * 5</gadget>
<output>175</output>

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

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

Choices:
A. 80 %
B. 50 %
C. 75 %
D. 40 %
E. 53 %

subtract(multiply(35, add(const_4, const_1)), multiply(25, const_4))

Explanation: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 175 ( 35 * 5 ) profit percentage = ( 175 - 100 ) / 100 * 100 = 75 % answer : c"


Question: how many 1 / 8 s are there in 37 1 / 2 ?

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

<gadget id="calculator">37 + (1/2)</gadget>
<output>75/2 = around 37.5</output>

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

<gadget id="calculator">(75/2) / (1/8)</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 300
B. 400
C. 500
D. 600
E. 700

divide(add(37, divide(1, 2)), divide(1, 8))

Explanation: "required number = ( 75 / 2 ) / ( 1 / 8 ) = ( 75 / 2 x 8 / 1 ) = 300 . answer : a"


Question: in triangle pqr , the angle q = 90 degree , pq = 5 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz

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

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

Choices:
A. 3.6 cm
B. 2.4 cm
C. 4.0 cm
D. 2.16 cm
E. 3.2 cm

Explanation: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 5 = 8 : 10 - - > qy = 4.0 . answer : c ."


Question: the average runs of a cricket player of 10 innings was 20 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?

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

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

<gadget id="calculator">11 * 24</gadget>
<output>264</output>

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

<gadget id="calculator">264 - 200</gadget>
<output>64</output>
<result>64</result>

Choices:
A. 22
B. 77
C. 64
D. 19
E. 17

subtract(multiply(add(10, const_1), add(20, 4)), multiply(20, 10))

Explanation: "explanation : average after 11 innings = 24 required number of runs = ( 24 * 11 ) – ( 20 * 10 ) = 264 – 200 = 64 answer : c"


Question: the sum of the even numbers between 1 and k is 79 * 80 , where k is an odd number , then k =

<gadget id="calculator">79 * 2</gadget>
<output>158</output>

<gadget id="calculator">158 + 1</gadget>
<output>159</output>
<result>159</result>

Choices:
A. 79
B. 80
C. 81
D. 157
E. 159

Explanation: "the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e ."


Question: how long does a train 125 m long running at the speed of 78 km / hr takes to cross a bridge 125 m length ?

<gadget id="calculator">125 + 125</gadget>
<output>250</output>

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

<gadget id="calculator">78 * (5/18)</gadget>
<output>65/3 = around 21.666667</output>

<gadget id="calculator">250 / (65/3)</gadget>
<output>150/13 = around 11.538462</output>
<result>150/13 = around 11.538462</result>

Choices:
A. 12.7 sec
B. 10.1 sec
C. 11.5 sec
D. 12.1 sec
E. 11.7 sec

Explanation: "speed = 78 * 5 / 18 = 21.7 m / sec total distance covered = 125 + 125 = 250 m . required time = 250 / 21.7 ' = 11.5 sec . answer : c"


Question: ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ?

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

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

<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 40
B. 48
C. 43
D. 45
E. 41

multiply(subtract(multiply(const_2, 15), 15), 3)

Explanation: ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d )


Question: a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is

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

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

<gadget id="calculator">30 - 2</gadget>
<output>28</output>

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

<gadget id="calculator">28 / 1</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28 years
B. 22 years
C. 23 years
D. 24 years
E. 26 years

divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))

Explanation: "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 2 ) = ( x + 30 + 2 ) = > 2 x + 4 = x + 32 = > x = 28 years option a"


Question: the length of the bridge , which a train 110 meters 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 - 110</gadget>
<output>265</output>
<result>265</result>

Choices:
A. 265
B. 244
C. 245
D. 238
E. 236

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 110)

Explanation: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 = = > 2 ( 110 + x ) = 750 = = > x = 265 m . answer : option a"


Question: cole drove from home to work at an average speed of 60 kmh . he then returned home at an average speed of 100 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?

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

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

<gadget id="calculator">200 / 160</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 60</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 66
B. 70
C. 72
D. 75
E. 78

multiply(divide(multiply(100, 2), add(60, 100)), const_60)

Explanation: "let the distance one way be x time from home to work = x / 60 time from work to home = x / 100 total time = 2 hrs ( x / 60 ) + ( x / 100 ) = 2 solving for x , we get x = 75 time from home to work in minutes = ( 75 ) * 60 / 60 = 75 minutes ans = d"


Question: if the radius of a circle is decreased 50 % , what happens to the area ?

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

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

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

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

Choices:
A. 10 % decrease
B. 20 % decrease
C. 75 % decrease
D. 40 % decrease
E. 50 % decrease

subtract(const_100, multiply(power(divide(50, const_100), const_2), const_100))

Explanation: "area of square = pi * radius ^ 2 new radius = 0.5 * old radius so new area = ( 0.5 ) ^ 2 old area = > 0.25 of old area = > 25 % old area ans : c"


Question: calculate the ratio between x and y if 90 % of x equal to 60 % of y ?

<gadget id="calculator">90 / 60</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>

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

Explanation: "explanation : 90 x = 60 y x : y = 90 : 60 = 3 : 2 answer : c"


Question: find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm ?

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

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

<gadget id="calculator">(1/2) * 20</gadget>
<output>10</output>

<gadget id="calculator">10 * 50</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 100 cm 2
B. 150 cm 2
C. 200 cm 2
D. 250 cm 2
E. 500 cm 2

multiply(multiply(divide(const_1, const_2), add(5, 15)), 50)

Explanation: "1 / 2 * 50 ( 15 + 5 ) = 500 cm 2 answer : e"


Question: a right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube . if the volume of the cube is 343 cc , what approximately is the volume of the cone ?

<gadget id="calculator">343 ** (1/3)</gadget>
<output>7</output>

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

<gadget id="calculator">pi * ((7/2) ** 2) * 7 / 3</gadget>
<output>343*pi/12 = around 89.79719</output>
<result>343*pi/12 = around 89.79719</result>

Choices:
A. 80 cc
B. 90 cc
C. 110 cc
D. 105 cc
E. 100 cc

Explanation: edge of the cube = 3 √ 334 = 7 cm ∴ radius of cone = 3.5 cm height = 7 cm volume of cone = 1 ⁄ 3 π r 2 h 1 ⁄ 3 π r 2 h = 1 ⁄ 3 × 22 ⁄ 7 × ( 3.5 ) 2 × 7 = 1 ⁄ 3 × 22 × 12.25 ≈ 90 sec answer b


Question: if the given two numbers are respectively 7 % and 28 % of a third number , then what percentage is the first of the second ?

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/100) / (7/25)</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. 18 %
D. 30 %
E. none of these

multiply(divide(divide(7, const_100), divide(28, const_100)), const_100)

Explanation: "here , l = 7 and m = 28 therefore , first number = l / m x 100 % of second number = 7 / 28 x 100 % of second number = 25 % of second number answer : b"


Question: a pupil ' s marks were wrongly entered as 83 instead of 53 . due to the average marks for the class got increased by half . the number of pupils in the class is ?

<gadget id="calculator">83 - 53</gadget>
<output>30</output>

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

Choices:
A. 18
B. 82
C. 60
D. 27
E. 29

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 53 ) = > x / 2 = 30 = > x = 60 . answer : c"


Question: the area of a rhombus is equal to the area of a rectangle whose length is 20 cm and the breadth is 10 cm . if one of the diagonals is 32 cm what is the length of other diagonal ?

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

<gadget id="calculator">200 * 2</gadget>
<output>400</output>

<gadget id="calculator">400 / 32</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 10
B. 12.5
C. 15
D. 16
E. 17.5

divide(multiply(rectangle_area(20, 10), const_2), 32)

Explanation: area of rectangle = 20 x 10 = 200 cm â ² let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b


Question: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2160 less than the principal . what was the principal ?

<gadget id="calculator">4 * 5</gadget>
<output>20</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">2_160 / (4/5)</gadget>
<output>2_700</output>
<result>2_700</result>

Choices:
A. 1500
B. 2500
C. 2700
D. 3200
E. 11500

divide(2160, subtract(const_1, divide(multiply(4, 5), const_100)))

Explanation: p - 2160 = ( p * 5 * 4 ) / 100 p = 2700 answer : c


Question: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 948 in total compensation , how many total hours did he work that week ?

<gadget id="calculator">16 * 40</gadget>
<output>640</output>

<gadget id="calculator">948 - 640</gadget>
<output>308</output>

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

<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>

<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>

<gadget id="calculator">308 / 28</gadget>
<output>11</output>

<gadget id="calculator">40 + 11</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 36
B. 40
C. 44
D. 48
E. 51

add(40, divide(subtract(948, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))

Explanation: "for 40 hrs = 40 * 16 = 640 excess = 948 - 640 = 308 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 308 / 28 = 77 / 7 = 11 total hrs = 40 + 11 = 51 answer e 51"


Question: a line has a slope of 3 / 4 and intersects the point w ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?

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

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

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

<gadget id="calculator">(-12) * (3/4)</gadget>
<output>-9</output>

<gadget id="calculator">(-39) - (-9)</gadget>
<output>-30</output>

<gadget id="calculator">(-30) / (3/4)</gadget>
<output>-40</output>

<gadget id="calculator">-(-40)</gadget>
<output>40</output>

<gadget id="calculator">40 * 10</gadget>
<output>400</output>
<result>400</result>

Choices:
A. ( 40,0 )
B. ( 30,0 )
C. ( 0,40 )
D. ( 40,30 )
E. ( 0,30 )

multiply(negate(divide(subtract(negate(39), multiply(negate(12), divide(3, 4))), divide(3, 4))), const_10)

Explanation: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point w of intersection is ( 40,0 ) . a is the correct answer ."


Question: a salesman commission is 5 % on all sales upto $ 10000 and 4 % on all sales exceeding this . he remits $ 31100 to his parent company after deducting his commission . find the total sales ?

<gadget id="calculator">5 * 10_000</gadget>
<output>50_000</output>

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

<gadget id="calculator">4 * 10_000</gadget>
<output>40_000</output>

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

<gadget id="calculator">500 - 400</gadget>
<output>100</output>

<gadget id="calculator">31_100 + 100</gadget>
<output>31_200</output>

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

<gadget id="calculator">1 - (1/25)</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">31_200 / (24/25)</gadget>
<output>32_500</output>
<result>32_500</result>

Choices:
A. $ 30000
B. $ 32500
C. $ 35120
D. $ 41520
E. $ 25460

divide(add(31100, subtract(divide(multiply(5, 10000), const_100), divide(multiply(4, 10000), const_100))), subtract(const_1, divide(4, const_100)))

Explanation: let his total sales be x total sales - commission = $ 31100 x - [ ( 5 % of 10000 ) + 4 % of ( x - 10000 ) ] = 31100 x - 500 - ( x - 10000 ) / 25 = 31100 x = 32500 answer is b


Question: how much 60 % of 50 is greater than 34 % of 30 ?

<gadget id="calculator">60 * 50</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>

<gadget id="calculator">34 * 30</gadget>
<output>1_020</output>

<gadget id="calculator">1_020 / 100</gadget>
<output>51/5 = around 10.2</output>

<gadget id="calculator">30 - (51/5)</gadget>
<output>99/5 = around 19.8</output>
<result>99/5 = around 19.8</result>

Choices:
A. 18
B. 19.8
C. 11
D. 17
E. 12

subtract(divide(multiply(60, 50), const_100), divide(multiply(34, 30), const_100))

Explanation: ( 60 / 100 ) * 50 – ( 34 / 100 ) * 30 30 - 10.2 = 19.8 answer : b


Question: a man can row 5 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

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

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

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

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

<gadget id="calculator">21 / 10</gadget>
<output>21/10 = around 2.1</output>

<gadget id="calculator">(21/10) * 2</gadget>
<output>21/5 = around 4.2</output>
<result>21/5 = around 4.2</result>

Choices:
A. 5.75
B. 5.7
C. 5.76
D. 4.2
E. 5.71

multiply(divide(multiply(add(5, 2), subtract(5, 2)), add(add(5, 2), subtract(5, 2))), const_2)

Explanation: "m = 5 s = 2 ds = 7 us = 3 x / 7 + x / 3 = 1 x = 2.1 d = 2.1 * 2 = 4.2 answer : d"


Question: how long does a truck of 200 m long traveling at 60 kmph takes to cross a bridge of 180 m in length ?

<gadget id="calculator">200 + 180</gadget>
<output>380</output>

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

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">380 / (50/3)</gadget>
<output>114/5 = around 22.8</output>
<result>114/5 = around 22.8</result>

Choices:
A. 36.7
B. 26.8
C. 22.8
D. 21.1
E. 16.2

Explanation: d = 200 + 180 = 380 m s = 60 * 5 / 18 = 50 / 3 t = 380 * 3 / 50 = 22.8 sec answer : c


Question: difference between the length & breadth of a rectangle is 10 m . if its perimeter is 206 m , then its area is ?

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

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

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

Choices:
A. 2400 m ^ 2
B. 1500 m ^ 2
C. 2520 m ^ 2
D. 1200 m ^ 2
E. 2580 m ^ 2

multiply(multiply(10, const_4), multiply(10, const_3))

Explanation: solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d


Question: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?

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

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

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

<gadget id="calculator">216 / 4</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 0
B. 1
C. 27
D. 54
E. can not be determined

divide(multiply(multiply(multiply(3, 2), multiply(3, 2)), multiply(3, 2)), const_4)

Explanation: "factorization of 45 = 3 * 3 * 5 factorization of 80 = 5 * 2 ^ 4 means the smallest value of k is \ sqrt { 3 ^ 2 * 5 * 2 ^ 4 } = 3 * 5 * 2 ^ 2 k ^ 3 = 3 ^ 3 * 5 ^ 3 * 2 ^ 6 * x = 3 ^ 3 * 2 * 4000 * x where x can be any integer k ^ 3 / 4000 = 3 ^ 3 * 2 * x = 54 x which obviously has different units digit depending on x answer : d"


Question: paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 40 % of his income to sam and 60 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?

<gadget id="calculator">60 * 100</gadget>
<output>6_000</output>

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

<gadget id="calculator">60 * 80</gadget>
<output>4_800</output>

<gadget id="calculator">6_000 + 4_800</gadget>
<output>10_800</output>

<gadget id="calculator">40 * 100</gadget>
<output>4_000</output>

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

<gadget id="calculator">60 * 60</gadget>
<output>3_600</output>

<gadget id="calculator">4_000 + 3_600</gadget>
<output>7_600</output>

<gadget id="calculator">10_800 / 7_600</gadget>
<output>27/19 = around 1.421053</output>
<result>27/19 = around 1.421053</result>

Choices:
A. 11 / 12
B. 13 / 17
C. 13 / 19
D. 12 / 19
E. 27 / 19

divide(add(multiply(60, const_100), multiply(60, subtract(const_100, 20))), add(multiply(40, const_100), multiply(add(40, 20), 60)))

Explanation: make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 7.6 and q 10.8 so 10.8 / 7.6 = 2.7 / 1.9 ans : e


Question: if p / q = 3 / 7 , then 2 p + q = ?

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

<gadget id="calculator">6 + 7</gadget>
<output>13</output>
<result>13</result>

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

Explanation: "let p = 3 , q = 7 then 2 * 3 + 7 = 13 so 2 p + q = 13 . answer : c"


Question: in a box of 9 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

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

<gadget id="calculator">7 / 9</gadget>
<output>7/9 = around 0.777778</output>

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

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

<gadget id="calculator">6 / 8</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(7/9) * (3/4)</gadget>
<output>7/12 = around 0.583333</output>
<result>7/12 = around 0.583333</result>

Choices:
A. 4 / 7
B. 5 / 9
C. 6 / 11
D. 7 / 12
E. 8 / 15

multiply(divide(subtract(9, 2), 9), divide(subtract(subtract(9, 2), const_1), subtract(9, const_1)))

Explanation: "# defective pens = 2 # good pens = 7 probability of the 1 st pen being good = 7 / 9 probability of the 2 nd pen being good = 6 / 8 total probability = 7 / 9 * 6 / 8 = 7 / 12 the answer is d ."


Question: if 36 men can do a piece of work in 25 hours , in how mwny hours will 15 men do it ?

<gadget id="calculator">36 * 25</gadget>
<output>900</output>

<gadget id="calculator">900 / 15</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 22
B. 38
C. 60
D. 88
E. 72

Explanation: "explanation : let the required no of hours be x . then less men , more hours ( indirct proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 15 } = 60 hence , 15 men can do it in 60 hours . answer : c ) 60"


Question: last year the price range ( per kg ) for 100 varieties of apples in wholesale market was $ 100 . if the prices of each of the 100 varieties increased by 10 percent this year over what it was last year , what is the range of the wholesale prices of the 1000 varieties of apples this year ?

<gadget id="calculator">10 + 100</gadget>
<output>110</output>

<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">100 * (11/10)</gadget>
<output>110</output>
<result>110</result>

Choices:
A. $ 50
B. $ 100
C. $ 110
D. $ 600
E. $ 300

multiply(100, divide(add(10, const_100), const_100))

Explanation: let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c


Question: the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?

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

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

<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>

<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>

<gadget id="calculator">(5/4) * 1_600</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. rs . 2000
B. rs . 2200
C. rs . 2400
D. data inadequate
E. can not be determined

multiply(divide(add(const_100, 25), const_100), divide(add(1920, 1280), const_2))

Explanation: "explanation : let the c . p . of the article be rs . x given that % profit earned by selling article at rs . 1920 = % loss incurred by selling article at rs . 1280 ( 1920 − x / x ) ∗ 100 = ( x − 1280 / x ) ∗ 100 = > 1920 - x = x - 1280 = > 2 x = 3200 = > x = 1600 s . p . for 25 % profit = rs . 1600 + 25 % of rs . 1600 = rs . 1600 * ( 125 / 100 ) = rs . 2000 answer : a"


Question: the tailor has a 10 meter long piece of fabric for which to sew a ball room dress . she has to cuts this fabric into strips of 200 centimeters each . how long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ?

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

<gadget id="calculator">10_000 / 200</gadget>
<output>50</output>

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

<gadget id="calculator">49 * 5</gadget>
<output>245</output>
<result>245</result>

Choices:
A. 150
B. 200
C. 188
D. 245
E. 123

multiply(subtract(divide(multiply(10, const_1000), 200), const_1), 5)

Explanation: the tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes . the answer is d


Question: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 4720 votes were polled , then how many valid votes did b get ?

<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">(4/5) * 4_720</gadget>
<output>3_776</output>

<gadget id="calculator">15 * 4_720</gadget>
<output>70_800</output>

<gadget id="calculator">70_800 / 100</gadget>
<output>708</output>

<gadget id="calculator">3_776 - 708</gadget>
<output>3_068</output>

<gadget id="calculator">3_068 / 2</gadget>
<output>1_534</output>
<result>1_534</result>

Choices:
A. 1534
B. 2999
C. 2834
D. 2777
E. 2991

divide(subtract(multiply(subtract(const_1, divide(20, const_100)), 4720), divide(multiply(15, 4720), const_100)), const_2)

Explanation: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 4720 32.5 k = 32.5 k / 100 k * 4720 = 1534 the number of valid votes polled in favour of b is 1534 . answer : a"


Question: if $ 1088 are divided between worker a and worker b in the ratio 5 : 11 , what is the share that worker b will get ?

<gadget id="calculator">5 + 11</gadget>
<output>16</output>

<gadget id="calculator">1_088 / 16</gadget>
<output>68</output>
<result>68</result>

Choices:
A. 62.45 %
B. 64.55 %
C. 66.65 %
D. 68.75 %
E. 70.85 %

Explanation: "worker b will get 11 / 16 = 68.75 % the answer is d ."


Question: the average age of 6 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?

<gadget id="calculator">20 + 24</gadget>
<output>44</output>

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

<gadget id="calculator">44 + 12</gadget>
<output>56</output>

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

Choices:
A. 24
B. 25
C. 26
D. 27
E. 28

divide(add(add(20, 24), multiply(6, 2)), const_2)

Explanation: "20 + 24 + 6 * 2 = 56 / 2 = 28 answer : e"


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

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

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

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

Choices:
A. 5
B. 9
C. 10
D. 13
E. 17

Explanation: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 4 = 10 / 2 + 4 = 9 . the correct answer is b .


Question: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 500 per sq . metre .

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>

<gadget id="calculator">500 * 20.625</gadget>
<output>10_312.5</output>
<result>10_312.5</result>

Choices:
A. $ 10312.50
B. $ 13512.50
C. $ 16512.50
D. $ 14512.50
E. $ 18512.50

Explanation: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 500 hence , total cost = 5.5 × 3.75 × 500 = $ 10312.50 a"


Question: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?

<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>

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

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

Choices:
A. 34
B. 40
C. 68
D. 21
E. 78

add(multiply(divide(10, 20), const_2), 20)

Explanation: "we have : l = 20 ft and lb = 10 sq . ft . so , b = 0.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 1 ) ft = 21 ft . answer : d"


Question: each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum k in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is

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

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

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

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

Choices:
A. 90 %
B. 80 %
C. 70 %
D. 60 %
E. 40 %

subtract(add(multiply(20, const_2), multiply(20, 3)), const_10)

Explanation: the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the “ 1 – x ” technique : what ’ s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn ’ t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don ’ t ) and in which z retains value ( while x and y don ’ t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it ’ s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated — and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent .


Question: a ferry can transport 50 tons of vehicles . automobiles range in weight from 1,600 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?

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

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

<gadget id="calculator">1_000 + 100</gadget>
<output>1_100</output>

<gadget id="calculator">1_100 + 100</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 + 100</gadget>
<output>1_300</output>

<gadget id="calculator">1_300 + 100</gadget>
<output>1_400</output>

<gadget id="calculator">1_400 + 100</gadget>
<output>1_500</output>

<gadget id="calculator">1_500 + 100</gadget>
<output>1_600</output>

<gadget id="calculator">100_000 / 1_600</gadget>
<output>125/2 = around 62.5</output>
<result>125/2 = around 62.5</result>

Choices:
A. 23
B. 41
C. 48
D. 62
E. 86

divide(multiply(multiply(50, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100))

Explanation: to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d


Question: what is the ratio between perimeters of two squares one having 8 times the diagonal then the other ?

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

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

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

Explanation: "d = 8 d d = d a √ 2 = 8 d a √ 2 = d a = 8 d / √ 2 a = d / √ 2 = > 8 : 1 answer : d"


Question: a bank pays interest to its customers on the last day of the year . the interest paid to a customer is calculated as 10 % of the average monthly balance maintained by the customer . john is a customer at the bank . on the last day , when the interest was accumulated into his account , his bank balance doubled to $ 5080 . what is the average monthly balance maintained by john in his account during the year ?

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

<gadget id="calculator">5_080 * 5</gadget>
<output>25_400</output>
<result>25_400</result>

Choices:
A. 2840
B. 5680
C. 6840
D. 25400
E. 28400

Explanation: bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d


Question: a bus 75 m long is running with a speed of 21 km / hr . in what time will it pass a woman who is walking at 3 km / hr in the direction opposite to that in which the bus is going ?

<gadget id="calculator">75 * 3_600</gadget>
<output>270_000</output>

<gadget id="calculator">21 + 3</gadget>
<output>24</output>

<gadget id="calculator">270_000 / 24</gadget>
<output>11_250</output>

<gadget id="calculator">11_250 / 1_000</gadget>
<output>45/4 = around 11.25</output>
<result>45/4 = around 11.25</result>

Choices:
A. 5.75
B. 7.62
C. 11.25
D. 4.25
E. 3.25

divide(divide(multiply(75, const_3600), add(21, 3)), const_1000)

Explanation: "speed of bus relative to woman = 21 + 3 = 24 km / hr . = 24 * 5 / 18 = 20 / 3 m / sec . time taken to pass the woman = 75 * 3 / 20 = 11.25 sec . answer : c"


Question: reeya obtained 40 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average

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

<gadget id="calculator">100 + 70</gadget>
<output>170</output>

<gadget id="calculator">170 + 80</gadget>
<output>250</output>

<gadget id="calculator">250 + 80</gadget>
<output>330</output>

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

<gadget id="calculator">330 / 5</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 66
B. 75
C. 80
D. 85
E. 90

Explanation: "explanation : ( 40 + 60 + 70 + 80 + 80 / 5 ) = 66 option a"


Question: the distance from city a to city b is 100 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?

<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>

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

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

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

Choices:
A. 45
B. 48
C. 50
D. 52
E. 54

divide(100, subtract(divide(100, 40), divide(30, const_60)))

Explanation: "the time it takes bob to drive to city b is 100 / 40 = 2.5 hours . alice needs to take less than 2 hours for the trip . alice needs to exceed a constant speed of 100 / 2 = 50 miles per hour . the answer is c ."


Question: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 24 , what is the remainder when k is divided by 7 ?

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

<gadget id="calculator">17 % 7</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 2
B. 5
C. 6
D. 3
E. 8

Explanation: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 } ( less than 24 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 } ( less than 24 ) 17 is the only common number in both the sets . hence k = 17 answer : d"


Question: is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?

<gadget id="calculator">32 - 2</gadget>
<output>30</output>

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

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

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

Choices:
A. 7
B. 8
C. 9
D. 10
E. 12

multiply(divide(subtract(32, const_2), add(const_3, const_2)), const_2)

Explanation: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e"


Question: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?

<gadget id="calculator">110 + 132</gadget>
<output>242</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">242 / 20</gadget>
<output>121/10 = around 12.1</output>
<result>121/10 = around 12.1</result>

Choices:
A. 12.6
B. 12.0
C. 12.1
D. 12.3
E. 12.2

Explanation: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 20 = 12.1 sec . answer : b"


Question: mary ' s income is 60 % more than tim ' s income and tim ' s income is 60 % less than juan ' s income . what % of juan ' s income is mary ' s income .

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

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

<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>

<gadget id="calculator">40 + 24</gadget>
<output>64</output>
<result>64</result>

Choices:
A. 124 %
B. b . 120 %
C. 64 %
D. 80 %
E. 64 %

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

Explanation: "even i got 96 % j = 100 t = 100 * 0.4 = 40 m = 40 * 1.6 = 64 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 64 * 100 / 100 = 64 ans : c"


Question: 11 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?

<gadget id="calculator">factorial(11)</gadget>
<output>39_916_800</output>

<gadget id="calculator">11 - 2</gadget>
<output>9</output>

<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>

<gadget id="calculator">39_916_800 / 362_880</gadget>
<output>110</output>

<gadget id="calculator">110 / 2</gadget>
<output>55</output>

<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">56 / 2</gadget>
<output>28</output>

<gadget id="calculator">55 * 28</gadget>
<output>1_540</output>
<result>1_540</result>

Choices:
A. 80
B. 160
C. 720
D. 1100
E. 1540

multiply(divide(divide(factorial(11), factorial(subtract(11, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2))

Explanation: "no . of ways of picking 2 biology books ( from 11 books ) = 11 c 2 = ( 11 * 10 ) / 2 = 55 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 55 * 28 = 1540 ( option e )"


Question: pipe a can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes . how long it will take to fill the tank if both pipes are operating together ?

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

<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">(1/30) - (1/90)</gadget>
<output>1/45 = around 0.022222</output>

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

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

divide(const_1, subtract(divide(const_1, 30), divide(const_1, 90)))

Explanation: pipe a fills 1 / 30 th of the tank in a minute and pipe b empties 1 / 90 th of the tank ( 1 / 30 ) - ( 1 / 90 ) = ( 1 / x ) 2 / 90 = 1 / x = > x = 45 answer : d


Question: an electric pump can fill a tank in 4 hours . because of a leak in the tank , it took 8 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?

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

Choices:
A. 10 hours
B. 12 hours
C. 8 hours
D. 5 hours
E. 15 hours

Explanation: work done by the leak in 1 hour = 1 / 4 - 1 / 8 = 1 / 8 the leak will empty the tank in 8 hours answer is c


Question: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 203 ?

<gadget id="calculator">203 / 22.95</gadget>
<output>8.845316</output>

<gadget id="calculator">8.845316 * 250</gadget>
<output>2_211.329</output>
<result>2_211.329</result>

Choices:
A. 1,108
B. 2,100
C. 2,108
D. 2,120
E. 2,256

Explanation: "i think it should be d . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 6 20 - pack for 3.05 * 5 = $ 18.30 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2120"


Question: if 3 girls can do 3 times of a particular work in 3 days , then , 7 girls can do 7 times of that work in

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

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

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

Explanation: answer : option ' d ' that is , 1 girl can do one time of the work in 3 days . therefore , 7 girls can do 7 times work in the same 3 days itself .


Question: a sum fetched a total simple interest of 4043.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?

<gadget id="calculator">4_043.25 * 100</gadget>
<output>404_325</output>

<gadget id="calculator">404_325 / 9</gadget>
<output>44_925</output>

<gadget id="calculator">44_925 / 5</gadget>
<output>8_985</output>
<result>8_985</result>

Choices:
A. 5768
B. 8985
C. 2345
D. 6474
E. 8723

divide(divide(multiply(4043.25, const_100), 9), 5)

Explanation: "principal = ( 100 x 4043.25 ) / ( 9 x 5 ) = 404325 / 45 = 8985 . answer b"


Question: arun is travelling on his cycle and has calculated to reach point a at 2 pm if he travels at 10 kmph . he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?

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

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

Choices:
A. 8 kmph
B. 12 kmph
C. 10 kmph
D. 14 kmph
E. 15 kmph

Explanation: let distance be x km travelling at 10 kmph reach at 2 pm travelling at 15 kmph reach at 12 noon = > time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs x / 10 - x / 15 = 2 3 x - 2 x * 30 x = 60 time needed if travelled at 10 kmph = 60 / 10 = 6 hrs = > reach at 1 pm = > ( 6 - 1 ) = 5 hrs req speed = 60 / 5 = 12 kmph answer b


Question: rs . 600 amounts to rs . 900 in 3 years at simple interest . if the interest is increased by 4 % , it would amount to how much ?

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

<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(26/25) ** 3</gadget>
<output>17_576/15_625 = around 1.124864</output>

<gadget id="calculator">(17_576/15_625) * 600</gadget>
<output>421_824/625 = around 674.9184</output>
<result>421_824/625 = around 674.9184</result>

Choices:
A. 672
B. 246
C. 258
D. 856
E. 653

multiply(power(add(const_1, divide(4, const_100)), 3), 600)

Explanation: "( 600 * 3 * 4 ) / 100 = 72 600 + 72 = 672 answer : a"


Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions .

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

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

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

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

<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>

<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>

<gadget id="calculator">140.8 * 600</gadget>
<output>84_480</output>

<gadget id="calculator">84_480 / 100</gadget>
<output>4_224/5 = around 844.8</output>
<result>4_224/5 = around 844.8</result>

Choices:
A. 843.03 m
B. 844.03 m
C. 845.03 m
D. 846.03 m
E. 847.03 m

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 600), const_100)

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84403 cm = 844.03 m answer : b"


Question: a certain bag contains 100 balls â € ” 50 white , 25 green , 10 yellow , 7 red , and 8 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?

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

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<result>17/20 = around 0.85</result>

Choices:
A. 0.9
B. 0.85
C. 0.6
D. 0.8
E. 0.5

Explanation: according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 25 + 10 ) / 100 = 85 / 100 = 0.85 . answer is b


Question: a 1 k . m . long wire is held by n poles . if one pole is removed , the length of the gap becomes 12 / 3 m . what is the number of poles initially ?

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

<gadget id="calculator">36 * 12</gadget>
<output>432</output>

<gadget id="calculator">432 + 10</gadget>
<output>442</output>

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

<gadget id="calculator">442 + 40</gadget>
<output>482</output>

<gadget id="calculator">482 + 10</gadget>
<output>492</output>

<gadget id="calculator">492 + 10</gadget>
<output>502</output>

<gadget id="calculator">502 - 1</gadget>
<output>501</output>
<result>501</result>

Choices:
A. 500
B. 501
C. 502
D. 503
E. 504

subtract(add(add(add(add(multiply(multiply(12, 3), const_12), const_10), multiply(const_10, const_4)), const_10), const_10), 1)

Explanation: length after removing pole is 12 / 3 = 4 then before removing pole is 2 ( ' coz | 2 | 2 | is | 4 | ) i . e . gap between two poles is 2 m 1 km = 1000 m then split 1000 m by 2 m = > we have 500 sections or gaps then no . of poles is 500 + 1 st pole = 501 poles therefore n = 501 . answer : b


Question: a certain deep blue paint contains 45 percent blue pigment and 55 percent red pigment by weight . a certain green paint contains 35 percent blue pigment and 65 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?

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

<gadget id="calculator">55 / 200</gadget>
<output>11/40 = around 0.275</output>

<gadget id="calculator">(11/40) * 10</gadget>
<output>11/4 = around 2.75</output>
<result>11/4 = around 2.75</result>

Choices:
A. 1.5
B. 2.5
C. 3.5
D. 2.75
E. 4.5

multiply(divide(55, multiply(const_100, const_2)), 10)

Explanation: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 55 = 2.75 grams of red pigment


Question: the average expenditure of a labourer for 6 months was 95 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i

<gadget id="calculator">95 * 6</gadget>
<output>570</output>

<gadget id="calculator">60 * 4</gadget>
<output>240</output>

<gadget id="calculator">570 + 240</gadget>
<output>810</output>

<gadget id="calculator">810 + 30</gadget>
<output>840</output>

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

<gadget id="calculator">840 / 10</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 70
B. 72
C. 75
D. 78
E. 84

divide(add(add(multiply(95, 6), multiply(60, 4)), 30), add(6, 4))

Explanation: "income of 6 months = ( 6 × 95 ) – debt = 570 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 840 average monthly income = 840 ÷ 10 = 84 answer e"


Question: if 60 % of 3 / 5 of a number is 18 , then the number is ?

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

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

<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">18 / (9/25)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 80
B. 100
C. 75
D. 50
E. none of these

divide(18, multiply(divide(60, const_100), divide(3, 5)))

Explanation: "let the number be x . then 60 % of 3 / 5 of x = 18 60 / 100 * 3 / 5 * x = 18 x = ( 18 * 25 / 9 ) = 50 required number = 50 . correct option : d"


Question: a driver just filled the car ' s gas tank with 18 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?

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

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

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

Choices:
A. 1
B. 1.5
C. 1.8
D. 2.4
E. 3

divide(multiply(18, 5), subtract(const_100, 10))

Explanation: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 18 ) + x = 0.1 ( 18 + x ) 0.9 x = 1.8 - 0.9 x = 1 liter the answer is a ."