Question: the ratio of the present age of viju to that of aju is 7 : 2 . 4 years from now , the ratio of the ages of viju to aju will be 5 : 2 . what was viju age 5 years ago ? ( rbi assistant 2015 )

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

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

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

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

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

<gadget id="calculator">7 * 6</gadget>
<output>42</output>

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

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

Choices:
A. 24
B. 18
C. 12
D. 16
E. 13

subtract(divide(multiply(7, divide(subtract(multiply(5, 4), multiply(2, 4)), subtract(7, 5))), 2), 5)

Explanation: let the present age of viju be 7 x years and that of aju be 2 x years . then , 4 years from now 7 x + 4 / 2 x + 4 = 5 / 2 or 4 x = 12 or x = 3 viju present age = 7 * 3 = 21 years viju age 5 years ago = 21 - 5 = 16 years answer : d


Question: yesterday it took robert 3 hours to drive from city a to city b . today it took robert 2.5 hours to drive back from city в to city a along the same route . if he had saved 30 minutes in both trips , the speed for the round trip would be 80 miles per hour . what is the distance between city a and city b ?

<gadget id="calculator">3 + 2.5</gadget>
<output>5.5</output>

<gadget id="calculator">5.5 - 1</gadget>
<output>4.5</output>

<gadget id="calculator">80 * 4.5</gadget>
<output>360</output>

<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 90
B. 180
C. 150
D. 240
E. 300

divide(multiply(80, subtract(add(3, 2.5), const_1)), const_2)

Explanation: "2 d / 80 = 4.5 ( because time = 3 + 2.5 - 1 hrs ) = > d = 180 answer - b"


Question: if abc = ab ^ 3 = 180 where a , b and c are positive integers , what is the value of ` c ’ ?

<gadget id="calculator">180 / 180</gadget>
<output>1</output>

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

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

Explanation: abc = a ( b ^ 3 ) = 180 on solving abc = a ( b ^ 3 ) we get c = b ^ 2 and for a ( b ^ 3 ) = 180 , there is only one possibility a = 180 and b = 1 so c = 1 ^ 2 = 1 answer : b


Question: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 95 % water by weight . what is the new weight of the cucumbers , in pounds ?

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

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

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

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

Choices:
A. 2
B. 20
C. 92
D. 96
E. 98

multiply(divide(subtract(100, 99), subtract(100, 95)), 100)

Explanation: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 95 % water and 5 % of non - water , so now 1 pound of non - water composes 5 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.05 = 20 pounds . answer : b ."


Question: a customer went to a shop and paid a total of $ 40 , out of which $ 1.28 was for sales tax on taxable purchases . if the tax rate was 8 % , then what was the cost of the tax free items ?

<gadget id="calculator">40 - 1.28</gadget>
<output>38.72</output>

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

<gadget id="calculator">38.72 - 16</gadget>
<output>22.72</output>
<result>22.72</result>

Choices:
A. $ 19.54
B. $ 2076
C. $ 21.36
D. $ 22.72
E. $ 23.58

subtract(subtract(40, 1.28), multiply(8, const_2))

Explanation: "the total cost was $ 40 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 40 - $ 16 - $ 1.28 = $ 22.72 the answer is d ."


Question: the average of first 12 even numbers is ?

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

Choices:
A. 19
B. 18
C. 16
D. 13
E. 17

Explanation: "sum of 12 even numbers = 12 * 13 = 156 average = 156 / 12 = 13 answer : d"


Question: if all 6 are replaced by 9 , the algebric sum of all numbers from 1 to 100 ( both inclusive ) varies by ,

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

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

<gadget id="calculator">3 * 100</gadget>
<output>300</output>

<gadget id="calculator">30 + 300</gadget>
<output>330</output>
<result>330</result>

Choices:
A. 980
B. 330
C. 660
D. 990
E. 300

add(multiply(subtract(9, 6), const_10), multiply(subtract(9, 6), const_100))

Explanation: 6 , 16,26 , 36,46 , 56,76 , 86,96 replace by 9 then 3 * 9 = 27 60,61 , 62,63 , 64,65 , 66,67 , 68,69 then increase by 30 i . e , 30 * 10 = 300 + 3 99 - 66 = 33 - 30 it will be 330 answer : b


Question: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number h of employees who take the subway to work ?

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

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

<gadget id="calculator">144 / 12</gadget>
<output>12</output>

<gadget id="calculator">48 - 12</gadget>
<output>36</output>

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

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

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

add(divide(multiply(48, 3), multiply(3, 4)), divide(subtract(48, multiply(3, 4)), divide(multiply(48, 3), multiply(3, 4))))

Explanation: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible h : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"


Question: a batsman in his 12 th innings makes a score of 60 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?

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

<gadget id="calculator">60 - 24</gadget>
<output>36</output>

<gadget id="calculator">36 + 2</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 38
B. 43
C. 44
D. 45
E. 46

Explanation: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 60 ∴ x = 38 answer a"


Question: john can complete a given task in 18 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 6 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?

<gadget id="calculator">18 * 12</gadget>
<output>216</output>

<gadget id="calculator">12 * 6</gadget>
<output>72</output>

<gadget id="calculator">216 - 72</gadget>
<output>144</output>

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

<gadget id="calculator">144 / 30</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">6 + (24/5)</gadget>
<output>54/5 = around 10.8</output>
<result>54/5 = around 10.8</result>

Choices:
A. 11
B. 34 / 5
C. 44 / 5
D. 54 / 5
E. 12

add(6, divide(subtract(multiply(18, 12), multiply(12, 6)), add(12, 18)))

Explanation: "in such questions , you need to start from the end . last 4 days john works alone and completes 6 * ( 1 / 18 ) = 1 / 3 of the work . so 2 / 3 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 18 + 1 / 12 = 5 / 36 time taken to complete 2 / 3 of the work = ( 2 / 3 ) / ( 5 / 36 ) = 24 / 5 days . so total number of days taken to complete the work = 24 / 5 + 6 = 54 / 5 days . d"


Question: a man walks at a rate of 10 mph . after every ten miles , he rests for 7 minutes . how much time does he take to walk 50 miles ?

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

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

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

<gadget id="calculator">28 + 300</gadget>
<output>328</output>
<result>328</result>

Choices:
A. 300
B. 318
C. 322
D. 328
E. 330

add(multiply(7, const_4), multiply(divide(50, 10), const_60))

Explanation: "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 7 = 28 minutes . total time = 300 + 28 = 328 minutes . answer : d ."


Question: by selling an article for $ 225 a person gains $ 75 . what is the gain % ?

<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>

<gadget id="calculator">225 - 75</gadget>
<output>150</output>

<gadget id="calculator">7_500 / 150</gadget>
<output>50</output>
<result>50</result>

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

divide(multiply(75, const_100), subtract(225, 75))

Explanation: "s . p . = $ 225 gain = $ 75 c . p . = 225 - 75 = 150 gain % = 75 / 150 * 100 = 50 % answer is c"


Question: a mixture of 150 liters of wine and water contains 15 % water . how much more water should be added so that water becomes 25 % of the new mixture ?

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

<gadget id="calculator">(1/4) * 150</gadget>
<output>75/2 = around 37.5</output>

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

<gadget id="calculator">(3/20) * 150</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">(75/2) - (45/2)</gadget>
<output>15</output>

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

<gadget id="calculator">15 / (3/4)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 10
B. 30
C. 20
D. 15
E. 17

divide(subtract(multiply(divide(25, const_100), 150), multiply(divide(15, const_100), 150)), subtract(const_1, divide(25, const_100)))

Explanation: "number of liters of water in 150 liters of the mixture = 15 % of 150 = 15 / 100 * 150 = 22.5 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 22.5 + p ) and total volume of mixture is ( 150 + p ) . ( 22.5 + p ) = 25 / 100 * ( 150 + p ) 90 + 4 p = 150 + p p = 20 liters . answer : c"


Question: it is only in the second option we find the sentence a in continuation with the opening sentence d . sentence a alone explains , why the fear has such enormous effect on the human beings .

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

Choices:
A. 28
B. 99
C. 728
D. 27
E. 271

Explanation: answer : b


Question: on a sum of money , the simple interest for 2 years is rs . 327 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is

<gadget id="calculator">327 / 2</gadget>
<output>327/2 = around 163.5</output>

<gadget id="calculator">340 - (327/2)</gadget>
<output>353/2 = around 176.5</output>

<gadget id="calculator">(353/2) - (327/2)</gadget>
<output>13</output>

<gadget id="calculator">100 * 13</gadget>
<output>1_300</output>

<gadget id="calculator">1_300 / (327/2)</gadget>
<output>2_600/327 = around 7.95107</output>
<result>2_600/327 = around 7.95107</result>

Choices:
A. 15 %
B. 14.25 %
C. 7.95 %
D. 10.5 %
E. 11.5 %

divide(multiply(const_100, subtract(subtract(340, divide(327, 2)), divide(327, 2))), divide(327, 2))

Explanation: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 327 = 13 ( r ã — si ) / ( 2 ã — 100 ) = 13 ( r ã — 327 ) / ( 2 ã — 100 ) = 13 r = 7.95 % answer : option c"


Question: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 120 years . can you tell me my age in years ?

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

<gadget id="calculator">120 / 20</gadget>
<output>6</output>

<gadget id="calculator">6 * 12</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 65
B. 72
C. 44
D. 73
E. 89

multiply(divide(120, add(const_10, const_10)), const_12)

Explanation: "b i am 72 years old . let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 120 years , g + s + m = 120 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows . m / 12 + 365 m / ( 52 x 12 ) + m = 120 or 52 m + 365 m + 624 m = 624 x 120 or m = 624 x 120 / 1041 = 72 . so , i am 72 years old ."


Question: the ratio between speed of the two trains is 7 : 8 . if the 2 nd train runs 400 km in 4 hrs , what is the speed of the 1 st train ?

<gadget id="calculator">400 / 4</gadget>
<output>100</output>

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

<gadget id="calculator">100 * (7/8)</gadget>
<output>175/2 = around 87.5</output>
<result>175/2 = around 87.5</result>

Choices:
A. 87.9
B. 87.5
C. 87.7
D. 87.6
E. 43.3

Explanation: answer : b explanation : speed of 2 nd train = 400 / 4 = 100 kmph since the ratios are in 7 : 8 speed of first train = 7 / 8 × 100 = 87.5 kmph answer : b


Question: the circulation for magazine p in 1961 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1962 - 1970 . what is the ratio of the circulation in 1961 to the total circulation during 1961 - 1970 for magazine p ?

<gadget id="calculator">1_970 - 1_962</gadget>
<output>8</output>

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

<gadget id="calculator">9 + 4</gadget>
<output>13</output>

<gadget id="calculator">13 + 1</gadget>
<output>14</output>

<gadget id="calculator">4 / 14</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>

Choices:
A. 2 / 7
B. 5 / 7
C. 3 / 7
D. 4 / 7
E. 1 / 7

divide(4, add(add(add(subtract(1970, 1962), const_1), 4), const_1))

Explanation: "there are 9 years from 1962 - 1970 , inclusive . let ' s say the average circulation every year between 1962 - 1970 inclusive is x . so the total circulation is 9 x from 1962 - 1970 , inclusive . in 1961 , the circulation is 4 x . so total circulation for 1961 - 1970 is 4 x + 9 x = 13 x . ratio of circulation in 1961 to total circulation during 1961 - 1970 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : a"


Question: in how many years rs 100 will produce the same interest at 5 % as rs . 200 produce in 2 years at 10 %

<gadget id="calculator">200 * 10</gadget>
<output>2_000</output>

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

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

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

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

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

Choices:
A. 8
B. 10
C. 9
D. 12
E. 11

divide(multiply(divide(multiply(200, 10), const_100), 2), multiply(divide(5, const_100), 100))

Explanation: "explanation : clue : firstly we need to calculate the si with prinical 200 , time 2 years and rate 10 % , it will be rs . 40 then we can get the time as time = ( 100 * 40 ) / ( 100 * 5 ) = 8 option a"


Question: the profit obtained by selling an article for rs . 54 is the same as the loss obtained by selling it for rs . 40 . what is the cost price of the article ?

<gadget id="calculator">54 + 40</gadget>
<output>94</output>

<gadget id="calculator">94 / 2</gadget>
<output>47</output>
<result>47</result>

Choices:
A. rs . 40
B. rs . 50
C. rs . 49
D. rs . 59
E. rs . 47

Explanation: "s . p 1 - c . p = c . p – s . p 2 54 - c . p = c . p - 40 2 c . p = 54 + 40 ; c . p = 94 / 2 = 47 answer : e"


Question: mary , peter , and lucy were picking chestnuts . mary picked twice as much chestnuts than peter . lucy picked 2 kg more than peter . together the 3 of them picked 26 kg of chestnuts . how many kilograms did mary pick ?

<gadget id="calculator">26 - 2</gadget>
<output>24</output>

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

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

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

Choices:
A. 12
B. 24
C. 48
D. 52
E. 37

multiply(divide(subtract(26, 2), add(2, 2)), 2)

Explanation: let x be the amount peter picked . then mary and lucy picked 2 x and x + 2 x , respectively . so x + 2 x + x + 2 = 26 4 x = 24 x = 6 so 2 x = 2 * 6 = 12 correct answer is a ) 12


Question: a train traveling at 72 kmph crosses a platform in 35 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>

<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>

<gadget id="calculator">20 * 35</gadget>
<output>700</output>

<gadget id="calculator">20 * 18</gadget>
<output>360</output>

<gadget id="calculator">700 - 360</gadget>
<output>340</output>
<result>340</result>

Choices:
A. 340 meters
B. 360 meters
C. 420 meters
D. 600 meters
E. can not be determined

subtract(multiply(divide(multiply(72, const_1000), const_3600), 35), multiply(divide(multiply(72, const_1000), const_3600), 18))

Explanation: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 35 = 700 m . so , length of platform = 700 - 360 = 340 m imo , answer a"


Question: a train of 30 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?

<gadget id="calculator">30 + 1</gadget>
<output>31</output>

<gadget id="calculator">31 * 60</gadget>
<output>1_860</output>

<gadget id="calculator">1_860 / 1_000</gadget>
<output>93/50 = around 1.86</output>

<gadget id="calculator">(93/50) + 1.5</gadget>
<output>3.36</output>
<result>3.36</result>

Choices:
A. 6
B. 3.3
C. 4
D. 9
E. 2

add(divide(multiply(add(30, const_1), 60), const_1000), 1.5)

Explanation: "d = 30 * 60 + 1500 = 3300 m t = 3300 / 60 * 18 / 5 = 198 sec = 3.3 mins answer : b"


Question: in the manufacture of a certain product , 8 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

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

<gadget id="calculator">8 * (1/20)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 0.2 %
B. 0.4 %
C. 0.8 %
D. 1.2 %
E. 2.0 %

Explanation: "0.08 * 0.05 = 0.004 = 0.4 % the answer is b ."


Question: a number when divided by 779 gives a remainder 47 . by dividing the same number by 19 , what would be the remainder ?

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

<gadget id="calculator">47 - 38</gadget>
<output>9</output>
<result>9</result>

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

Explanation: "number = ( 779 x a ) + 47 , where ` ` a ' ' is the quotient = ( 19 x 41 x a ) + ( 19 x 2 ) + 9 = 19 x ( 41 a + 2 ) + 9 = 19 x ( new quotient ) + 9 \ inline \ fn _ jvn \ therefore required remainder = 9 answer : a"


Question: the cost price of 30 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?

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

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

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

Choices:
A. 20
B. 21
C. 23
D. 25
E. 27

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

Explanation: "let the cost price = y the cost price of 30 articles = 30 y the selling price of x articles = 1.20 y * x 1.20 y * x = 30 y x = 30 / 1.2 = 25 the answer is d ."


Question: if 32.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?

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

<gadget id="calculator">100 - 32.5</gadget>
<output>67.5</output>

<gadget id="calculator">(44/5) * 67.5</gadget>
<output>594</output>
<result>594</result>

Choices:
A. 110
B. 330
C. 550
D. 594
E. 880

multiply(divide(880, const_100), subtract(const_100, 32.5))

Explanation: "students enrolled in biology are 32.5 % and therefore not enrolled are 67.5 % . so of 880 is 880 * . 675 = 594 answer is d 594"


Question: a sum fetched a total simple interest of $ 4151.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?

<gadget id="calculator">4_151.25 * 100</gadget>
<output>415_125</output>

<gadget id="calculator">415_125 / 9</gadget>
<output>46_125</output>

<gadget id="calculator">46_125 / 5</gadget>
<output>9_225</output>
<result>9_225</result>

Choices:
A. $ 8829
B. $ 2840
C. $ 6578
D. $ 7782
E. $ 8928

divide(divide(multiply(4151.25, const_100), 9), 5)

Explanation: "e 8928 principal = $ 100 x 4151.25 / 9 x 5 = $ 415125 / 45 = $ 8928 ."


Question: a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip . if the average speed for the entire trip is 34 miles per hour , how many hours long is the trip ?

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

<gadget id="calculator">30 * 5</gadget>
<output>150</output>

<gadget id="calculator">170 - 150</gadget>
<output>20</output>

<gadget id="calculator">42 - 34</gadget>
<output>8</output>

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

<gadget id="calculator">(5/2) + 5</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>

Choices:
A. 6.5
B. 7.5
C. 8.5
D. 9.5
E. 10.5

add(divide(subtract(multiply(34, 5), multiply(30, 5)), subtract(42, 34)), 5)

Explanation: let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 34 t 8 t = 210 - 150 t = 7.5 the answer is b .


Question: if jack walked 6 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?

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

<gadget id="calculator">15 + 60</gadget>
<output>75</output>

<gadget id="calculator">360 / 75</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>

Choices:
A. 4
B. 4.8
C. 6
D. 6.25
E. 15

divide(multiply(6, const_60), add(15, const_60))

Explanation: "distance walked in 1 hour and 15 mins = 6 miles speed per hour = distance / time = 6 / ( 5 / 4 ) = 4.8 miles per hour answer b"


Question: in a group of cows and hens , the number of legs are 8 more than twice the number of heads . the number of cows is :

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

Choices:
A. 5
B. 6
C. 7
D. 10
E. 4

Explanation: let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 8 2 x = 8 x = 4 . answer : e


Question: the number of positive integer solutions for the equation x + y + z + t = 30 is

Choices:
A. 3854
B. 3654
C. 3764
D. 3960
E. 4964

divide(factorial(subtract(30, const_1)), multiply(factorial(subtract(const_4, const_1)), factorial(subtract(subtract(30, const_1), subtract(const_4, const_1)))))

Explanation: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 30 - 1 c 4 - 1 = 29 c 3 = 3654 answer : b"


Question: reeya obtained 55 , 67 , 76 , 82 and 85 out of 100 in different subjects , what will be the average

<gadget id="calculator">55 + 67</gadget>
<output>122</output>

<gadget id="calculator">122 + 76</gadget>
<output>198</output>

<gadget id="calculator">198 + 82</gadget>
<output>280</output>

<gadget id="calculator">280 + 85</gadget>
<output>365</output>

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

<gadget id="calculator">365 / 5</gadget>
<output>73</output>
<result>73</result>

Choices:
A. 70
B. 75
C. 73
D. 85
E. 90

Explanation: "explanation : ( 55 + 67 + 76 + 82 + 85 / 5 ) = 73 option c"


Question: one night 17 percent of the female officers on a police force were on duty . if 204 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?

<gadget id="calculator">204 / 2</gadget>
<output>102</output>

<gadget id="calculator">17 / 100</gadget>
<output>17/100 = around 0.17</output>

<gadget id="calculator">102 / (17/100)</gadget>
<output>600</output>
<result>600</result>

Choices:
A. 420
B. 480
C. 540
D. 600
E. 660

divide(divide(204, const_2), divide(17, const_100))

Explanation: "let x be the number of female police officers on the police force . the number of female police officers on duty was 102 . 0.17 x = 102 x = 600 the answer is d ."


Question: the workforce of company x is 60 % female . the company hired 24 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?

<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">(11/20) * 24</gadget>
<output>66/5 = around 13.2</output>

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

<gadget id="calculator">(3/5) - (11/20)</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(66/5) / (1/20)</gadget>
<output>264</output>

<gadget id="calculator">264 + 24</gadget>
<output>288</output>
<result>288</result>

Choices:
A. 160
B. 220
C. 288
D. 360
E. 420

add(divide(multiply(divide(55, const_100), 24), subtract(divide(60, const_100), divide(55, const_100))), 24)

Explanation: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 24 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 24 ) 0.05 x = 13.2 x = 264 - this is quantity of employees before adding 24 men so after adding it will be 288 answer is c"


Question: 1370 , x , 1070 , - 180 , - 6430

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

<gadget id="calculator">1_370 - 180</gadget>
<output>1_190</output>

<gadget id="calculator">20 + 1_190</gadget>
<output>1_210</output>

<gadget id="calculator">1_210 + 100</gadget>
<output>1_310</output>
<result>1_310</result>

Choices:
A. 1320
B. 6530
C. 6630
D. 6730
E. 6830

add(add(multiply(const_10, const_2), subtract(1370, 180)), const_100)

Explanation: 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a .


Question: the perimeter of a square is equal to the perimeter of a rectangle of length 17 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )

<gadget id="calculator">14 + 17</gadget>
<output>31</output>

<gadget id="calculator">2 * 31</gadget>
<output>62</output>

<gadget id="calculator">62 / 4</gadget>
<output>31/2 = around 15.5</output>

<gadget id="calculator">(31/2) / 2</gadget>
<output>31/4 = around 7.75</output>

<gadget id="calculator">2 * pi * (31/4)</gadget>
<output>31*pi/2 = around 48.694686</output>

<gadget id="calculator">(31*pi/2) / 2</gadget>
<output>31*pi/4 = around 24.347343</output>

<gadget id="calculator">floor(31*pi/4)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 23.57
B. 23.54
C. 23.5
D. 24.35
E. 24.51

floor(divide(circumface(divide(divide(multiply(const_2, add(14, 17)), const_4), const_2)), const_2))

Explanation: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 17 + 14 ) = 62 cm perimeter of the square = 62 cm i . e . 4 a = 62 a = 15.5 diameter of the semicircle = 15.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 15.5 ) = 1 / 2 ( 22 / 7 ) ( 15.5 ) = 24.35 cm to two decimal places answer : d"


Question: ? % of 360 = 180

<gadget id="calculator">180 * 100</gadget>
<output>18_000</output>

<gadget id="calculator">18_000 / 360</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 277
B. 36
C. 50
D. 72
E. none of these

Explanation: "? % of 360 = 180 or , ? = 180 × 100 / 360 = 50 answer c"


Question: the average of runs of a cricket player of 10 innings was 33 . 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">4 + 33</gadget>
<output>37</output>

<gadget id="calculator">11 * 37</gadget>
<output>407</output>

<gadget id="calculator">10 * 33</gadget>
<output>330</output>

<gadget id="calculator">407 - 330</gadget>
<output>77</output>
<result>77</result>

Choices:
A. 77
B. 79
C. 85
D. 87
E. 89

subtract(multiply(add(10, const_1), add(4, 33)), multiply(10, 33))

Explanation: "explanation : average = total runs / no . of innings = 33 so , total = average x no . of innings = 33 x 10 = 330 . now increase in avg = 4 runs . so , new avg = 33 + 4 = 37 runs total runs = new avg x new no . of innings = 37 x 11 = 407 runs made in the 11 th inning = 407 - 330 = 77 answer : a"


Question: the average score of a cricketer in 2 matches is 60 and in other 3 matches is 50 . then find the average score in all the 5 matches ?

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

<gadget id="calculator">3 * 50</gadget>
<output>150</output>

<gadget id="calculator">120 + 150</gadget>
<output>270</output>

<gadget id="calculator">270 / 5</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 54
B. 27
C. 30
D. 35
E. 42

divide(add(multiply(2, 60), multiply(3, 50)), 5)

Explanation: "average in 5 matches = ( 2 * 60 + 3 * 50 ) / 2 + 3 = 120 + 150 / 5 = 270 / 5 = 54 answer is a"


Question: albert invested rs . 8000 in a scheme for 2 years at compound interest rate 5 % p . a . how much amount will albert get on maturity of the fixed deposit ?

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

<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>

<gadget id="calculator">8_000 * (441/400)</gadget>
<output>8_820</output>
<result>8_820</result>

Choices:
A. 8840
B. 2776
C. 2998
D. 2662
E. 8820

multiply(8000, power(add(const_1, divide(5, const_100)), 2))

Explanation: "amount = [ 8000 * ( 1 + 5 / 100 ) 2 ] = 8000 * 21 / 20 * 21 / 20 = rs . 8820 answer : e"


Question: a person buys an article at $ 600 . at what price should he sell the article so as to make a profit of 8 % ?

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

<gadget id="calculator">600 * (2/25)</gadget>
<output>48</output>

<gadget id="calculator">600 + 48</gadget>
<output>648</output>
<result>648</result>

Choices:
A. 670
B. 689
C. 648
D. 740
E. 889

add(600, multiply(600, divide(8, const_100)))

Explanation: "c 648 cost price = $ 600 profit = 8 % of 600 = $ 48 selling price = cost price + profit = 600 + 48 = 648"


Question: what is the remainder when ( 63 ) ( 65 ) is divided by 8 ?

<gadget id="calculator">65 * 63</gadget>
<output>4_095</output>

<gadget id="calculator">4_095 % 8</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 1
B. 2
C. 4
D. 5
E. 7

Explanation: "( 63 ) ( 65 ) = ( 64 - 1 ) ( 64 + 1 ) = 64 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ."


Question: if shares of two persons in profits are rs . 1600 and rs . 1200 then ratio of their capitals is

<gadget id="calculator">1_600 / 1_200</gadget>
<output>4/3 = around 1.333333</output>
<result>4/3 = around 1.333333</result>

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

Explanation: "profit = time * capital so 1600 : 1200 = 4 : 3 answer : c"


Question: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 148 cookies , what percent of the cookies did ingrid bake ?

<gadget id="calculator">148 * 5.17</gadget>
<output>765.16</output>

<gadget id="calculator">9.18 + 5.17</gadget>
<output>14.35</output>

<gadget id="calculator">14.35 + 2.05</gadget>
<output>16.4</output>

<gadget id="calculator">765.16 / 16.4</gadget>
<output>46.656098</output>

<gadget id="calculator">46.656098 / 148</gadget>
<output>0.315244</output>

<gadget id="calculator">0.315244 * 100</gadget>
<output>31.5244</output>
<result>31.5244</result>

Choices:
A. 0.125 %
B. 1.25 %
C. 31.7 %
D. 125 %
E. 0.152 %

Explanation: 9.18 x + 5.17 x + 2.05 x = 16.4 x = 148 cookies x = 148 / 16.4 = 9 ( approx ) so , ingrid baked 9 * 5.17 cookies or 47 cookies ( approx ) % share = 47 / 148 = 31.7 approx hence , answer is c .


Question: two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 3 . find the larger integer .

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

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

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

<gadget id="calculator">18 * 4</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 4
B. 24
C. 30
D. 72
E. 80

multiply(divide(multiply(3, 6), subtract(4, 3)), 4)

Explanation: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 6 to the smaller integer makes the ratio 1 to 3 , then 3 ( x + 6 ) = y . substituting y = 4 x into the second equation yields 3 x + 18 = 4 x . so , x = 18 ( smaller integer ) and , y = 4 x = 72 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 4 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 1 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 1 ) , we get 7 . so , the new ratio is 7 to 4 . no good . we want a resulting ratio of 1 to 3 eliminate a b ) the larger number is 24 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 6 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 6 ) , we get 12 so , the new ratio is 12 to 24 which is 1 to 2 . no good . we want a resulting ratio of 1 to 3 eliminate b c ) the larger number is 30 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 7.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 30 . eliminate c d ) the larger number is 72 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 18 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 18 ) , we get 24 so , the new ratio is 24 to 72 . this is the same as the ratio of 1 to 3 therefore ( d ) is correct e ) the larger number is 80 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 20 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 20 ) , we get 26 so , the new ratio is 26 to 80 which is 13 to 40 . no good . we want a resulting ratio of 1 to 3 eliminate e therefore d is the only correct choice ."


Question: a , b and c are partners in a business . their capitals are respectively , rs . 5000 , rs . 6000 and rs . 4000 . a gets 30 % of the total profit for managing the business . the remaining profit is divided among 3 in the ratio of their capitals . in the end of the year , the profit of a is rs . 200 more than the sum of the profits of b and c . find the total profit ?

<gadget id="calculator">5_000 + 6_000</gadget>
<output>11_000</output>

<gadget id="calculator">11_000 + 4_000</gadget>
<output>15_000</output>

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

<gadget id="calculator">15_000 / 1_000</gadget>
<output>15</output>

<gadget id="calculator">15 * 200</gadget>
<output>3_000</output>
<result>3_000</result>

Choices:
A. 3089
B. 3098
C. 3057
D. 3000
E. 3012

multiply(divide(add(add(5000, 6000), 4000), multiply(const_100, const_10)), 200)

Explanation: a : b : c = 5 : 6 : 4 let the total profit = 100 - 30 = 70 5 / 15 * 70 = 70 / 3 a share = 70 / 3 + 30 = 160 / 3 b + c share = 100 - 160 / 3 = 140 / 3 a - ( b + c ) = 160 / 3 - 140 / 3 = 20 / 3 20 / 3 - - - - 200 100 - - - - ? = > 3000 answer : d


Question: $ 100 is divided amongst a , b and c so that a may get 1 / 4 as much as b and c together , b may get 3 / 5 as much as a and c together , then the share of a is

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

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

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

<gadget id="calculator">80 * (1/4)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. $ 15
B. $ 20
C. $ 25
D. $ 18
E. $ 30

multiply(divide(100, add(divide(1, 4), const_1)), divide(1, 4))

Explanation: "a : ( b + c ) = 1 : 4 a ' s share = 100 * 1 / 5 = $ 20 answer is b"


Question: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 3 red ?

<gadget id="calculator">binomial(6, 1)</gadget>
<output>6</output>

<gadget id="calculator">binomial(5, 3)</gadget>
<output>10</output>

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

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

<gadget id="calculator">11 + 8</gadget>
<output>19</output>

<gadget id="calculator">binomial(19, 4)</gadget>
<output>3_876</output>

<gadget id="calculator">60 / 3_876</gadget>
<output>5/323 = around 0.01548</output>
<result>5/323 = around 0.01548</result>

Choices:
A. 1 / 969
B. 2 / 969
C. 4 / 969
D. 5 / 323
E. 21 / 789

divide(multiply(choose(6, 1), choose(5, 3)), choose(add(add(5, 6), 8), 4))

Explanation: sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue balls and 3 red were drawn from bag = 6 c 1 * 5 c 3 = 60 probability = 60 / 3876 = 5 / 323 ans - d


Question: how many positive even integers less than 100 contain digits 5 or 9 ?

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

Choices:
A. 16
B. 10
C. 18
D. 19
E. 20

Explanation: two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 9 at tens place : 90 , 92,94 , 96,98 if 5 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer b


Question: farm tax is levied on the 45 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :

<gadget id="calculator">480 / 3_840</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 100</gadget>
<output>1_250</output>

<gadget id="calculator">1_250 / 45</gadget>
<output>250/9 = around 27.777778</output>
<result>250/9 = around 27.777778</result>

Choices:
A. 15 %
B. 25 %
C. 15.125 %
D. 27.78 %
E. none

divide(multiply(multiply(divide(480, 3840), const_100), const_100), 45)

Explanation: "only trick n this question is to ignore 45 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 45 ) = 27.78 % and the answer is not there in the options . the correct answer is ( d ) ."


Question: johnson completes a piece of work in 10 days , vincent completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is

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

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">(1/10) + (1/40)</gadget>
<output>1/8 = around 0.125</output>

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

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

Explanation: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days . b )


Question: in triangle pqr , the angle q = 90 degree , pq = 4 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">4 * 8</gadget>
<output>32</output>

<gadget id="calculator">32 / 10</gadget>
<output>16/5 = around 3.2</output>
<result>16/5 = around 3.2</result>

Choices:
A. 1.2 cm
B. 2.4 cm
C. 4.8 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 : 4 = 8 : 10 - - > qy = 3.2 . answer : e"


Question: a local elementary school has 1049 students and 9 teachers , how many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom ?

<gadget id="calculator">1_049 / 9</gadget>
<output>1_049/9 = around 116.555556</output>

<gadget id="calculator">floor(1_049/9)</gadget>
<output>116</output>

<gadget id="calculator">9 * 116</gadget>
<output>1_044</output>

<gadget id="calculator">1_049 - 1_044</gadget>
<output>5</output>

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

Choices:
A. 4
B. 6
C. 5
D. 1
E. 2

subtract(9, subtract(1049, multiply(9, floor(divide(1049, 9)))))

Explanation: using the rule on the divisibility of nine , we add the digits of 1049 together to get 14 . since we are doing addition , the next number that is divisible by nine would be 18 . therefore , our answer 4 ( option a )


Question: the average marks of 30 students in a class is 100 . but a student mark is wrongly noted as 70 instead of 10 then find the correct average marks ?

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

<gadget id="calculator">3_000 - 70</gadget>
<output>2_930</output>

<gadget id="calculator">2_930 + 10</gadget>
<output>2_940</output>

<gadget id="calculator">2_940 / 30</gadget>
<output>98</output>
<result>98</result>

Choices:
A. 78
B. 82
C. 98
D. 91
E. 85

divide(add(subtract(multiply(100, 30), 70), 10), 30)

Explanation: "correct avg marks = 100 + ( 10 - 70 ) / 30 avg = 100 - 2 = 98 answer is c"


Question: a 440 - liter solution of kola is made from 88 % water , 8 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?

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

<gadget id="calculator">440 * (22/25)</gadget>
<output>1_936/5 = around 387.2</output>

<gadget id="calculator">440 - (1_936/5)</gadget>
<output>264/5 = around 52.8</output>

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

<gadget id="calculator">440 * (2/25)</gadget>
<output>176/5 = around 35.2</output>

<gadget id="calculator">(264/5) - (176/5)</gadget>
<output>88/5 = around 17.6</output>

<gadget id="calculator">(88/5) + 3.2</gadget>
<output>20.8</output>

<gadget id="calculator">440 + 3.2</gadget>
<output>443.2</output>

<gadget id="calculator">443.2 + 10</gadget>
<output>453.2</output>

<gadget id="calculator">453.2 + 6.8</gadget>
<output>460</output>

<gadget id="calculator">20.8 / 460</gadget>
<output>0.045217</output>

<gadget id="calculator">0.045217 * 100</gadget>
<output>4.5217</output>
<result>4.5217</result>

Choices:
A. 4.52 % .
B. 7.5 % .
C. 9.2 % .
D. 10.5 % .
E. 11 % .

multiply(divide(add(subtract(subtract(440, multiply(440, divide(88, const_100))), multiply(440, divide(8, const_100))), 3.2), add(add(add(440, 3.2), 10), 6.8)), const_100)

Explanation: "denominator : 440 + 10 + 3.2 + 6.8 = 460 numerator : 440 ( 1 - . 88 - . 08 ) + 3.2 440 ( 0.04 ) + 3.2 17.6 + 3.2 20.8 ratio : 20.8 / 460 = 0.045 answer : a"


Question: a wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule , whose length and breadth are in the ratio of 6 : 5 . what is the area of the rectangle ?

Choices:
A. 65 cm 2
B. 30 cm 2
C. 76 cm 2
D. 68 cm 2
E. 46 cm 2

rectangle_area(multiply(6, divide(circumface(3.5), multiply(add(6, 5), const_2))), multiply(5, divide(circumface(3.5), multiply(add(6, 5), const_2))))

Explanation: the circumference of the circle is equal to the permeter of the rectangle . let l = 6 x and b = 5 x 2 ( 6 x + 5 x ) = 2 * 22 / 7 * 3.5 = > x = 1 therefore l = 6 cm and b = 5 cm area of the rectangle = 6 * 5 = 30 cm 2 answer : b


Question: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 50 marks . how many sums did sandy get correct ?

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

<gadget id="calculator">60 + 50</gadget>
<output>110</output>

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

<gadget id="calculator">110 / 5</gadget>
<output>22</output>
<result>22</result>

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

divide(add(multiply(2, 30), 50), add(2, 3))

Explanation: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 50 5 x = 110 x = 22 the answer is b ."


Question: a person borrows 20000 for 6 years at 8 % p . a . simple interest . he immediately lends it to another person at 9 % p . a . for 6 years . find his gain in the transaction per year .

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

<gadget id="calculator">20_000 * (1/100)</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 200
B. 250
C. 210
D. 190
E. 180

Explanation: gain in 6 years = [ ( 20000 ã — 9 ã — 6 / 100 ) â ˆ ’ ( 20000 ã — 6 ã — 8 / 100 ) ] = ( 10800 â € “ 9600 ) = 1200 â ˆ ´ gain in 6 year = ( 1200 / 6 ) = 200 answer a


Question: if m is a positive integer and m ^ 2 is divisible by 24 , then the largest positive integer that must divide m is ?

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

<gadget id="calculator">8 / 3</gadget>
<output>8/3 = around 2.666667</output>

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

Choices:
A. 3
B. 6
C. 8
D. 12
E. 16

multiply(const_3, divide(divide(24, const_3), const_3))

Explanation: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 8 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? c"


Question: a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be ?

<gadget id="calculator">17.5 / 40.25</gadget>
<output>0.434783</output>

<gadget id="calculator">28.75 * 0.434783</gadget>
<output>12.500011</output>
<result>12.500011</result>

Choices:
A. 10 m
B. 12.5 m
C. 12 m
D. 13 m
E. 14 m

Explanation: "let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : b"


Question: average monthly income of a family of 4 earning members was rs . 840 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?

<gadget id="calculator">840 * 4</gadget>
<output>3_360</output>

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

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

<gadget id="calculator">3_360 - 1_950</gadget>
<output>1_410</output>
<result>1_410</result>

Choices:
A. rs . 692.80
B. rs . 820
C. rs . 990
D. rs . 1410
E. none

subtract(multiply(840, 4), multiply(650, subtract(4, const_1)))

Explanation: answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 840 x 4 - 650 x 3 rs . = 1410 rs . correct option : d


Question: x and y are two towns . ganesh covers the distance from x to y at an average speed of 43 km / hr . however , he covers the distance from y to x at an average speed of 34 km / hr . his average speed during the whole journey in km / hr . is :

<gadget id="calculator">43 - 10</gadget>
<output>33</output>

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

<gadget id="calculator">133 + 133</gadget>
<output>266</output>

<gadget id="calculator">133 / 43</gadget>
<output>133/43 = around 3.093023</output>

<gadget id="calculator">133 / 34</gadget>
<output>133/34 = around 3.911765</output>

<gadget id="calculator">(133/43) + (133/34)</gadget>
<output>10_241/1_462 = around 7.004788</output>

<gadget id="calculator">266 / (10_241/1_462)</gadget>
<output>2_924/77 = around 37.974026</output>
<result>2_924/77 = around 37.974026</result>

Choices:
A. 34
B. 43
C. 40
D. 38
E. 29

divide(add(add(subtract(43, const_10), const_100), add(subtract(43, const_10), const_100)), add(divide(add(subtract(43, const_10), const_100), 43), divide(add(subtract(43, const_10), const_100), 34)))

Explanation: "solution : average speed = 2 xy / x + y = 2 * 43 * 34 / 43 + 34 = 2924 / 77 = 37.974 . . . = 38 answer : d"


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

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

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

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


Question: visitors to show were charged rs . 15 each on the first day . rs . 7.50 on the second day , rs . 2.50 on the third day and total attendance on the 3 days were in ratio 2 : 5 : 13 respectively . the average charge per person for the whole show is ?

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

<gadget id="calculator">7.5 * 5</gadget>
<output>37.5</output>

<gadget id="calculator">30 + 37.5</gadget>
<output>67.5</output>

<gadget id="calculator">2.5 * 13</gadget>
<output>32.5</output>

<gadget id="calculator">67.5 + 32.5</gadget>
<output>100</output>

<gadget id="calculator">13 + 5</gadget>
<output>18</output>

<gadget id="calculator">18 + 2</gadget>
<output>20</output>

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

Choices:
A. 1
B. 4
C. 5
D. 6
E. 8

divide(add(add(multiply(15, 2), multiply(7.5, 5)), multiply(2.5, 13)), add(add(13, 5), 2))

Explanation: 2 : 5 : 13 2 x 5 x 13 x 15 7.5 2.5 30 x + 37.5 x + 32.5 x = 100 x / 20 x average = 5 answer : c


Question: hillary and eddy are climbing to the summit of mt . everest from a base camp 4,900 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 900 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?

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

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

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

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

<gadget id="calculator">800 / 900</gadget>
<output>8/9 = around 0.888889</output>

<gadget id="calculator">500 / 900</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">(8/9) - (5/9)</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">(5/9) + 1</gadget>
<output>14/9 = around 1.555556</output>

<gadget id="calculator">(5/3) / (14/9)</gadget>
<output>15/14 = around 1.071429</output>

<gadget id="calculator">4 / (8/9)</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">(15/14) + (9/2)</gadget>
<output>39/7 = around 5.571429</output>

<gadget id="calculator">6 + (39/7)</gadget>
<output>81/7 = around 11.571429</output>
<result>81/7 = around 11.571429</result>

Choices:
A. 10.0
B. 11.0
C. 13.0
D. 12.0
E. 14.0

add(06, add(divide(multiply(divide(subtract(divide(500, const_100), const_1), divide(800, 1,000)), subtract(divide(800, 900), divide(500, 900))), add(divide(500, 900), const_1)), divide(subtract(divide(500, const_100), const_1), divide(800, 900))))

Explanation: "solution : h stopped 900 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . d"


Question: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 70 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?

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

<gadget id="calculator">170 / 100</gadget>
<output>17/10 = around 1.7</output>

<gadget id="calculator">36 / (17/10)</gadget>
<output>360/17 = around 21.176471</output>

<gadget id="calculator">33 - (360/17)</gadget>
<output>201/17 = around 11.823529</output>

<gadget id="calculator">(201/17) / (360/17)</gadget>
<output>67/120 = around 0.558333</output>
<result>67/120 = around 0.558333</result>

Choices:
A. 1 : 120
B. 67 : 120
C. 67 : 8
D. 8 : 120
E. 1 : 2

divide(subtract(33, divide(36, divide(add(const_100, 70), const_100))), divide(36, divide(add(const_100, 70), const_100)))

Explanation: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 20 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.70 = $ 36 cost = 36 / 1.7 = 360 / 12 = $ 30 if he wants a 70 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 21.17 well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 21.17 / 33 = 120 / 187 of a liter . if milk is 120 / 87 of the liter , then water is 67 / 187 of the liter , and the ratio of water to milk is 67 : 120 . answer choice ( b )"


Question: the price of a book is increased from $ 300 to $ 390 . what is the % of increase in its price ?

<gadget id="calculator">390 - 300</gadget>
<output>90</output>

<gadget id="calculator">90 / 300</gadget>
<output>3/10 = around 0.3</output>

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

Choices:
A. 10 %
B. 20 %
C. 30 %
D. 35 %
E. 45 %

multiply(divide(subtract(390, 300), 300), const_100)

Explanation: "explanation : change in the price = rs 390 – rs 300 = rs 90 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 90 / 300 ) * 100 = 30 % c"


Question: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 1170 , what will be b ' s share of the earnings ?

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

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

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

<gadget id="calculator">(1/6) + (1/8)</gadget>
<output>7/24 = around 0.291667</output>

<gadget id="calculator">(1/12) + (7/24)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(1/8) / (3/8)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1_170 * (1/3)</gadget>
<output>390</output>
<result>390</result>

Choices:
A. $ 390
B. $ 520
C. $ 1080
D. $ 1170
E. $ 630

multiply(1170, divide(inverse(8), add(inverse(12), add(inverse(6), inverse(8)))))

Explanation: "explanatory answer a , b and c will share the amount of $ 1170 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 1170 will be 4 : 3 : 2 . hence , b ' s share will be 3 * 1170 / 9 = 390 . correct choice is ( a )"


Question: if jack walked 8 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?

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

<gadget id="calculator">15 + 60</gadget>
<output>75</output>

<gadget id="calculator">480 / 75</gadget>
<output>32/5 = around 6.4</output>
<result>32/5 = around 6.4</result>

Choices:
A. 4
B. 4.5
C. 6
D. 6.4
E. 15

divide(multiply(8, const_60), add(15, const_60))

Explanation: "distance walked in 1 hour and 15 mins = 8 miles speed per hour = distance / time = 8 / ( 5 / 4 ) = 6.4 miles per hour answer d"


Question: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 67 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

<gadget id="calculator">75 - 67</gadget>
<output>8</output>

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

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

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

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

divide(subtract(75, 67), subtract(const_1, divide(80, const_100)))

Explanation: "there are 8 books less ( 75 - 68 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 40 answer d"


Question: if a farmer wants to plough a farm field on time , he must plough 120 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?

<gadget id="calculator">2 * 85</gadget>
<output>170</output>

<gadget id="calculator">40 + 170</gadget>
<output>210</output>

<gadget id="calculator">120 - 85</gadget>
<output>35</output>

<gadget id="calculator">210 / 35</gadget>
<output>6</output>

<gadget id="calculator">6 * 120</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 600
B. 490
C. 720
D. 435
E. 679

multiply(divide(add(40, multiply(2, 85)), subtract(120, 85)), 120)

Explanation: let x be the number of days in the initial plan . therefore , the whole field is 120 ⋅ x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 120 x = 85 ( x + 2 ) + 40 35 x = 210 x = 6 so the farmer planned to have the work done in 6 days , and the area of the farm field is 120 ⋅ 6 = 720 hectares correct answer c


Question: for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?

<gadget id="calculator">1.7 * 40</gadget>
<output>68</output>

<gadget id="calculator">1.2 * 40</gadget>
<output>48</output>

<gadget id="calculator">68 - 48</gadget>
<output>20</output>
<result>20</result>

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

subtract(multiply(1.70, 40), multiply(1.20, 40))

Explanation: "the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 40 * $ 0.50 = $ 20 the answer is d ."


Question: in a school of 300 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?

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

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

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

<gadget id="calculator">300 * 18</gadget>
<output>5_400</output>

<gadget id="calculator">5_400 / 100</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 54
B. 63
C. 70
D. 42
E. 31

divide(multiply(300, subtract(const_100, add(add(44, 28), 10))), const_100)

Explanation: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 300 * 18 / 100 = 54 answer : a"


Question: a number x is 12 times another number y . the percentage that y is less than x is

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

<gadget id="calculator">11 / 12</gadget>
<output>11/12 = around 0.916667</output>

<gadget id="calculator">(11/12) * 100</gadget>
<output>275/3 = around 91.666667</output>
<result>275/3 = around 91.666667</result>

Choices:
A. 91.6 %
B. 87.5 %
C. 80 %
D. 11 %
E. 1 %

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

Explanation: "say y = 1 and x = 12 . then y = 1 is less than x = 12 by ( 12 - 1 ) / 12 * 100 = 11 / 12 * 100 = 91.6 % . answer : a ."


Question: a train 90 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?

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

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

<gadget id="calculator">66 * (5/18)</gadget>
<output>55/3 = around 18.333333</output>

<gadget id="calculator">90 / (55/3)</gadget>
<output>54/11 = around 4.909091</output>
<result>54/11 = around 4.909091</result>

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

divide(90, multiply(add(60, 6), const_0_2778))

Explanation: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 90 * 3 / 55 = 5 sec . answer d"


Question: the average age of a family of 5 members is 20 years . if the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member ?

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

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

<gadget id="calculator">90 / 4</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">(45/2) - 10</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 13.5
B. 14
C. 15
D. 12.5
E. none

subtract(divide(subtract(multiply(5, 20), 10), const_4), 10)

Explanation: solution : at present the total age of the family = 5 * 20 = 100 . the total age of the family at the time of the birth of the youngest member , = [ 100 − 10 − ( 10 * 4 ) ] = 50 . therefore , average age of the family at the time of birth of the youngest member , = 50 / 4 = 12.5 . answer : option d


Question: how many unique positive odd integers less than 90 are equal to the product of a positive multiple of 5 and an odd number ?

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

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

Choices:
A. 4
B. 9
C. 11
D. 12
E. 15

Explanation: "the question basically asks how many positive odd integers less than 90 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , 55,65 , 75,85 = 9 ans b"


Question: if # is an operation which results in adding the digits of integer until a single digit is left , what is the probability that a number picked up in first 90 positive integers will have the result of # as an odd digit ? ( example 99 = 9 + 9 = 18 = 1 + 8 = 9 , so # = 9 )

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

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

<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<result>5/9 = around 0.555556</result>

Choices:
A. 4 / 10
B. 4 / 9
C. 1 / 2
D. 6 / 10
E. 5 / 9

Explanation: first of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90 . that will be 17 ( 8 + 9 + 17 ) why did i calculate this ? i will come to that in a moment . so to get an odd digit by carrying out the operation # , the sum of the digits of the integer should be 1 , 3 , 5 , 7 , 9 , 10 , 12 , 14 , and 16 ( why not 18 ? because we know the maximum sum can be 17 ) number of integers , whose digits add to 1 : 1 and 10 = 2 number of integers , whose digits add to 3 : 3 , 12 , 21 , 30 = 4 number of integers , whose digits add to 5 : 5 , 14 , 23 , 32 , 41 , 50 = 6 number of integers , whose digits add to 7 : 7 , 16 , 25 , 34 , 43 , 52 , 61 , 70 = 8 number of integers , whose digits add to 9 : 10 multiples of 9 up to 90 = 10 number of integers , whose digits add to 10 : 19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 = 8 number of integers , whose digits add to 12 : 39 , 48 , 57 , 66 , 75 , 84 = 6 number of integers , whose digits add to 14 : 59 , 68 , 77 , 86 = 4 number of integers , whose digits add to 16 : 79 , 88 = 2 so in total there are 2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2 = 50 such numbers probability = 50 / 90 = 5 / 9 correct answer e


Question: jerry and michelle play a card game . in the beginning of the game they have an equal number of cards . each player , at her turn , gives the other a third of her cards . michelle plays first , giving jerry a third of her cards . jerry plays next , and michelle follows . then the game ends . jerry ended up with 14 more cards than michelle . how many cards did each player have originally ?

<gadget id="calculator">14 * 3</gadget>
<output>42</output>

<gadget id="calculator">42 - 14</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 27
B. 30
C. 34
D. 36
E. 38

Explanation: game michelle jerry michelle initially 2727 assume after game 1 1836 after game 2 3024 after game 3 2034 now jerry has 14 cards more than michelle . so the answer is a


Question: a circular swimming pool is surrounded by a concrete wall 4 feet wide . if the area of the wall is 11 / 25 of the area of the pool , then the radius of the pool in feet is ?

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

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

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

<gadget id="calculator">(11/25) * 4</gadget>
<output>44/25 = around 1.76</output>

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

<gadget id="calculator">(44/25) * 16</gadget>
<output>704/25 = around 28.16</output>

<gadget id="calculator">64 + (704/25)</gadget>
<output>2_304/25 = around 92.16</output>

<gadget id="calculator">(2_304/25) ** (1/2)</gadget>
<output>48/5 = around 9.6</output>

<gadget id="calculator">8 + (48/5)</gadget>
<output>88/5 = around 17.6</output>

<gadget id="calculator">(88/5) / (11/25)</gadget>
<output>40</output>

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

Choices:
A. 22
B. 20
C. 9
D. 8
E. 1

divide(divide(add(multiply(const_2, 4), sqrt(add(power(multiply(const_2, 4), const_2), multiply(multiply(divide(11, 25), const_4), power(4, const_2))))), divide(11, 25)), const_2)

Explanation: let the radius of the pool be r . then area of the wall and pool = π ( r + 4 ) 2 π ( r + 4 ) 2 area of the pool = π ( r ) 2 π ( r ) 2 area of the wall = π ( r + 4 ) 2 − π ( r ) 2 π ( r + 4 ) 2 − π ( r ) 2 given π ( r + 4 ) 2 − π ( r ) 2 π ( r + 4 ) 2 − π ( r ) 2 = 1125 ( π r 2 ) 1125 ( π r 2 ) r 2 + 8 r + 16 − r 2 = 1125 r 2 r 2 + 8 r + 16 − r 2 = 1125 r 2 11 r 2 − 200 r − 400 = 011 r 2 − 200 r − 400 = 0 solving r = 20 answer : b


Question: a truck travels 20 miles due north , 30 miles due east , and then 20 miles due north . how many miles is the truck from the starting point ?

<gadget id="calculator">20 ** 2</gadget>
<output>400</output>

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

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

<gadget id="calculator">400 + 225</gadget>
<output>625</output>

<gadget id="calculator">625 ** (1/2)</gadget>
<output>25</output>

<gadget id="calculator">25 + 25</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 20.3
B. 44.7
C. 50
D. 70
E. 120

add(sqrt(add(power(20, const_2), power(divide(30, const_2), const_2))), sqrt(add(power(20, const_2), power(divide(30, const_2), const_2))))

Explanation: we have two right angle triangles with sides 20 and 15 the distance between starting and end point = sum of the hypotenuse of both the triangles . hypotenuse = [ 400 + 225 ] ^ ( 1 / 2 ) = 25 hence the total distance between end point and starting point = 25 + 25 = 50 correct option : c


Question: find the area of a parallelogram with base 22 cm and height 14 cm ?

<gadget id="calculator">22 * 14</gadget>
<output>308</output>
<result>308</result>

Choices:
A. 298 cm 2
B. 384 cm 2
C. 308 cm 2
D. 286 cm 2
E. 276 cm 2

Explanation: "area of a parallelogram = base * height = 22 * 14 = 308 cm 2 answer : c"


Question: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 4180 . what was his original salary ?

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

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

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

<gadget id="calculator">1 - (1/20)</gadget>
<output>19/20 = around 0.95</output>

<gadget id="calculator">(11/10) * (19/20)</gadget>
<output>209/200 = around 1.045</output>

<gadget id="calculator">4_180 / (209/200)</gadget>
<output>4_000</output>
<result>4_000</result>

Choices:
A. 2277
B. 2999
C. 4000
D. 2651
E. 1971

divide(4180, multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(5, const_100))))

Explanation: "x * ( 110 / 100 ) * ( 95 / 100 ) = 4180 x * ( 11 / 10 ) * ( 1 / 100 ) = 44 x = 4000 answer : c"


Question: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum t of all the digits of the integers from 0 to 99 inclusive ?

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

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

<gadget id="calculator">90 / 2</gadget>
<output>45</output>

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

<gadget id="calculator">45 * 20</gadget>
<output>900</output>
<result>900</result>

Choices:
A. 450
B. 810
C. 900
D. 1000
E. 1100

multiply(divide(multiply(9, add(9, 1)), 2), multiply(2, const_10))

Explanation: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just t = 900 : the answer is c ."


Question: in δ pqs above , if pq = 2 and ps = 3 , then

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

Choices:
A. 3 / 2
B. 12 / 5
C. 16 / 5
D. 15 / 4
E. 20 / 3

Explanation: there are two ways to calculate area of pqs . area remains same , so both are equal . 2 * 3 / 2 = pr * 4 / 2 pr = 3 / 2 a


Question: a man whose speed is 8 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 3 kmph , find his average speed for the total journey ?

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

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

<gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>
<result>13/2 = around 6.5</result>

Choices:
A. 1 kmph
B. 5 kmph
C. 6 kmph
D. 4 kmph
E. 6.8 kmph

Explanation: "explanation : speed of man = 8 kmph speed of stream = 3 kmph speed in downstream = 11 kmph speed in upstream = 5 kmph average speed = ( 2 x 11 x 5 ) / 16 = 6.8 kmph . answer : e"


Question: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 9 feet between each tree . how many trees can be planted if the road is 151 feet long ?

<gadget id="calculator">151 - 1</gadget>
<output>150</output>

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

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

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

Choices:
A. 8
B. 9
C. 10
D. 11
E. 16

add(divide(subtract(151, const_1), add(9, const_1)), const_1)

Explanation: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 9 feet spaces will be t - 1 . then , the length of sidewalk required for 9 feet spaces will be 9 * ( t - 1 ) it is given that total lenght of sidewalk is 151 feet . or 9 ( t - 1 ) + t = 151 or 9 t - 9 + t = 151 or 10 t = 160 or t = 16 answer : - e"


Question: the slant height of a cone is 35 cm and radius of the base is 14 cm , find the curved surface of the cone .

<gadget id="calculator">pi * 14</gadget>
<output>14*pi = around 43.982297</output>

<gadget id="calculator">(14*pi) * 35</gadget>
<output>490*pi = around 1_539.3804</output>
<result>490*pi = around 1_539.3804</result>

Choices:
A. 4150
B. 1780
C. 1540
D. 1500
E. 6100

Explanation: π * 14 * 35 = 1540 answer : c


Question: if a ã — b = 2 a - 3 b + ab , then 3 ã — 2 + 2 ã — 3 is equal to :

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

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

<gadget id="calculator">6 - 6</gadget>
<output>0</output>

<gadget id="calculator">0 + 6</gadget>
<output>6</output>

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

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

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

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

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

Choices:
A. 7
B. 8
C. 9
D. 25
E. 26

add(add(subtract(multiply(2, 3), multiply(3, 2)), multiply(3, 2)), add(subtract(multiply(2, 2), multiply(3, 3)), multiply(2, 3)))

Explanation: "explanation : 3 ã — 2 + 2 ã — 3 = ( 2 ã — 3 - 3 ã — 2 + 2 ã — 3 ) + ( 2 ã — 2 - 3 ã — 3 + 2 ã — 3 ) = ( 6 + 4 - 9 + 6 ) = 7 . answer : a"


Question: a 20 % stock yielding 12 % is quoted at :

<gadget id="calculator">100 / 12</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">(25/3) * 20</gadget>
<output>500/3 = around 166.666667</output>
<result>500/3 = around 166.666667</result>

Choices:
A. rs . 83.33
B. rs . 167
C. rs . 112
D. rs . 120
E. rs . 140

Explanation: "income of rs 12 on investment of rs 100 income of rs 20 on investment of ? = ( 20 * 100 ) / 12 = 167 answer : b"


Question: if the length of the sides of two cubes are in the ratio 6 : 1 , what is the ratio of their total surface area ?

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

Choices:
A. 6 : 1
B. 12 : 1
C. 24 : 1
D. 36 : 1
E. 72 : 1

Explanation: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 6 x ) ^ 2 = 216 x ^ 2 . the ratio of surface areas is 36 : 1 . the answer is d ."


Question: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 12 seconds . the length of the faster train is

<gadget id="calculator">36 + 45</gadget>
<output>81</output>

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

<gadget id="calculator">81 * (5/18)</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">(45/2) * 12</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 80 m
B. 270 m
C. 120 m
D. 180 m
E. none

multiply(multiply(add(36, 45), const_0_2778), 12)

Explanation: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 12 ) m = 270 m . answer b"


Question: if the perimeter of a rectangular garden is 1800 m , its length when its breadth is 400 m is ?

<gadget id="calculator">1_800 / 2</gadget>
<output>900</output>

<gadget id="calculator">900 - 400</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 500
B. 600
C. 700
D. 800
E. 900

Explanation: 2 ( l + 400 ) = 1800 = > l = 500 m answer : a


Question: sarah is driving to the airport . after driving at 15 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 60 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?

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

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

Choices:
A. 45
B. 175
C. 210
D. 245
E. 280

Explanation: after driving at 15 miles per hourfor one hour , this distance left to cover is d - 15 . say this distance is x miles . now , we know that the difference in time between covering this distance at 15 miles per hour and 60 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 15 - x / 60 = 3 / 2 - - > 4 x / 60 - x / 60 = 3 / 2 - - > 3 x / 60 = 3 / 2 - - > x = 30 . total distance = x + 15 = 45 miles . answer : a


Question: a shopkeeper sells 600 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?

<gadget id="calculator">18_000 / 600</gadget>
<output>30</output>

<gadget id="calculator">30 + 5</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 12
B. 27
C. 29
D. 35
E. 21

Explanation: sp per metre = 18000 / 600 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d


Question: a certain number of men can finish a piece of work in 100 days . if there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?

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

<gadget id="calculator">100 / 110</gadget>
<output>10/11 = around 0.909091</output>

<gadget id="calculator">1 - (10/11)</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">10 / (1/11)</gadget>
<output>110</output>
<result>110</result>

Choices:
A. 120
B. 105
C. 115
D. 110
E. 140

divide(10, subtract(const_1, divide(100, add(100, 10))))

Explanation: originally let there be x men . less men , more days ( indirect proportion ) therefore ( x - 10 ) : x : : 100 : 110 = ( x - 10 ) x 110 - x ( 100 ) = 10 x = 1100 x = 110 answer is d .


Question: find the cost of fencing around a circular field of diameter 16 m at the rate of rs . 3 a meter ?

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

<gadget id="calculator">2 * pi * 8</gadget>
<output>16*pi = around 50.265482</output>

<gadget id="calculator">(16*pi) * 3</gadget>
<output>48*pi = around 150.796447</output>
<result>48*pi = around 150.796447</result>

Choices:
A. 150.84
B. 160.6
C. 150.45
D. 160.99
E. 180.4

Explanation: "2 * 22 / 7 * 8 = 50.28 50.28 * 3 = rs . 150.84 answer : a"


Question: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3200 . with the help of c , they completed the work in 3 days . how much is to be paid to c

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

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

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

<gadget id="calculator">(1/8) + (1/6)</gadget>
<output>7/24 = around 0.291667</output>

<gadget id="calculator">(1/3) - (7/24)</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">(1/24) * 3_200</gadget>
<output>400/3 = around 133.333333</output>

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

Choices:
A. rs . 300
B. rs . 400
C. rs . 500
D. rs . 600
E. none of these

multiply(multiply(subtract(inverse(3), add(inverse(8), inverse(6))), 3200), 3)

Explanation: "explanation : c ' s 1 day ' s work = 1 / 3 − ( 1 / 6 + 1 / 8 ) = ( 1 / 3 − 7 / 24 ) = 1 / 24 a : b : c = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ′ sshare = 1 / 8 ∗ 3200 = 400 option b"


Question: a worker can load one truck in 6 hours . a second worker can load the same truck in 4 hours . if both workers load one truck simultaneously while maintaining their constant rates , how long , in hours , will it take them to fill one truck ?

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

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

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

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

Choices:
A. 2.1
B. 2.4
C. 2.7
D. 3.0
E. 3.3

inverse(add(divide(const_1, 6), divide(const_1, 4)))

Explanation: the workers fill the truck at a rate of 1 / 6 + 1 / 4 = 10 / 24 = 5 / 12 of the truck per hour . then the time to fill one truck is 12 / 5 which is 2.4 hours . the answer is b .


Question: 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 3 like all . how many people like apple ?

<gadget id="calculator">40 - 3</gadget>
<output>37</output>

<gadget id="calculator">37 + 7</gadget>
<output>44</output>

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

<gadget id="calculator">44 + 3</gadget>
<output>47</output>
<result>47</result>

Choices:
A. 47
B. 46
C. 54
D. 58
E. 62

add(add(subtract(40, const_3), 7), subtract(10, 7))

Explanation: orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 3 40 + 10 + 3 - 7 = 46 like apple answer : b


Question: 3 candidates in an election and received 1256 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?

<gadget id="calculator">1_256 + 7_636</gadget>
<output>8_892</output>

<gadget id="calculator">8_892 + 11_628</gadget>
<output>20_520</output>

<gadget id="calculator">11_628 / 20_520</gadget>
<output>17/30 = around 0.566667</output>

<gadget id="calculator">(17/30) * 100</gadget>
<output>170/3 = around 56.666667</output>
<result>170/3 = around 56.666667</result>

Choices:
A. 56.7 %
B. 55 %
C. 57 %
D. 60 %
E. 62 %

Explanation: "total number of votes polled = ( 1256 + 7636 + 11628 ) = 20520 so , required percentage = 11628 / 20520 * 100 = 56.7 % a"


Question: the ratio of the radius of two circles is 1 : 3 , and then the ratio of their areas is ?

<gadget id="calculator">pi * (1 ** 2)</gadget>
<output>pi = around 3.141593</output>

<gadget id="calculator">pi * (3 ** 2)</gadget>
<output>9*pi = around 28.274334</output>

<gadget id="calculator">pi / (9*pi)</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

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

Explanation: "r 1 : r 2 = 1 : 3 π r 12 : π r 22 r 12 : r 22 = 1 : 9 answer : c"


Question: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 63 more . what was his original selling price ?

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

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

<gadget id="calculator">(9/10) * (13/10)</gadget>
<output>117/100 = around 1.17</output>

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(117/100) - (11/10)</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">63 / (7/100)</gadget>
<output>900</output>

<gadget id="calculator">900 * (11/10)</gadget>
<output>990</output>
<result>990</result>

Choices:
A. $ 850
B. $ 990
C. $ 1050
D. $ 1180
E. $ 1340

multiply(divide(63, subtract(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(30, const_100))), add(const_1, divide(10, const_100)))), add(const_1, divide(10, const_100)))

Explanation: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 63 0.07 = 63 p = 900 the original selling price was 900 * 1.1 = 990 . the correct answer is b ."


Question: one - third of 1206 is what percent of 162 ?

<gadget id="calculator">1_206 / 3</gadget>
<output>402</output>

<gadget id="calculator">402 / 162</gadget>
<output>67/27 = around 2.481481</output>

<gadget id="calculator">100 * (67/27)</gadget>
<output>6_700/27 = around 248.148148</output>
<result>6_700/27 = around 248.148148</result>

Choices:
A. 324.11
B. 300.12
C. 248.14
D. none of these
E. can not be determined

multiply(const_100, divide(divide(1206, const_3), 162))

Explanation: "answer let one - third of 1206 is n % of 162 . ∵ 1206 / 3 = ( n x 162 ) / 100 ∴ n = ( 402 x 100 ) / 162 = 248.14 correct option : c"


Question: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 50 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?

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

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

<gadget id="calculator">(1/10) * (1/2)</gadget>
<output>1/20 = around 0.05</output>

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

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

Choices:
A. 10.5 %
B. 12.5 %
C. 15 %
D. 22 %
E. 20 %

divide(const_100, multiply(multiply(divide(10, const_100), divide(50, const_100)), const_100))

Explanation: 0.1 m = 0.50 e = > e / m = 1 / 5 * 100 = 20 % so answer is e . m - # of motorists e - # of motorists exceeding speed


Question: in a group of 7 boys and 8 girls , 5 members are to be selected . in how many different ways can they be selected such that at least 3 boys should be there ?

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

<gadget id="calculator">5_040 * 5_040</gadget>
<output>25_401_600</output>

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

<gadget id="calculator">25_401_600 / 40_320</gadget>
<output>630</output>

<gadget id="calculator">630 * 2</gadget>
<output>1_260</output>

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

<gadget id="calculator">1_260 + 21</gadget>
<output>1_281</output>
<result>1_281</result>

Choices:
A. 1200
B. 1500
C. 1281
D. 1339
E. 1296

add(multiply(divide(multiply(factorial(7), factorial(7)), factorial(8)), const_2), multiply(3, 7))

Explanation: no of boys = 7 no of girls = 8 therefore , no of ways at least 3 boy can be selected = 7 c 5 * 8 c 0 + 7 c 4 * 8 c 1 + 7 c 3 * 8 c 2 = 1281 ans - c


Question: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x + 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?

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

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

<gadget id="calculator">3 / 12</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>

Choices:
A. 1 / 12
B. 1 / 6
C. 1 / 4
D. 1 / 3
E. 1 / 2

Explanation: roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = - 5 , x = - 10 andx = 5 / 2 = 2.5 . so , three solutions present in our set of 12 distinct numbers , therefore p = 3 / 12 = 1 / 4 . answer : c .


Question: a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is

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

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

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

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

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

<gadget id="calculator">1 - (18/25)</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/25) * 100</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28 %
B. 30 %
C. 32 %
D. 38 %
E. 40 %

multiply(subtract(const_1, multiply(divide(subtract(const_100, 20), const_100), divide(subtract(const_100, 10), const_100))), const_100)

Explanation: "let original length = x and original breadth = y . decrease in area = xy - 80 x x 90 y 100 100 = xy - 18 xy 25 = 7 xy . 25 decrease % = 7 xy x 1 x 100 % = 28 % . 25 xy a )"


Question: the average of 10 numbers is calculated as 18 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?

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

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

<gadget id="calculator">18 + 1</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 16
B. 18
C. 19
D. 22
E. 24

Explanation: "explanation : 10 * 18 + 36 – 26 = 190 = > 190 / 10 = 19 c )"


Question: the speed of a boat in still water in 42 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 44 minutes is :

<gadget id="calculator">42 + 5</gadget>
<output>47</output>

<gadget id="calculator">44 / 60</gadget>
<output>11/15 = around 0.733333</output>

<gadget id="calculator">47 * (11/15)</gadget>
<output>517/15 = around 34.466667</output>
<result>517/15 = around 34.466667</result>

Choices:
A. 86.6 km
B. 46.6 km
C. 34.5 km
D. 35.6 km
E. 26.6 km

multiply(add(42, 5), divide(44, const_60))

Explanation: "speed downstream = ( 42 + 5 ) = 47 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 47 = 34.5 km answer : c"


Question: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1240 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?

<gadget id="calculator">30 + 1</gadget>
<output>31</output>

<gadget id="calculator">30 * 31</gadget>
<output>930</output>

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

<gadget id="calculator">60 + 1</gadget>
<output>61</output>

<gadget id="calculator">930 * 61</gadget>
<output>56_730</output>

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

<gadget id="calculator">56_730 / 6</gadget>
<output>9_455</output>

<gadget id="calculator">9_455 - 1_240</gadget>
<output>8_215</output>
<result>8_215</result>

Choices:
A. 2480
B. 3490
C. 6785
D. 8215
E. 9255

subtract(divide(multiply(multiply(30, add(30, 1)), add(multiply(2, 30), 1)), add(3, 3)), 1240)

Explanation: "sum of square of n numbers is found using the formula [ n ( n + 1 ) ( 2 n + 1 ) ] / 6 we have sum of 1 st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1 st 30 + ve integers - sum of squares of 1 st 15 + ve integers . we will get d - 8215 ; answer : d"


Question: in a department store prize box , 40 % of the notes give the winner a dreamy vacation ; the other notes are blank . what is the approximate probability that 3 out of 5 people that draw the notes one after the other , and immediately return their note into the box get a dreamy vacation ?

<gadget id="calculator">binomial(5, 3)</gadget>
<output>10</output>

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

<gadget id="calculator">(3/5) ** 2</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">10 * (9/25)</gadget>
<output>18/5 = around 3.6</output>

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

<gadget id="calculator">(2/5) ** 3</gadget>
<output>8/125 = around 0.064</output>

<gadget id="calculator">(18/5) * (8/125)</gadget>
<output>144/625 = around 0.2304</output>
<result>144/625 = around 0.2304</result>

Choices:
A. 0.12
B. 0.23
C. 0.35
D. 0.45
E. 0.65

multiply(multiply(choose(5, 3), power(divide(const_3, 5), const_2)), power(divide(const_2, 5), const_3))

Explanation: the probability of winning is 40 % = 40 / 100 = 2 / 5 . the probability of not winning is 60 % = 3 / 5 . p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 ( we multiply by 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! , because wwwnn scenario can occur in several ways : wwwnn , wwnwn , wnwwn , nwwwn , . . . the # of such cases basically equals to the # of permutations of 5 letters wwwnn , which is 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! ) . answer : b .


Question: if the volume of the cube is 729 cm 3 , then the surface area of the cube will be

<gadget id="calculator">729 ** (1/3)</gadget>
<output>9</output>

<gadget id="calculator">6 * (9 ** 2)</gadget>
<output>486</output>
<result>486</result>

Choices:
A. 486 sq . cm
B. 456 sq . cm
C. 446 sq . cm
D. 476 sq . cm
E. none of these

Explanation: explanation : a 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 cm 2 answer : a


Question: what is the rate percent when the simple interest on rs . 1600 amount to rs . 200 in 4 years ?

<gadget id="calculator">100 * 200</gadget>
<output>20_000</output>

<gadget id="calculator">1_600 * 4</gadget>
<output>6_400</output>

<gadget id="calculator">20_000 / 6_400</gadget>
<output>25/8 = around 3.125</output>
<result>25/8 = around 3.125</result>

Choices:
A. 4 %
B. 3.125 %
C. 5 %
D. 6 %
E. 7 %

divide(multiply(const_100, 200), multiply(1600, 4))

Explanation: "interest for 1 year = 200 / 4 = 50 interest on rs 1600 p / a = 50 interest rate = 50 / 1600 * 100 = 3.125 % answer : b"


Question: if the simple interest on a certain sum of money for 2 years is one – fifth of the sum , then the rate of interest per annum is

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

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

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

Choices:
A. 14 %
B. 7 %
C. 10 %
D. 15 %
E. 3 %

divide(divide(const_100, add(const_1, const_4)), 2)

Explanation: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 2 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 2 ) = 20 / 2 = 10 % answer : option c"


Question: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , c sitting together ?

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

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

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

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

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>

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

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

<gadget id="calculator">4_320 / 40_320</gadget>
<output>3/28 = around 0.107143</output>
<result>3/28 = around 0.107143</result>

Choices:
A. 3 / 14
B. 5 / 28
C. 3 / 28
D. 1 / 7
E. 9 / 28

divide(multiply(factorial(add(subtract(add(const_4, const_4), const_3), const_1)), factorial(const_3)), factorial(add(const_4, const_4)))

Explanation: total number of arrangement is = 8 ! = 40320 favorable event i . e ) a , b and c can be arranged in 3 ! and the remaining can be arranged in 6 ! since ab can be in any of the four positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : c


Question: there are 2 sections a and b in a class , consisting of 50 and 50 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?

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

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

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

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

<gadget id="calculator">7_000 / 100</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 50.78 kg
B. 49.32 kg
C. 61.67 kg
D. 70 kg
E. 70.89 kg

divide(add(multiply(50, 60), multiply(50, 80)), add(50, 50))

Explanation: "total weight of 50 + 50 students = 50 * 60 + 50 * 80 = 3000 + 4000 average weight of the class is = 7000 / 100 = 70 kg answer is d"