Question: the list price of an article is rs . 70 . a customer pays rs . 59.22 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

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

<gadget id="calculator">70 * (1/10)</gadget>
<output>7</output>

<gadget id="calculator">70 - 7</gadget>
<output>63</output>

<gadget id="calculator">63 - 59.22</gadget>
<output>3.78</output>

<gadget id="calculator">3.78 / 63</gadget>
<output>0.06</output>

<gadget id="calculator">0.06 * 100</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 8 %
B. 7 %
C. 10 %
D. 12 %
E. 6 %

multiply(divide(subtract(subtract(70, multiply(70, divide(10, const_100))), 59.22), subtract(70, multiply(70, divide(10, const_100)))), const_100)

Explanation: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.22 x = 6 %"


Question: a train crosses a platform of 200 m in 15 sec , same train crosses another platform of length 300 m in 20 sec . then find the length of the train ?

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

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

<gadget id="calculator">300 * 3</gadget>
<output>900</output>

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

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

<gadget id="calculator">900 - 800</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 100 m
B. 180 m
C. 159 m
D. 250 m
E. 152 m

subtract(multiply(300, divide(15, divide(15, const_3))), multiply(200, divide(20, divide(15, const_3))))

Explanation: "length of the train be ‘ x ’ x + 200 / 15 = x + 300 / 20 4 x + 800 = 3 x + 900 x = 100 m answer : a"


Question: one man can do a piece of work in 10 days . one boys join him & he complete the work in 6 days . if he gets 50 rs for his work then what will be the share of the boy .

<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">50 / (5/2)</gadget>
<output>20</output>
<result>20</result>

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

Explanation: 1 day work of man = 1 / 10 , if boy ' s 1 day work = 1 / x , then ( 1 / 10 ) + ( 1 / x ) = 1 / 6 , x = 15 ratio of work of man & boy = 1 / 10 : 1 / 15 = 3 : 2 so out of 50 rs . boy ' s share = 2 * 50 / ( 3 + 2 ) = 20 answer : b


Question: evaluate : 10111 - 10 * 2 * 5 = ?

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

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

<gadget id="calculator">10_111 - 100</gadget>
<output>10_011</output>
<result>10_011</result>

Choices:
A. 10101
B. 10110
C. 11100
D. 11001
E. 11011

subtract(10111, multiply(multiply(10, 2), 5))

Explanation: according to order of operations , 10 ? 2 ? 5 ( division and multiplication ) is done first from left to right 10 / 2 = 5 * 2 = 10 hence 10111 - 10 * 2 * 5 = 10111 - 10 = 10101 correct answer a


Question: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 35 percent ryegrass , what percent of the weight of this mixture is x ?

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

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

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

<gadget id="calculator">(2/5) - (1/4)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">10 / (3/20)</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>

Choices:
A. 10 %
B. 33.33 %
C. 40 %
D. 50 %
E. 66.66 %

divide(subtract(35, 25), subtract(divide(40, const_100), divide(25, const_100)))

Explanation: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 35 % 0.4 x + ( m - x ) 0.25 = 0.35 m 0.15 x = 0.10 m x = 0.6666 m x = 66.66 % of m e"


Question: a rectangular garden is to be twice as long as it is wide . if 150 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?

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

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

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

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

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

multiply(divide(150, multiply(add(const_2, const_1), const_2)), const_2)

Explanation: alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 150 so , 2 ( l + b ) = 150 or , l + b = 75 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 80 l = 80 ; b = 40 l + b = 120 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( b )


Question: a jar of 364 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?

<gadget id="calculator">364 * 2</gadget>
<output>728</output>

<gadget id="calculator">728 * 4</gadget>
<output>2_912</output>

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

<gadget id="calculator">2_912 + 4</gadget>
<output>2_916</output>

<gadget id="calculator">2_916 ** (1/2)</gadget>
<output>54</output>

<gadget id="calculator">54 - 2</gadget>
<output>52</output>

<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>26</result>

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

divide(subtract(sqrt(add(multiply(multiply(364, 2), const_4), power(2, 2))), 2), 2)

Explanation: "364 = 26 * 14 = 28 * 13 there are 26 people in the group today . the answer is d ."


Question: peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ?

<gadget id="calculator">400 - 300</gadget>
<output>100</output>

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

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

<gadget id="calculator">300 - 60</gadget>
<output>240</output>

<gadget id="calculator">20 / 240</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<result>25/3 = around 8.333333</result>

Choices:
A. 12 %
B. 12.5 %
C. 6.67 %
D. 6.25 %
E. 8.33 %

multiply(divide(divide(subtract(400, 300), 5), subtract(300, multiply(divide(subtract(400, 300), 5), 3))), const_100)

Explanation: "now after a time of 3 years the principal p amounts to $ 300 and after a time of 8 years ( question says after another 5 years so 3 + 5 ) p becomes $ 400 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 300 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 8 r / 100 ) = 400 dividing a 2 by a 1 we get ( 1 + 8 r / 100 ) / ( 1 + 3 r / 100 ) = 4 / 3 after cross multiplication we are left with 12 r = 100 which gives r = 8.33 % answer : e"


Question: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 5 years ?

<gadget id="calculator">900 - 750</gadget>
<output>150</output>

<gadget id="calculator">150 / 750</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) / 5</gadget>
<output>1/25 = around 0.04</output>

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

Choices:
A. 6
B. 5
C. 4
D. 78
E. 2

multiply(divide(divide(subtract(900, 750), 750), 5), const_100)

Explanation: "150 = ( 750 * 5 * r ) / 100 r = 4 % . answer : c"


Question: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .

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

<gadget id="calculator">30_000 * 2</gadget>
<output>60_000</output>

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

<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>

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

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

<gadget id="calculator">600 - 400</gadget>
<output>200</output>

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

Choices:
A. 100 rs
B. 150 rs
C. 160 rs
D. 180 rs
E. 200 rs

divide(subtract(divide(multiply(multiply(5000, 6), 2), const_100), divide(multiply(multiply(5000, 4), 2), const_100)), 2)

Explanation: "gain in 2 years = [ ( 5000 * 6 * 2 ) / 100 ] - [ ( 5000 * 4 * 2 ) / 100 ] 600 - 400 = 200 gain in 1 year = ( 200 / 2 ) = 100 rs answer : a"


Question: if 1 / 5 th of a number decreased by 5 is 5 , then the number is

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

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

<gadget id="calculator">10 / (1/5)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 25
B. 50
C. 60
D. 75
E. none

Explanation: explanation : let the number be a , then a / 5 − 5 = 5 ⇒ a / 5 = 10 ⇒ a = 50 correct option : b


Question: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 240 envelopes

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

<gadget id="calculator">36 / (3/2)</gadget>
<output>24</output>

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

<gadget id="calculator">240 / 60</gadget>
<output>4</output>
<result>4</result>

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

divide(240, add(36, divide(36, divide(const_3, const_2))))

Explanation: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 240 envelopes they will take 240 / 60 mins . i . e . , 4 mins . answer : e"


Question: if ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 , then the difference between the two possible values of x is :

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

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

<gadget id="calculator">45 - 9</gadget>
<output>36</output>

<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>

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

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

multiply(sqrt(subtract(multiply(15, 3), multiply(const_3, 3))), const_2)

Explanation: ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 ( x + 3 ) ^ 2 = 3 ( 2 x + 15 ) x ^ 2 + 6 x + 9 = 6 x + 45 x ^ 2 - 36 = 0 ( x - 6 ) ( x + 6 ) = 0 x = 6 or x = - 6 the answer is c .


Question: what is the measure of the angle y 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 60 . c"


Question: a placed 3 sheets with two carbons to get two extra copies of the original . then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half . then he typed . how many carbon copies did he get ?

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

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

Explanation: explanation : since the number of carbons is 2 , only two copies can be obtained . answer : b


Question: the average age of applicants for a new job is 30 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?

<gadget id="calculator">30 + 8</gadget>
<output>38</output>

<gadget id="calculator">30 - 8</gadget>
<output>22</output>

<gadget id="calculator">38 - 22</gadget>
<output>16</output>

<gadget id="calculator">16 + 1</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 8
B. 16
C. 17
D. 18
E. 34

add(subtract(add(30, 8), subtract(30, 8)), const_1)

Explanation: "minimum age = average - 1 standard deviation = 30 - 8 = 22 maximum age = average + 1 standard deviation = 30 + 8 = 38 maximum number of different ages of the applicants = 38 - 22 + 1 = 17 answer c"


Question: hcf and lcm two numbers are 16 and 396 respectively . if one of the numbers is 36 , then the other number is ?

<gadget id="calculator">16 * 396</gadget>
<output>6_336</output>

<gadget id="calculator">6_336 / 36</gadget>
<output>176</output>
<result>176</result>

Choices:
A. 36
B. 66
C. 132
D. 176
E. 364

Explanation: "16 * 396 = 36 * x x = 176 answer : d"


Question: a 10000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?

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

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

<gadget id="calculator">10_000 / 2</gadget>
<output>5_000</output>

<gadget id="calculator">12 * 5_000</gadget>
<output>60_000</output>

<gadget id="calculator">60_000 / 1_000</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 8
B. 12
C. 18
D. 24
E. 60

divide(multiply(add(add(6, 4), 2), divide(10000, 2)), const_1000)

Explanation: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 5,000 by that net inflow to get the minutes ) - 60 min . answer e ."


Question: in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 60 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?

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

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

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

<gadget id="calculator">26 * 100</gadget>
<output>2_600</output>

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

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

<gadget id="calculator">1_200 * (2/5)</gadget>
<output>480</output>

<gadget id="calculator">2_600 - 480</gadget>
<output>2_120</output>

<gadget id="calculator">2_120 / 2_600</gadget>
<output>53/65 = around 0.815385</output>
<result>53/65 = around 0.815385</result>

Choices:
A. 4 / 5
B. 5 / 7
C. 13 / 15
D. 37 / 45
E. 79 / 90

divide(subtract(multiply(const_26, divide(multiply(const_5, const_5), const_0_25)), multiply(1200, subtract(const_1, divide(60, divide(multiply(const_5, const_5), const_0_25))))), multiply(const_26, divide(multiply(const_5, const_5), const_0_25)))

Explanation: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.4 * 1200 = 480 the number of males older than 70 years old is 900 - 480 = 420 the number of people who are either male or younger than 70 is 1800 + 420 = 2220 . p ( a person is younger than 70 or male ) = 2220 / 2700 = 37 / 45 the answer is d ."


Question: the cost of 8 dozen pencil and 2 dozen note book is 520 rupee . if cost of 3 pencil and 4 note book is 60 rupee , then sum of the cost of 1 pencil and 1 note book will be ( in rupee )

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

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

<gadget id="calculator">520 - 360</gadget>
<output>160</output>

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

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

<gadget id="calculator">96 - 18</gadget>
<output>78</output>

<gadget id="calculator">160 / 78</gadget>
<output>80/39 = around 2.051282</output>

<gadget id="calculator">(80/39) * 3</gadget>
<output>80/13 = around 6.153846</output>

<gadget id="calculator">60 - (80/13)</gadget>
<output>700/13 = around 53.846154</output>

<gadget id="calculator">(700/13) / 4</gadget>
<output>175/13 = around 13.461538</output>

<gadget id="calculator">(80/39) + (175/13)</gadget>
<output>605/39 = around 15.512821</output>
<result>605/39 = around 15.512821</result>

Choices:
A. rs 13.51
B. rs 15.51
C. rs 16.51
D. rs 14.51
E. rs 17.51

add(divide(subtract(520, multiply(60, add(const_3, const_3))), subtract(multiply(8, const_12), multiply(3, add(const_3, const_3)))), divide(subtract(60, multiply(divide(subtract(520, multiply(60, add(const_3, const_3))), subtract(multiply(8, const_12), multiply(3, add(const_3, const_3)))), 3)), 4))

Explanation: let cost of pencil = rs x cost of notebook = rs y cost of 8 dozen pencils are 96 x cost of 2 dozen pencils are 24 y cost of 3 pencils are 3 x cost of 4 notebooks are 4 y equations are 96 x + 24 y = 520 - - - - - 1 3 x + 4 y = 60 - - - - - 2 multiplying 6 with equation ( 2 ) and then subtracting eqn ( 1 ) - eqn ( 2 ) , we get 96 x + 24 y = 520 18 x + 24 y = 360 after solving the equations , we get x = 2.05 y = 13.46 cost of 1 pencil and 1 notebook is 2.05 + 13.46 = rs 15.51 answer : b


Question: 8 years ago , p was half of q ' s age . if the ratio of their present ages is 3 : 4 what will be the total of their present ages ?

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

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

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

Choices:
A. 33
B. 67
C. 28
D. 31
E. 35

Explanation: let present age of p and q be 3 x 3 x and 4 x 4 x respectively . eight years ago , p was half of q ' s age â ‡ ’ ( 3 x â ˆ ’ 8 ) = 1 / 2 ( 4 x â ˆ ’ 8 ) â ‡ ’ 6 x â ˆ ’ 16 = 4 x â ˆ ’ 8 â ‡ ’ 2 x = 8 â ‡ ’ x = 4 total of their present ages = 3 x + 4 x = 7 x = 7 ã — 4 = 28 c


Question: selling an kite for rs . 30 , a shop keeper gains 15 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?

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

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

<gadget id="calculator">(3/10) * 90</gadget>
<output>27</output>

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

<gadget id="calculator">15 + 100</gadget>
<output>115</output>

<gadget id="calculator">3_000 / 115</gadget>
<output>600/23 = around 26.086957</output>

<gadget id="calculator">27 - (600/23)</gadget>
<output>21/23 = around 0.913043</output>

<gadget id="calculator">(21/23) / (600/23)</gadget>
<output>7/200 = around 0.035</output>

<gadget id="calculator">(7/200) * 100</gadget>
<output>7/2 = around 3.5</output>
<result>7/2 = around 3.5</result>

Choices:
A. 3.5 %
B. 10 %
C. 11 %
D. 15 %
E. 20 %

multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(15, const_100))), divide(multiply(30, const_100), add(15, const_100))), const_100)

Explanation: "explanation : marked price = rs . 30 c . p . = 100 / 115 * 30 = rs . 26.08 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.92 / 26.08 * 100 = 3.5 % . answer : a"


Question: john makes $ 40 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?

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

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

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

Choices:
A. 16 %
B. 16.66 %
C. 17.9 %
D. 18.12 %
E. 100 %

multiply(divide(subtract(80, 40), 40), const_100)

Explanation: increase = ( 40 / 40 ) * 100 = ( 1 ) * 100 = 100 % . e


Question: the average of 6 no . ' s is 4.60 . the average of 2 of them is 3.4 , while the average of the other 2 is 3.8 . what is the average of the remaining 2 no ' s ?

<gadget id="calculator">6 * 4.6</gadget>
<output>27.6</output>

<gadget id="calculator">2 * 3.4</gadget>
<output>6.8</output>

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

<gadget id="calculator">6.8 + 7.6</gadget>
<output>14.4</output>

<gadget id="calculator">27.6 - 14.4</gadget>
<output>13.2</output>

<gadget id="calculator">13.2 / 2</gadget>
<output>6.6</output>
<result>6.6</result>

Choices:
A. 2.3
B. 6.6
C. 3.6
D. 4.5
E. 4.6

divide(subtract(multiply(6, 4.60), add(multiply(2, 3.4), multiply(2, 3.8))), 2)

Explanation: "sum of the remaining two numbers = ( 4.6 * 6 ) - [ ( 3.4 * 2 ) + ( 3.8 * 2 ) ] = 27.60 - ( 6.8 + 7.6 ) = 27.60 - 14.40 = 13.20 . required average = ( 13.2 / 2 ) = 6.6 . answer : b"


Question: what least number must be subtracted from 13294 so that the remainder is exactly divisible by 97 ?

<gadget id="calculator">13_294 / 97</gadget>
<output>13_294/97 = around 137.051546</output>

<gadget id="calculator">floor(13_294/97)</gadget>
<output>137</output>

<gadget id="calculator">137 * 97</gadget>
<output>13_289</output>

<gadget id="calculator">13_294 - 13_289</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 3
B. 5
C. 7
D. 9
E. 10

subtract(13294, multiply(floor(divide(13294, 97)), 97))

Explanation: "sol . on dividing 13924 by 97 , we get remainder = 5 . ∴ required number to be subtracted = 5 . answer b"


Question: amar takes as much time in running 18 meters as a car takes in covering 12 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?

<gadget id="calculator">1.6 * 1_000</gadget>
<output>1_600</output>

<gadget id="calculator">18 * 1_600</gadget>
<output>28_800</output>

<gadget id="calculator">28_800 / 12</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 6200 m
B. 2400 m
C. 300 m
D. 4300 m
E. 1200 m

divide(multiply(18, multiply(1.6, const_1000)), 12)

Explanation: "b 2400 m distance covered by amar = 18 / 1.2 ( 1.6 km ) = 3 / 8 ( 1600 ) = 2400 m answer is b"


Question: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity w of the pool ?

<gadget id="calculator">48 / 60</gadget>
<output>4/5 = around 0.8</output>

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

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

<gadget id="calculator">60 * 4</gadget>
<output>240</output>

<gadget id="calculator">50 * 240</gadget>
<output>12_000</output>
<result>12_000</result>

Choices:
A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

multiply(50, multiply(const_60, multiply(divide(48, const_60), add(const_4, const_1))))

Explanation: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."


Question: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?

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

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

<gadget id="calculator">575 / 23</gadget>
<output>25</output>

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

<gadget id="calculator">(9/5) * 50</gadget>
<output>90</output>

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

Choices:
A. 300 km
B. 320 km
C. 360 km
D. 390 km
E. 400 km

multiply(multiply(add(1, divide(4, 5)), multiply(const_2, divide(575, 23))), 4)

Explanation: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 4 h is 90 × 4 = 360 km ans . ( c )"


Question: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 5 less , he would have made a profit of 10 % . the c . p . of the article was

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

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

<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 960
B. 980
C. 900
D. 970
E. 1000

multiply(multiply(multiply(5, const_4.0), 10), 5)

Explanation: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 1 = > x = 1000 answer : e ) rs 1000"


Question: the difference between a number and its 3 - fourth is 100 . what is 25 % of that number ?

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

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

<gadget id="calculator">100 / (1/4)</gadget>
<output>400</output>

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

<gadget id="calculator">400 * (1/4)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 120
B. 100
C. 125
D. 150
E. none of these

multiply(divide(100, subtract(const_1, divide(3, const_4))), divide(25, 100))

Explanation: explanation : solution : let the number be x . then , x - 3 / 4 x = 100 = > x / 4 = 100 = > x = 400 . 25 % of x = 25 % of 400 = 25 / 100 * 400 = 100 . answer : b


Question: i chose a number and divide it by 4 . then i subtracted 175 from the result and got 10 . what was the number i chose ?

<gadget id="calculator">175 + 10</gadget>
<output>185</output>

<gadget id="calculator">185 * 4</gadget>
<output>740</output>
<result>740</result>

Choices:
A. 200
B. 740
C. 780
D. 500
E. 100

Explanation: "let x be the number i chose , then x / 4 − 175 = 10 x / 4 = 185 x = 740 answer is b ."


Question: ramu bought an old car for rs . 42000 . he spent rs . 15000 on repairs and sold it for rs . 64900 . what is his profit percent ?

<gadget id="calculator">42_000 + 15_000</gadget>
<output>57_000</output>

<gadget id="calculator">64_900 - 57_000</gadget>
<output>7_900</output>

<gadget id="calculator">7_900 / 57_000</gadget>
<output>79/570 = around 0.138596</output>

<gadget id="calculator">(79/570) * 100</gadget>
<output>790/57 = around 13.859649</output>
<result>790/57 = around 13.859649</result>

Choices:
A. 13.8
B. 77
C. 18
D. 99
E. 88

Explanation: "total cp = rs . 42000 + rs . 15000 = rs . 57000 and sp = rs . 64900 profit ( % ) = ( 64900 - 57000 ) / 57000 * 100 = 13.8 % answer : a"


Question: how many 3 digit numbers n are divisible by 78 or 91 ?

<gadget id="calculator">91 - 78</gadget>
<output>13</output>

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

<gadget id="calculator">13 + 6</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 17
B. 19
C. 20
D. 21
E. 22

add(subtract(91, 78), multiply(3, const_2))

Explanation: the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b


Question: the length and breadth of a rectangle is increased by 3 % and 6 % respectively . what is the increase in the area ?

<gadget id="calculator">3 + 100</gadget>
<output>103</output>

<gadget id="calculator">6 + 100</gadget>
<output>106</output>

<gadget id="calculator">103 * 106</gadget>
<output>10_918</output>

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

<gadget id="calculator">10_918 - 10_000</gadget>
<output>918</output>

<gadget id="calculator">918 * 100</gadget>
<output>91_800</output>

<gadget id="calculator">91_800 / 10_000</gadget>
<output>459/50 = around 9.18</output>
<result>459/50 = around 9.18</result>

Choices:
A. 9.18
B. 9.25
C. 9.5
D. 8.98
E. 8.88

divide(multiply(subtract(rectangle_area(add(3, const_100), add(6, const_100)), rectangle_area(const_100, const_100)), const_100), rectangle_area(const_100, const_100))

Explanation: "100 * 100 = 10000 103 * 106 = 10918 - - - - - - - - - - - 918 10000 - - - - - - - 918 100 - - - - - - - - - - 9.18 ans a"


Question: a sells a bicycle to b and makes a profit of 60 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .

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

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

<gadget id="calculator">225 / (5/4)</gadget>
<output>180</output>

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

<gadget id="calculator">160 / 100</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">180 / (8/5)</gadget>
<output>225/2 = around 112.5</output>
<result>225/2 = around 112.5</result>

Choices:
A. 237
B. 126
C. 971
D. 611
E. 112.5

divide(divide(225, divide(add(const_100, 25), const_100)), divide(add(60, const_100), const_100))

Explanation: "explanation : let cp be 100 a sells at 60 % profit so sp = 160 b sells at 25 % profit = 160 x ( 1 + 25 / 100 ) = 200 cp sp 100 - - - 200 x - - - 225 cp = 225 x 100 / 200 = 112.5 answer : e"


Question: if x is 50 percent greater than 88 , then x =

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

<gadget id="calculator">(1/2) * 88</gadget>
<output>44</output>

<gadget id="calculator">88 + 44</gadget>
<output>132</output>
<result>132</result>

Choices:
A. 68
B. 132
C. 86
D. 105.6
E. 108

add(88, multiply(divide(50, const_100), 88))

Explanation: "x = 88 * 1.5 = 132 so the answer is b ."


Question: if x represents the product of the first 15 positive integers , then x is not a multiple of :

<gadget id="calculator">15 + 4</gadget>
<output>19</output>

<gadget id="calculator">19 * 3</gadget>
<output>57</output>
<result>57</result>

Choices:
A. 99
B. 84
C. 72
D. 57
E. 67

Explanation: a ) 99 = 9 * 11 b ) 84 = 4 * 7 * 3 c ) 72 = 9 * 11 d ) 65 = 5 * 13 e ) 57 = 19 * 3 since 19 is not there in first 15 positive numbers it is the only possibility d )


Question: a can complete a project in 20 days and b can complete the same project in 40 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?

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

<gadget id="calculator">(1/40) * 10</gadget>
<output>1/4 = around 0.25</output>

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

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

<gadget id="calculator">(1/20) + (1/40)</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(3/4) / (3/40)</gadget>
<output>10</output>

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

Choices:
A. 18 days
B. 20 days
C. 26.67 days
D. 16 days
E. 12 days

add(divide(subtract(const_1, multiply(divide(const_1, 40), 10)), add(divide(const_1, 20), divide(const_1, 40))), 10)

Explanation: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 40 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 40 ) * ( x ) = 1 ( x / 20 ) + ( x / 40 ) - ( 10 / 20 ) = 1 3 x / 40 = 3 / 2 x = 20 therefore , the answer is b : 20 ."


Question: a can finish a work in 12 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?

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

<gadget id="calculator">(1/12) * 2</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/12) + (1/6)</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>

Choices:
A. 1 / 4
B. 1 / 6
C. 1 / 7
D. 1 / 8
E. none of these

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

Explanation: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 6 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 12 + 1 / 6 ) = 1 / 4 so in one day 1 / 4 work will be done answer : a"


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 e 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, const_1)), const_2), multiply(const_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 e = 900 : the answer is c .


Question: subtracting 3 % of a from a is equivalent to multiplying a by how much ?

<gadget id="calculator">100 - 3</gadget>
<output>97</output>

<gadget id="calculator">97 / 100</gadget>
<output>97/100 = around 0.97</output>
<result>97/100 = around 0.97</result>

Choices:
A. 0.97
B. 9.4
C. 0.094
D. 94
E. none

Explanation: "answer let a - 3 % of a = ab . ⇒ ( 97 x a ) / 100 = ab ∴ b = 0.97 correct option : a"


Question: sachin is older than rahul by 7 years . if the ratio of their ages is 11 : 9 , find the age of sachin

<gadget id="calculator">11 * 7</gadget>
<output>77</output>

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

<gadget id="calculator">77 / 2</gadget>
<output>77/2 = around 38.5</output>
<result>77/2 = around 38.5</result>

Choices:
A. 24.5
B. 24.8
C. 38.5
D. 24.88
E. 24.19

divide(multiply(11, 7), subtract(11, 9))

Explanation: explanation : if rahul age is x , then sachin age is x + 7 , so , 9 x + 63 = 11 x 2 x = 63 x = 31.5 so sachin age is 31.5 + 7 = 38.5 answer : c ) 38.5


Question: when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ?

<gadget id="calculator">24 % 5</gadget>
<output>4</output>
<result>4</result>

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

Explanation: "when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ? putting a value say x = 24 we get remainder as 24 when divided by 61 . when 24 divided by 5 we get 4 as remainder . c is the answer ."


Question: solve below question 2 x + 1 = - 19

<gadget id="calculator">19 + 1</gadget>
<output>20</output>

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

<gadget id="calculator">(-20) / 2</gadget>
<output>-10</output>
<result>-10</result>

Choices:
A. - 8
B. - 9
C. 9
D. 8
E. - 10

Explanation: "2 x + 1 = - 19 x = - 10 e"


Question: a train 150 m long can cross an electric pole in 3 sec and then find the speed of the train ?

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

<gadget id="calculator">3 / 3_600</gadget>
<output>1/1_200 = around 0.000833</output>

<gadget id="calculator">(3/20) / (1/1_200)</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 180
B. 120
C. 72
D. 27
E. 28

divide(divide(150, const_1000), divide(3, const_3600))

Explanation: "length = speed * time speed = l / t s = 150 / 3 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : a"


Question: approximately how many revolutions will be made by a car tire with a 10 - inch diameter if the car travels 1 ⁄ 2 mile ?

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

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

<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(8/5) / 10</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">(4/25) + 4</gadget>
<output>104/25 = around 4.16</output>

<gadget id="calculator">(104/25) / 10</gadget>
<output>52/125 = around 0.416</output>

<gadget id="calculator">(52/125) + 1</gadget>
<output>177/125 = around 1.416</output>

<gadget id="calculator">(177/125) / 10</gadget>
<output>177/1_250 = around 0.1416</output>

<gadget id="calculator">(177/1_250) + 3</gadget>
<output>3_927/1_250 = around 3.1416</output>

<gadget id="calculator">(3_927/1_250) * 10</gadget>
<output>3_927/125 = around 31.416</output>

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

<gadget id="calculator">60 + 3</gadget>
<output>63</output>

<gadget id="calculator">63 * 10</gadget>
<output>630</output>

<gadget id="calculator">630 + 3</gadget>
<output>633</output>

<gadget id="calculator">633 * 10</gadget>
<output>6_330</output>

<gadget id="calculator">6_330 + 3</gadget>
<output>6_333</output>

<gadget id="calculator">6_333 + 2</gadget>
<output>6_335</output>

<gadget id="calculator">6_335 * 10</gadget>
<output>63_350</output>

<gadget id="calculator">(3_927/125) / 63_350</gadget>
<output>561/1_131_250 = around 0.000496</output>

<gadget id="calculator">(1/2) / (561/1_131_250)</gadget>
<output>565_625/561 = around 1_008.244207</output>
<result>565_625/561 = around 1_008.244207</result>

Choices:
A. 120
B. 180
C. 1003
D. 1000
E. 1,440

divide(divide(1, 2), divide(multiply(add(divide(add(divide(add(divide(add(divide(multiply(const_3, 2), const_10), 1), const_10), const_4), const_10), 1), const_10), const_3), 10), multiply(add(add(multiply(add(multiply(add(multiply(multiply(const_3, 2), const_10), const_3), const_10), const_3), const_10), const_3), 2), const_10)))

Explanation: "diameter of car tire = 10 inches radius of car tire = 5 inches = 5 * 2.54 cm = 12.7 cm circumference of the car tire = 2 * pi * 12.7 = 2 * 3.14 * 12.7 = 79.76 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 79.76 = 1003 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"


Question: calculate the share of z , if rs . 3720 is divided among x , y and z in the ratio 7 : 8 : 11 ?

Choices:
A. 1564.1
B. 1214.1
C. 1574.1
D. 1271.1
E. 1044.1

Explanation: 7 + 8 + 11 = 26 3720 / 26 = 143.1 so z ' s share = 11 * 143.1 answer : c


Question: the area of a triangle is with base 18 m and height 6 m ?

<gadget id="calculator">(18 * 6) / 2</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 88 m 2
B. 10 m 2
C. 66 m 2
D. 54 m 2
E. 31 m 2

Explanation: "1 / 2 * 18 * 6 = 54 m 2 answer : d"


Question: if a population of women in a town is 50 % of men . what is the population of men as a % of population of women ?

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

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

Choices:
A. 200 %
B. 100 %
C. 50 %
D. 65 %
E. 110 %

Explanation: "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . if . . . . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 5 = 2 = 200 % answer is a"


Question: 225 mtrs long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees ?

<gadget id="calculator">26 - 1</gadget>
<output>25</output>

<gadget id="calculator">225 / 25</gadget>
<output>9</output>

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

Choices:
A. 10
B. 12
C. 14
D. 16
E. 18

add(divide(225, subtract(26, const_1)), const_1)

Explanation: 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 a


Question: in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection ?

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

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

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

<gadget id="calculator">(25/4) * 8</gadget>
<output>50</output>

<gadget id="calculator">50 * 64</gadget>
<output>3_200</output>

<gadget id="calculator">3_200 - 64</gadget>
<output>3_136</output>

<gadget id="calculator">3_136 / 8</gadget>
<output>392</output>

<gadget id="calculator">64 + 392</gadget>
<output>456</output>
<result>456</result>

Choices:
A. 72
B. 192
C. 456
D. 256
E. 264

add(64, divide(subtract(multiply(multiply(add(divide(const_60, const_10), const_0_25), 8), 64), 64), 8))

Explanation: total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c


Question: the rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 400 meters per second , what was the speed , in meters per second , when the stopwatch was started ?

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

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

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

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

<gadget id="calculator">2 ** 5</gadget>
<output>32</output>

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

<gadget id="calculator">(25/2) / 2</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>

Choices:
A. 25 / 2
B. 25 / 4
C. 25 / 8
D. 25 / 16
E. 25 / 32

divide(divide(400, power(const_2, subtract(divide(add(divide(const_60, const_2), const_60), 15), const_1))), const_2)

Explanation: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 6 times . 2 ^ 6 * x = 400 x = ( 2 ^ 4 * 25 ) / 2 ^ 6 = 25 / 4 the answer is b ."


Question: the area of a parallelogram is 288 sq m and its altitude is twice the corresponding base . then the length of the base is ?

<gadget id="calculator">288 / 2</gadget>
<output>144</output>

<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 9
C. 7
D. 6
E. 5

Explanation: "2 x * x = 288 = > x = 12 answer : a"


Question: robert ' s salary was increased by 50 % and subsequently decreased by 10 % . how much percentage does he gain ?

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

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

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

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

<gadget id="calculator">(3/2) * (9/10)</gadget>
<output>27/20 = around 1.35</output>

<gadget id="calculator">(27/20) * 100</gadget>
<output>135</output>

<gadget id="calculator">135 - 100</gadget>
<output>35</output>

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

<gadget id="calculator">35 - 20</gadget>
<output>15</output>
<result>15</result>

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

subtract(subtract(multiply(multiply(divide(add(const_100, 50), const_100), divide(subtract(const_100, const_10), const_100)), const_100), const_100), multiply(10, const_2))

Explanation: let original salary be $ 100 increased salary = 10 % of ( 150 % of $ 100 ) = ( 10 / 100 ) * ( 150 / 100 ) * 100 = $ 15 increase = 15 % correct option is a


Question: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 29.16 , the number of the member is the group is :

<gadget id="calculator">29.16 * 100</gadget>
<output>2_916</output>

<gadget id="calculator">2_916 ** (1/2)</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 57
B. 54
C. 77
D. 87
E. 97

Explanation: money collected = ( 29.16 x 100 ) paise = 29.16 paise numbers of members = 2916 squareroot = 54 answer b


Question: a dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg , what is his percent ?

<gadget id="calculator">100 / 800</gadget>
<output>1/8 = around 0.125</output>

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

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

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

<gadget id="calculator">(1/8) * 1_000</gadget>
<output>125</output>

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

Choices:
A. 25 %
B. 25 %
C. 29 %
D. 55 %
E. 45 %

subtract(multiply(divide(const_100, 800), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

Explanation: "800 - - - 200 100 - - - ? = > 25 % answer : b"


Question: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg . what might be the weight of the new person ?

<gadget id="calculator">8 * 2.5</gadget>
<output>20</output>

<gadget id="calculator">20 + 66</gadget>
<output>86</output>
<result>86</result>

Choices:
A. 56 kg
B. 90 kg
C. 86 kg
D. data inadequate
E. none of these

Explanation: "c 86 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 66 + 20 ) kg = 86 kg ."


Question: if ( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) , what is the value of x ?

<gadget id="calculator">5 ** 9</gadget>
<output>1_953_125</output>

<gadget id="calculator">9 ** 5</gadget>
<output>59_049</output>

<gadget id="calculator">1_953_125 * 59_049</gadget>
<output>115_330_078_125</output>

<gadget id="calculator">115_330_078_125 / 3</gadget>
<output>38_443_359_375</output>

<gadget id="calculator">log(38_443_359_375)</gadget>
<output>log(38443359375) = around 24.372452</output>

<gadget id="calculator">log(15)</gadget>
<output>log(15) = around 2.70805</output>

<gadget id="calculator">log(38443359375) / log(15)</gadget>
<output>log(38443359375)/log(15) = around 9</output>
<result>log(38443359375)/log(15) = around 9</result>

Choices:
A. 7
B. 9
C. 11
D. 13
E. 15

divide(log(divide(multiply(power(5, 9), power(9, 5)), 3)), log(15))

Explanation: "( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) = > 5 ^ 9 * 3 ^ 10 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 9 * 3 ^ 10 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 9 answer b"


Question: a boat having a length 8 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

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

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

<gadget id="calculator">16 * (1/100)</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">(4/25) * 1_000</gadget>
<output>160</output>
<result>160</result>

Choices:
A. 12 kg
B. 60 kg
C. 72 kg
D. 160 kg
E. none of these

multiply(multiply(multiply(8, 2), divide(1, const_100)), const_1000)

Explanation: "explanation : volume of water displaced = ( 8 x 2 x 0.01 ) m 3 = 0.16 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.16 x 1000 ) kg = 160 kg . answer : d"


Question: what is the sum between the place values of two 3 ' s in the numeral 63130

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

<gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>

<gadget id="calculator">30 + 3_000</gadget>
<output>3_030</output>
<result>3_030</result>

Choices:
A. 3111
B. 300
C. 3029
D. 3030
E. 3003

add(multiply(3, const_10), multiply(3, const_1000))

Explanation: required sum = 3000 + 30 = 3030 answer is d


Question: lloyd normally works 7.5 hours per day and earns $ 4.00 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?

<gadget id="calculator">7.5 * 4</gadget>
<output>30</output>

<gadget id="calculator">10.5 - 7.5</gadget>
<output>3</output>

<gadget id="calculator">3 * 1.5</gadget>
<output>4.5</output>

<gadget id="calculator">4.5 * 4</gadget>
<output>18</output>

<gadget id="calculator">30 + 18</gadget>
<output>48</output>
<result>48</result>

Choices:
A. $ 33.75
B. $ 48.00
C. $ 51.75
D. $ 54.00
E. $ 70.00

Explanation: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.0 + 3 * 4.0 * 1.5 = 48 answer b"


Question: the average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .

<gadget id="calculator">20 * 50.25</gadget>
<output>1_005</output>

<gadget id="calculator">8 * 45.15</gadget>
<output>361.2</output>

<gadget id="calculator">1_005 + 361.2</gadget>
<output>1_366.2</output>

<gadget id="calculator">20 + 8</gadget>
<output>28</output>

<gadget id="calculator">1_366.2 / 28</gadget>
<output>48.792857</output>
<result>48.792857</result>

Choices:
A. 48.79286
B. 42.25
C. 50.87364
D. 51.25
E. 52.25474

Explanation: "explanation : average weight of 20 boys = 50.25 total weight of 20 boys = 50.25 × 20 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 20 ) + ( 45.15 × 8 ) total boys = 20 + 8 = 28 average weight of all the boys = ( 50.25 × 20 ) + ( 45.15 × 8 ) / 28 = answer : option a"


Question: what is the difference between the c . i . on rs . 9000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?

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

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

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

<gadget id="calculator">(2_601/2_500) * (51/50)</gadget>
<output>132_651/125_000 = around 1.061208</output>

<gadget id="calculator">9_000 * (132_651/125_000)</gadget>
<output>1_193_859/125 = around 9_550.872</output>

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

<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(51/50) * (26/25)</gadget>
<output>663/625 = around 1.0608</output>

<gadget id="calculator">9_000 * (663/625)</gadget>
<output>47_736/5 = around 9_547.2</output>

<gadget id="calculator">(1_193_859/125) - (47_736/5)</gadget>
<output>459/125 = around 3.672</output>
<result>459/125 = around 3.672</result>

Choices:
A. s . 2.04
B. s . 2.08
C. s . 3.67
D. s . 2.83
E. s . 2.42

subtract(multiply(9000, multiply(multiply(add(const_1, divide(2, const_100)), add(const_1, divide(2, const_100))), add(const_1, divide(2, const_100)))), multiply(9000, multiply(add(const_1, divide(2, const_100)), add(const_1, divide(4, const_100)))))

Explanation: c . i . when interest is compounded yearly = [ 9000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 9000 * 26 / 25 * 51 / 50 = rs . 9547.2 c . i . when interest is compounded half - yearly = [ 9000 * ( 1 + 2 / 100 ) 2 ] = ( 9000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 9550.87 difference = ( 9550.87 - 9547.2 ) = rs . 3.67 . answer : c


Question: a tank is filled by 3 pipes a , b , c in 3 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?

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

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

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

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

Choices:
A. 25 hr
B. 35 hr
C. 40 hr
D. 20 hr
E. 21 hr

multiply(add(add(multiply(const_2, const_2), const_2), const_1), 3)

Explanation: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 3 7 / x = 1 / 3 x = 21 hours answer is e"


Question: a girl multiplies 987 by a certain number and obtains 559981 as her answer . if in the answer , both 9 ’ s are wrong but the other digits are correct , then the correct answer will be

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

<gadget id="calculator">90 + 9</gadget>
<output>99</output>

<gadget id="calculator">99 * 100</gadget>
<output>9_900</output>

<gadget id="calculator">559_981 - 9_900</gadget>
<output>550_081</output>

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

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

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

<gadget id="calculator">6 + 50</gadget>
<output>56</output>

<gadget id="calculator">56 * 100</gadget>
<output>5_600</output>

<gadget id="calculator">550_081 + 5_600</gadget>
<output>555_681</output>
<result>555_681</result>

Choices:
A. 553681
B. 555181
C. 555681
D. 556581
E. none of these

add(subtract(559981, multiply(add(multiply(9, const_10), 9), const_100)), multiply(add(multiply(const_2, const_3), multiply(const_10, add(const_1, const_4))), const_100))

Explanation: 987 = 3 x 7 x 47 . so , required number must be divisible by each one of 3 , 7 , 47 . none of the numbers in 553681 and 555181 are divisible by 3 . while 556581 is not divisible by 7 . correct answer is 555681 . answer : c


Question: a couple spent $ 198 in total while dining out and paid this amount using a credit card . the $ 198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?

<gadget id="calculator">198 * 100</gadget>
<output>19_800</output>

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

<gadget id="calculator">19_800 / 120</gadget>
<output>165</output>

<gadget id="calculator">165 * 100</gadget>
<output>16_500</output>

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

<gadget id="calculator">16_500 / 110</gadget>
<output>150</output>
<result>150</result>

Choices:
A. $ 130
B. $ 140
C. $ 150
D. $ 160
E. $ 170

divide(multiply(divide(multiply(198, const_100), add(const_100, 20)), const_100), add(const_100, 10))

Explanation: let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 198 x = $ 150 the correct answer is c .


Question: in an election , candidate douglas won 58 percent of the total vote in counties x and y . he won 64 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?

<gadget id="calculator">58 / 100</gadget>
<output>29/50 = around 0.58</output>

<gadget id="calculator">64 / 100</gadget>
<output>16/25 = around 0.64</output>

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

<gadget id="calculator">(16/25) * (2/3)</gadget>
<output>32/75 = around 0.426667</output>

<gadget id="calculator">(29/50) - (32/75)</gadget>
<output>23/150 = around 0.153333</output>

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

<gadget id="calculator">(23/150) / (1/3)</gadget>
<output>23/50 = around 0.46</output>

<gadget id="calculator">(23/50) * 100</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 15 %
B. 18 %
C. 25 %
D. 36 %
E. 46 %

multiply(divide(subtract(divide(58, const_100), multiply(divide(64, const_100), divide(2, const_3))), divide(1, const_3)), const_100)

Explanation: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 64 % voted means 64 * 200 = 128 votes combined for xy has 300 voters and voted 58 % so total votes = 174 balance votes = 174 - 128 = 46 as y has 100 voters so 46 votes means 46 % of votes required ans e"


Question: if x is an integer and 2.134 × 10 ^ x is less than 21,000 , what is the greatest possible value for x ?

<gadget id="calculator">21_000 / 2.134</gadget>
<output>9_840.674789</output>

<gadget id="calculator">log(9_840.674789)</gadget>
<output>9.19428</output>

<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>

<gadget id="calculator">9.19428 / log(10)</gadget>
<output>9.19428/log(10) = around 3.993025</output>

<gadget id="calculator">floor(9.19428/log(10))</gadget>
<output>3</output>
<result>3</result>

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

Explanation: "x is an integer and 2.134 × 10 x is less than 21,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 21,000 to remain true , the greatest number is 2,134 , which makes x = 3 e . 3"


Question: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ? a . 480 liters

<gadget id="calculator">24 * 4</gadget>
<output>96</output>

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

<gadget id="calculator">96 / 4</gadget>
<output>24</output>

<gadget id="calculator">24 * 20</gadget>
<output>480</output>
<result>480</result>

Choices:
A. 480
B. 489
C. 486
D. 482
E. 483

multiply(divide(multiply(24, 4), subtract(24, 20)), 20)

Explanation: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a


Question: the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 78 kg and 93 kg join the group . find the initial number of members in the group ?

<gadget id="calculator">78 + 93</gadget>
<output>171</output>

<gadget id="calculator">51 * 2</gadget>
<output>102</output>

<gadget id="calculator">171 - 102</gadget>
<output>69</output>

<gadget id="calculator">51 - 48</gadget>
<output>3</output>

<gadget id="calculator">69 / 3</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 87
B. 67
C. 23
D. 75
E. 25

divide(subtract(add(78, 93), multiply(51, const_2)), subtract(51, 48))

Explanation: let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 78 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 69 = > n = 23 therefore there were 23 members in the group initially . answer : c


Question: convert 0.34 in to a vulgar fraction ?

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

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

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

<gadget id="calculator">100 * 0.34</gadget>
<output>34</output>

<gadget id="calculator">34 / 100</gadget>
<output>17/50 = around 0.34</output>
<result>17/50 = around 0.34</result>

Choices:
A. 18 / 50
B. 16 / 50
C. 17 / 50
D. 19 / 50
E. none

divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.34), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))

Explanation: "answer 0.34 = 34 / 100 = 17 / 50 correct option : c"


Question: dhoni bought 5 toys with the average cost of $ 10 . if david also buys the sixth toy with the price of $ 16 , what is the average ( arithmetic mean ) price of those 6 toys ?

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

<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<result>11</result>

Choices:
A. $ 10
B. $ 7
C. $ 8.5
D. $ 9
E. $ 11

Explanation: 5 toys - > total cost = 5 * avg cost = 5 * 10 = 50 sixth toy cost = 16 total cost for 6 toys = 50 + 16 = 66 am = 66 / 6 = 11 hence e


Question: a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds . what is the length of the train in meters ?

<gadget id="calculator">100 - 64</gadget>
<output>36</output>

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

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

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

Choices:
A. 400 meters
B. 1111 meters
C. 1777 meters
D. 1822 meters
E. none of these

multiply(multiply(subtract(100, 64), const_0_2778), 40)

Explanation: "relative speed of the train with respect to the motorbike should be the speed with which the length of the train is covered in 40 secs . calculate the relative speed = > 100 - 64 = 36 kmph and time is 40 sec = 40 / 3600 hrs distance ( in this case the length of the train ) = s * t = 36 * 40 / 3600 . 4 km or 400 meters . so answer ( a )"


Question: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 350 m long platform ?

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

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

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

<gadget id="calculator">350 + 120</gadget>
<output>470</output>

<gadget id="calculator">470 / 10</gadget>
<output>47</output>
<result>47</result>

Choices:
A. 44 sec
B. 49 sec
C. 42 sec
D. 47 sec
E. none of these

divide(add(350, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36))

Explanation: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 350 ) / 36 * 5 / 18 = 47 min . answer : d"


Question: gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?

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

<gadget id="calculator">10 - 8</gadget>
<output>2</output>

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

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

Explanation: "g = 10 w c = 6 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 6 wx = x + 1 * 8 w 10 + 6 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"


Question: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction q of the area of triangle abc is the area of triangle xyz ?

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

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

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

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>

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

<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 1 / 9
B. 1 / 8
C. 1 / 6
D. 1 / 5
E. 1 / 3

divide(divide(power(const_4, const_2), const_2), divide(power(add(const_10, const_2), const_2), const_2))

Explanation: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives q = 1 / 9 . a"


Question: a waitress ' s income consists of her salary and tips . during one week , her tips were 3 / 4 of her salary . what fraction of her income for the week came from tips ?

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

<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>

Choices:
A. 1 / 9
B. 1 / 6
C. 3 / 7
D. 4 / 9
E. 5 / 9

Explanation: "her tips were 3 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 3 / 4 ) ( $ 4 ) = $ 3 so , her total income = $ 4 + $ 3 = $ 7 what fraction of her income for the week came from tips $ 3 / $ 7 = 3 / 7 = c"


Question: the height of a triangle is decreased by 5 % and its base increased by 10 % . its area will

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

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

<gadget id="calculator">95 * 110</gadget>
<output>10_450</output>

<gadget id="calculator">10_450 / 100</gadget>
<output>209/2 = around 104.5</output>

<gadget id="calculator">(209/2) - 100</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>

Choices:
A. decrease by 12.5 %
B. increase by 12.5 %
C. increase by 4.5 %
D. increase by 25 %
E. none of these

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

Explanation: explanation : let the initial height be 100 and the base be 200 units . â ˆ ´ area = 1 / 2 x 100 x 200 = 10000 sq units now , height = 95 units and base = 220 units â ˆ ´ new area = 1 / 2 x 95 x 220 = 10450 â ˆ ´ area is increased by ( 10450 - 10000 ) / 10000 x 10 = 4.5 % answer : option c


Question: the average age of 20 students of a class is 20 years . out of these , the average age of 9 students is 11 years and that of the other 10 students is 24 years . the age of the 20 th student is ?

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

<gadget id="calculator">9 * 11</gadget>
<output>99</output>

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

<gadget id="calculator">99 + 240</gadget>
<output>339</output>

<gadget id="calculator">400 - 339</gadget>
<output>61</output>
<result>61</result>

Choices:
A. 65
B. 61
C. 59
D. 63
E. 64

subtract(multiply(20, 20), add(multiply(9, 11), multiply(10, 24)))

Explanation: "age of the 20 th student = 20 * 20 - ( 9 * 11 + 10 * 24 ) = 400 - 339 = 61 years answer is b"


Question: a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 300 , find the price of the uniform ?

<gadget id="calculator">9 * 500</gadget>
<output>4_500</output>

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

<gadget id="calculator">12 * 300</gadget>
<output>3_600</output>

<gadget id="calculator">4_500 - 3_600</gadget>
<output>900</output>

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

<gadget id="calculator">900 / 12</gadget>
<output>75</output>

<gadget id="calculator">75 * 4</gadget>
<output>300</output>
<result>300</result>

Choices:
A. s . 80
B. s . 85
C. s . 90
D. s . 300
E. s . 120

multiply(divide(subtract(multiply(9, 500), multiply(multiply(const_3, const_4), 300)), multiply(multiply(const_3, const_4), const_1)), const_4)

Explanation: "9 / 12 = 3 / 4 * 500 = 375 300 - - - - - - - - - - - - - 75 1 / 4 - - - - - - - - 75 1 - - - - - - - - - ? = > rs . 300 answer : d"


Question: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 800 sq . ft , how many feet of fencing will be required ?

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

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

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

Choices:
A. 100 feet
B. 120 feet
C. 150 feet
D. 180 feet
E. 186 feet

add(multiply(divide(800, 20), const_2), 20)

Explanation: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 800 = > breadth = 40 feet area to be fenced = 2 b + l = 2 * 40 + 20 = 100 feet answer : option a"


Question: every day daniel drives 60 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?

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

<gadget id="calculator">60 - 32</gadget>
<output>28</output>

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

<gadget id="calculator">16 + 56</gadget>
<output>72</output>

<gadget id="calculator">72 - 60</gadget>
<output>12</output>

<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>

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

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

multiply(divide(subtract(add(divide(32, 2), multiply(subtract(60, 32), 2)), 60), 60), const_100)

Explanation: "let ' s test x = 4 . . . . on sunday , daniel drove 60 miles at 4 miles / hour . d = ( r ) ( t ) 60 = ( 4 ) ( t ) 60 / 4 = 15 = t it takes 15 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 28 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 28 = ( 2 ) ( t ) 28 / 2 = 14 = t it takes 14 hours for the second part total time to drive home on monday = 4 + 14 = 18 hours we ' re asked by what percent 18 hours is greater than 15 hours . 18 / 15 = 1.2 , so it is 20 % greater . b"


Question: the length of a rectangle is halved , while its breadth is tripled . watis the % change in area ?

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

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

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

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

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

Choices:
A. 43 %
B. 47 %
C. 50 %
D. 65 %
E. 68 %

multiply(divide(subtract(multiply(const_3, divide(const_1, const_2)), const_1), const_1), const_100)

Explanation: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"


Question: the number of sailors on a ship is 85 % more than the number of officers . the ratio of sailors to officers would be

<gadget id="calculator">85 + 100</gadget>
<output>185</output>

<gadget id="calculator">185 / 100</gadget>
<output>37/20 = around 1.85</output>
<result>37/20 = around 1.85</result>

Choices:
A. 37 : 20
B. 47 : 20
C. 47 : 25
D. 22 : 25
E. 97 : 50

Explanation: "sailor = 1.85 * officer sailor / officer = 1.85 / 1 = 185 / 100 = 37 / 20 answer will be a"


Question: a goods train runs at the speed of 72 km / hr and crosses a 270 m long platform in 26 sec . what is the length of the goods train ?

<gadget id="calculator">72 / 3_600</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">(1/50) * 1_000</gadget>
<output>20</output>

<gadget id="calculator">20 * 26</gadget>
<output>520</output>

<gadget id="calculator">520 - 270</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 278
B. 166
C. 151
D. 250
E. 109

subtract(multiply(multiply(divide(72, const_3600), const_1000), 26), 270)

Explanation: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 270 ) / 26 = 20 x = 250 m . answer : d"


Question: the volume of water inside a swimming pool doubles every hour . if the pool is filled to its full capacity within 8 hours , in how many hours was it filled to one quarter of its capacity ?

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

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

Choices:
A. 2
B. 4
C. 5
D. 6
E. 7

Explanation: d


Question: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure y in inches of the width of the foil covered prism ?

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

<gadget id="calculator">128 / 2</gadget>
<output>64</output>

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

<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>

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

<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 4
B. 6
C. 8
D. 9
E. 10

add(multiply(power(divide(128, multiply(1, multiply(1, const_2))), inverse(const_3)), multiply(1, const_2)), multiply(1, const_2))

Explanation: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = y = 10 ans e ."


Question: a train 200 m long can cross an electric pole in 5 sec and then find the speed of the train ?

<gadget id="calculator">200 / 1_000</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">5 / 3_600</gadget>
<output>1/720 = around 0.001389</output>

<gadget id="calculator">(1/5) / (1/720)</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 114
B. 124
C. 134
D. 144
E. 154

divide(divide(200, const_1000), divide(5, const_3600))

Explanation: "length = speed * time speed = l / t s = 200 / 5 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"


Question: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 9 meters . what is value of the radius in meters ?

<gadget id="calculator">10 * 0.31</gadget>
<output>3.1</output>

<gadget id="calculator">3.1 / 1</gadget>
<output>3.1</output>
<result>3.1</result>

Choices:
A. 2
B. 3
C. 4
D. 6
E. 9

Explanation: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 9 ) which is about 9 r = 3 the answer is b ."


Question: a person crosses a 800 m long street in 5 minutes . what is his speed in km per hour ?

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

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

<gadget id="calculator">300 / 3_600</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(4/5) / (1/12)</gadget>
<output>48/5 = around 9.6</output>
<result>48/5 = around 9.6</result>

Choices:
A. 1.23
B. 2.86
C. 4.36
D. 9.25
E. 9.61

divide(divide(800, const_1000), divide(multiply(5, const_60), const_3600))

Explanation: "distance = 800 meter time = 5 minutes = 5 x 60 seconds = 300 seconds speed = distance / time = 800 / 300 = 2.67 m / s = 2.67 ã — 18 / 5 km / hr = 9.61 km / hr answer : e"


Question: in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 15 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

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

Choices:
A. 4 seconds
B. 25 seconds
C. 29 seconds
D. 21 seconds
E. 17 seconds

Explanation: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 15 m ahead . that means jhon was 15 m away from finishing line when they started together . so he will cover 15 m in 5 seconds . so his speed = 15 / 5 = 3 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 17 seconds . correct answer = e"


Question: in an examination , 300 students appeared . out of these students ; 29 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .

<gadget id="calculator">29 + 54</gadget>
<output>83</output>

<gadget id="calculator">100 - 83</gadget>
<output>17</output>

<gadget id="calculator">300 * 17</gadget>
<output>5_100</output>

<gadget id="calculator">5_100 / 100</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 51
B. 37
C. 54
D. 99
E. 01

divide(multiply(300, subtract(const_100, add(29, 54))), const_100)

Explanation: "the number of students with first division = 29 % of 300 = 29 / 100 × 300 = 8700 / 100 = 87 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 87 + 162 ) = 51 answer : a"


Question: the length of rectangle is thrice its breadth and its perimeter is 104 m , find the area of the rectangle ?

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

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

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

<gadget id="calculator">104 / 8</gadget>
<output>13</output>

<gadget id="calculator">13 * 3</gadget>
<output>39</output>

<gadget id="calculator">39 * 13</gadget>
<output>507</output>
<result>507</result>

Choices:
A. 507 sq m
B. 356 sq m
C. 452 sq m
D. 428 sq m
E. 525 sq m

multiply(multiply(divide(104, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(104, add(multiply(const_3, const_2), multiply(const_1, const_2))))

Explanation: "2 ( 3 x + x ) = 104 l = 39 b = 13 lb = 39 * 13 = 507 answer : a"


Question: if x + y = 20 , x - y = 36 , for integers of x and y , x = ?

<gadget id="calculator">20 + 36</gadget>
<output>56</output>

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

Choices:
A. 20
B. 25
C. 28
D. 20
E. 42

Explanation: "x + y = 20 x - y = 36 2 x = 56 x = 28 answer is c"


Question: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 14 % , then the cost price of the article is :

<gadget id="calculator">616 * 100</gadget>
<output>61_600</output>

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

<gadget id="calculator">61_600 / 110</gadget>
<output>560</output>

<gadget id="calculator">560 * 110</gadget>
<output>61_600</output>

<gadget id="calculator">100 + 14</gadget>
<output>114</output>

<gadget id="calculator">61_600 / 114</gadget>
<output>30_800/57 = around 540.350877</output>
<result>30_800/57 = around 540.350877</result>

Choices:
A. 500
B. 540
C. 555
D. 664
E. 5598

divide(multiply(divide(multiply(616, const_100), add(const_100, 10)), add(const_100, 10)), add(const_100, 14))

Explanation: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 114 = rs . 540 answer : option b"


Question: the speed of a boat in still water is 14 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 8 minutes is

<gadget id="calculator">8 / 60</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">14 + 5</gadget>
<output>19</output>

<gadget id="calculator">(2/15) * 19</gadget>
<output>38/15 = around 2.533333</output>
<result>38/15 = around 2.533333</result>

Choices:
A. 1.6 km
B. 2.5 km
C. 3.6 km
D. 4 km
E. none of these

multiply(divide(8, const_60), add(14, 5))

Explanation: "explanation : speed downstreams = ( 14 + 5 ) kmph = 19 kmph . distance travelled = ( 19 x 8 / 60 ) km = 2.5 km option b"


Question: what is the tens digit of 6 ^ 19 ?

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

<gadget id="calculator">19 % 5</gadget>
<output>4</output>

<gadget id="calculator">6 ** 4</gadget>
<output>1_296</output>

<gadget id="calculator">1_296 % 100</gadget>
<output>96</output>

<gadget id="calculator">96 / 10</gadget>
<output>48/5 = around 9.6</output>

<gadget id="calculator">floor(48/5)</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 1
B. 3
C. 5
D. 7
E. 9

floor(divide(reminder(power(6, reminder(19, add(const_4, const_1))), const_100), const_10))

Explanation: the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 19 has the form 5 n + 4 , so the tens digit of 6 ^ 19 is 9 . the answer is e .


Question: aa is two digit number then m times its cube of aa has 1 in its tens place then what is m .

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

<gadget id="calculator">11 ** 3</gadget>
<output>1_331</output>

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

<gadget id="calculator">1_331 * 7</gadget>
<output>9_317</output>

<gadget id="calculator">9_317 / 1_331</gadget>
<output>7</output>
<result>7</result>

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

divide(multiply(power(add(const_10, 1), const_3), add(const_3, const_4)), power(add(const_10, 1), const_3))

Explanation: when aa = 11 7 * ( 11 ) ^ 3 = 7 * 1331 = 9317 m = 7 answer : e


Question: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability w that out of the two , one is white and one is blue ?

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

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

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

<gadget id="calculator">8 * 7</gadget>
<output>56</output>

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

<gadget id="calculator">15 / 28</gadget>
<output>15/28 = around 0.535714</output>
<result>15/28 = around 0.535714</result>

Choices:
A. 15 / 56
B. 41 / 56
C. 13 / 28
D. 15 / 28
E. 5 / 14

divide(multiply(3, 5), divide(multiply(add(3, 5), add(5, const_2)), const_2))

Explanation: "the required probability w = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."


Question: the curved surface of a sphere is 64 π cm 2 . find its radius ?

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

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

Choices:
A. 8
B. 3
C. 4
D. 9
E. 7

Explanation: explanation : 4 π r 2 = 64 = > r = 4 answer : option c


Question: dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?

<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">25 * (9/10)</gadget>
<output>45/2 = around 22.5</output>

<gadget id="calculator">25 + (45/2)</gadget>
<output>95/2 = around 47.5</output>

<gadget id="calculator">100 - (95/2)</gadget>
<output>105/2 = around 52.5</output>
<result>105/2 = around 52.5</result>

Choices:
A. 50 %
B. 55 %
C. 60 %
D. 62 %
E. 52.5 %

subtract(const_100, add(25, multiply(25, subtract(const_1, divide(10, const_100)))))

Explanation: "say dhoni ' s earning last month was $ 100 . dhoni spent 30 percent of his earning last month on rent - - > $ 25 on rent ; 10 percent less than what he spent on rent to purchase a new dishwasher - - > $ 25 * 0.9 = $ 22.5 on the dishwasher . left over amount 100 - ( 25 + 22.5 ) = $ 52.5 answer : e"


Question: a present value of a machine is $ 800 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?

<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">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>

<gadget id="calculator">800 * (81/100)</gadget>
<output>648</output>
<result>648</result>

Choices:
A. $ 900
B. $ 810
C. $ 915
D. $ 715
E. $ 648

multiply(800, power(subtract(const_1, divide(10, const_100)), 2))

Explanation: "p = $ 800 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 800 * 9 / 10 * 9 / 10 = $ 648 answer is e"


Question: the effective annual rate of interest corresponding to a nominal rate of 16 % per annum payable half - yearly is ?

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

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

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

<gadget id="calculator">64 / 100</gadget>
<output>16/25 = around 0.64</output>

<gadget id="calculator">16 + (16/25)</gadget>
<output>416/25 = around 16.64</output>
<result>416/25 = around 16.64</result>

Choices:
A. 16.64 %
B. 16.07 %
C. 16.08 %
D. 16.09 %
E. 16.19 %

add(add(divide(16, const_2), divide(16, const_2)), divide(multiply(divide(16, const_2), divide(16, const_2)), const_100))

Explanation: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 8 / 100 ) 2 ] = rs . 116.64 effective rate = ( 116.64 - 100 ) = 116.64 % answer : a"


Question: cost of 2 bats and 3 balls is rs . 1300 . the cost of 3 bats and 2 balls is rs . 1200 . the cost of each balls is more than that of each bat by ?

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

Choices:
A. 50
B. 100
C. 110
D. 120
E. 130

Explanation: 2 bats + 3 ball = 1300 - - - ( 1 ) 3 bats + 3 ball = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - bats + ball = 100 = > ball - bats = 100 b


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

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

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

Explanation: answer e . total # of outcomes : 5 * 5 = 25 # of outcomes where product is - ve : ( - 6,1 ) , ( - 6,2 ) , ( - 6,3 ) . . . hence , total : 15 probability : 15 / 25 = 3 / 5


Question: what is the total cost of 2 sandwiches at $ 2.45 each and 4 sodas at $ 0.87 each ?

<gadget id="calculator">2 * 2.45</gadget>
<output>4.9</output>

<gadget id="calculator">4 * 0.87</gadget>
<output>3.48</output>

<gadget id="calculator">4.9 + 3.48</gadget>
<output>8.38</output>
<result>8.38</result>

Choices:
A. $ 8.38
B. $ 6.85
C. $ 8.46
D. $ 10.08
E. $ 11.85

add(multiply(2, 2.45), multiply(4, 0.87))

Explanation: "answer = a 2 * 2.45 + 4 * 0.87 = 2 ( 2.50 - 0.05 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.1 - 0.52 = 9 - 0.62 = 8.38"


Question: a woman complete a journey in 5 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .

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

<gadget id="calculator">24 + 21</gadget>
<output>45</output>

<gadget id="calculator">120 / 45</gadget>
<output>8/3 = around 2.666667</output>

<gadget id="calculator">(8/3) * 21</gadget>
<output>56</output>

<gadget id="calculator">56 * 2</gadget>
<output>112</output>
<result>112</result>

Choices:
A. 334 km .
B. 216 km .
C. 112 km .
D. 224 km .
E. 544 km .

multiply(multiply(divide(multiply(5, 24), add(24, 21)), 21), const_2)

Explanation: "0.5 x / 21 + 0.5 x / 24 = 5 - - > x / 21 + x / 24 = 10 - - > x = 112 km . c"


Question: a rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?

<gadget id="calculator">680 / 34</gadget>
<output>20</output>

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

<gadget id="calculator">40 + 34</gadget>
<output>74</output>
<result>74</result>

Choices:
A. 74 ft
B. 88 ft
C. 22 ft
D. 11 ft
E. 66 ft

add(multiply(divide(680, 34), const_2), 34)

Explanation: "given that length and area , so we can find the breadth . length x breadth = area 34 x breadth = 680 breadth = 20 feet area to be fenced = 2 b + l = 2 ( 20 ) + 34 = 88 feet answer : a ) 74 ft"


Question: how many shots of 1 cm radius can be prepared from a sphere of 6 cm radius ?

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

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

Choices:
A. 33
B. 88
C. 216
D. 288
E. 299

Explanation: "4 / 3 ï € * 6 * 6 * 6 = 4 / 3 ï € * 1 * 1 * 1 * x x = 216 answer : c"


Question: a man can do a piece of work in 5 days , but with the help of his son , he can finish it in 4 days . in what time can the son do it alone ?

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

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

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

Choices:
A. 5
B. 5 1 / 2
C. 7 1 / 2
D. 6
E. 20

Explanation: "son ' s 1 day work = 1 / 4 - 1 / 5 = 1 / 20 son alone can do the work in 20 days = 20 days answer is e"


Question: a man & his wife appear in an interview for 2 vacancies in the same post . the probability of husband ' s selection is 1 / 7 & the probability of wife ' s selection is 1 / 5 . what is the probability that only 1 of them is selected ?

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

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

<gadget id="calculator">1 - (1/7)</gadget>
<output>6/7 = around 0.857143</output>

<gadget id="calculator">(1/5) * (6/7)</gadget>
<output>6/35 = around 0.171429</output>

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

<gadget id="calculator">(1/7) * (4/5)</gadget>
<output>4/35 = around 0.114286</output>

<gadget id="calculator">(6/35) + (4/35)</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>

Choices:
A. 1 / 3
B. 2 / 3
C. 2 / 7
D. 3 / 11
E. 4 / 5

add(multiply(divide(1, 5), subtract(1, divide(1, 7))), multiply(divide(1, 7), subtract(1, divide(1, 5))))

Explanation: let a = event that the husband is selected and b = event that the wife is selected . then , p ( a ) = 1 / 7 and p ( b ) = 1 / 5 ∴ p ( a ¯ ) = ( 1 - 17 / 5 ) = 6 / 7 and = ( 1 - 1 / 5 ) = 4 / 5 required probability = p [ ( a and not b ) or ( b and not a ) ] = p [ ( a and b ¯ ) or ( b and a ¯ ) ] = p ( a and b ¯ ) + p ( b and a ¯ ) = p ( a ) . p ( b ¯ ) + p ( b ) . p ( a ¯ ) = ( 1 / 7 * 4 / 5 ) + ( 1 / 5 * 6 / 7 ) = 10 / 35 = 2 / 7 c


Question: find the length of the wire required to go 11 times round a square field containing 27889 m 2 .

<gadget id="calculator">27_889 ** (1/2)</gadget>
<output>167</output>

<gadget id="calculator">4 * 167</gadget>
<output>668</output>

<gadget id="calculator">668 * 11</gadget>
<output>7_348</output>
<result>7_348</result>

Choices:
A. 7348
B. 3388
C. 2667
D. 8766
E. 66711

Explanation: "a 2 = 27889 = > a = 167 4 a = 668 668 * 11 = 7348 answer : a"


Question: there are 25 balls in a jar . you take out 5 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?

<gadget id="calculator">25 - 5</gadget>
<output>20</output>

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

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

Choices:
A. 12 .
B. 9 .
C. 8 .
D. 7 .
E. 6 .

Explanation: "9 = 5 blue balls + 20 / 5 answer : b"


Question: a circular well with a diameter of 4 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?

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

<gadget id="calculator">pi * (2 ** 2) * 24</gadget>
<output>96*pi = around 301.592895</output>
<result>96*pi = around 301.592895</result>

Choices:
A. 32 m 3
B. 36 m 3
C. 40 m 3
D. 44 m 3
E. 301.6

Explanation: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 2 × 2 × 24 ) m 3 ‹ = › 301.6 m 3 . answer e"


Question: priya and her father differ in their ages by 31 years . after 8 years . if the sum of their ages will be 69 , their present ages are

<gadget id="calculator">69 - 8</gadget>
<output>61</output>

<gadget id="calculator">61 - 8</gadget>
<output>53</output>

<gadget id="calculator">53 + 31</gadget>
<output>84</output>

<gadget id="calculator">84 / 2</gadget>
<output>42</output>

<gadget id="calculator">42 - 31</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 11 , 42
B. 12 , 24
C. 15 , 42
D. 16 , 19
E. 33 , 44

subtract(divide(add(subtract(subtract(69, 8), 8), 31), const_2), 31)

Explanation: a 11 , 42 let the age of priya = x years then , the age of her father = ( x + 31 ) years atq , ( x + 8 ) + ( x + 31 + 8 ) = 69 2 x + 47 = 69 2 x = 69 – 47 = 22 x = 11 the age of priya = 11 years the age of her father = 11 + 31 = 42 years


Question: if 7 spiders make 7 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?

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

Choices:
A. 1
B. 7
C. 3
D. 14
E. 16

Explanation: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 7 : 1 ( webs ) 1 : 7 } : : x : 7 ⇒ 7 × 1 × 7 = 1 × 7 × x ⇒ x = 7 answer : option b"


Question: the price of lunch for 13 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

<gadget id="calculator">207 * 85</gadget>
<output>17_595</output>

<gadget id="calculator">17_595 / 100</gadget>
<output>3_519/20 = around 175.95</output>

<gadget id="calculator">(3_519/20) / 13</gadget>
<output>3_519/260 = around 13.534615</output>
<result>3_519/260 = around 13.534615</result>

Choices:
A. 11.73
B. 12
C. 13.85
D. 14
E. 15.87

divide(divide(multiply(207, subtract(const_100, 15)), const_100), 13)

Explanation: "clearly c is the answer i used poe here lets consider option ( c ) 13 * 13.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo c"


Question: find the principle on a certain sum of money at 5 % per annum for 2 years if the amount being rs . 1120 ?

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

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

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

<gadget id="calculator">1_120 / (11/10)</gadget>
<output>11_200/11 = around 1_018.181818</output>
<result>11_200/11 = around 1_018.181818</result>

Choices:
A. 1018
B. 1067
C. 1977
D. 1056
E. 1097

divide(1120, add(const_1, divide(multiply(5, 2), const_100)))

Explanation: "1120 = p [ 1 + ( 5 * 2 ) / 100 ] p = 1018 answer : a"


Question: a man swims downstream 24 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?

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

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

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

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

Choices:
A. 8
B. 5
C. 24
D. 12
E. 36

divide(add(divide(16, 4), divide(24, 4)), const_2)

Explanation: "24 - - - 4 ds = 6 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b"


Question: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 38 , what is the remainder when k is divided by 7 ?

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

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

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

Explanation: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 38 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 38 ) 17 is the only common number in both the sets . hence k = 17 answer : c"