Question: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many r ways can the test be completed if every question is unanswered ?

<gadget id="calculator">5 ** 4</gadget>
<output>625</output>
<result>625</result>

Choices:
A. 24
B. 120
C. 625
D. 720
E. 1024

Explanation: "5 choices for each of the 4 questions , thus total r of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."


Question: a 3 - digit positive integer is chosen at random . what is the probability that the product of its digits is even ?

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

<gadget id="calculator">(1/2) ** 3</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">1 - (1/8)</gadget>
<output>7/8 = around 0.875</output>
<result>7/8 = around 0.875</result>

Choices:
A. 1 / 2
B. 31 / 36
C. 49 / 54
D. 7 / 8
E. 11 / 12

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

Explanation: p ( three odd digits ) = 5 / 9 * 5 / 10 * 5 / 10 = 5 / 36 ( first digit can not be 0 , so we have a total of 9 digits , 4 even and 5 odd ) . therefore , p ( at least one even digit ) = 1 - 5 / 36 = 31 / 36 . answer b .


Question: the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 72 , then 1 / m + 1 / n is equal to

<gadget id="calculator">6 * 210</gadget>
<output>1_260</output>

<gadget id="calculator">72 / 1_260</gadget>
<output>2/35 = around 0.057143</output>
<result>2/35 = around 0.057143</result>

Choices:
A. 1 / 35
B. 3 / 35
C. 5 / 37
D. 2 / 35
E. none

Explanation: answer we have , m x n = 6 x 210 = 1260 ∴ 1 / m + 1 / n = ( m + n ) / mn = 72 / 1260 = 4 / 70 = 2 / 35 correct option : d


Question: in a kilometer race , a beats b by 48 meters or 12 seconds . what time does a take to complete the race ?

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

<gadget id="calculator">48 / 12</gadget>
<output>4</output>

<gadget id="calculator">1_000 / 4</gadget>
<output>250</output>

<gadget id="calculator">250 - 12</gadget>
<output>238</output>
<result>238</result>

Choices:
A. 238 sec
B. 190 sec
C. 667 sec
D. 167 sec
E. 176 sec

subtract(divide(multiply(const_1, const_1000), divide(48, 12)), 12)

Explanation: "time taken by b run 1000 meters = ( 1000 * 12 ) / 48 = 250 sec . time taken by a = 250 - 12 = 238 sec . answer : a"


Question: in a school of 650 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?

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

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

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

<gadget id="calculator">650 * 18</gadget>
<output>11_700</output>

<gadget id="calculator">11_700 / 100</gadget>
<output>117</output>
<result>117</result>

Choices:
A. 173
B. 163
C. 153
D. 143
E. 117

divide(multiply(650, subtract(const_100, add(add(44, 28), 10))), const_100)

Explanation: 44 + 28 + 10 = 82 % 100 – 82 = 18 % 650 * 18 / 100 = 117 answer : e


Question: a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it 2 hours . how long will b alone take to do it ?

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

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

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

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

<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>

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

Choices:
A. 8 hours
B. 10 hours
C. 12 hours
D. 24 hours
E. none of these

divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4))))

Explanation: "solution a ’ s 1 hour ’ s work = 1 / 4 ; ( b + c ) ' s 1 hour ’ s work = 1 / 3 ; ( a + c ) ' s 1 hour ’ s work = 1 / 2 ( a + b + c ) ’ s 1 hour ’ s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ’ s 1 hour ’ s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 ∴ b alone will take 12 hours to do the work . answer c"


Question: in a group of 160 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?

<gadget id="calculator">160 - 90</gadget>
<output>70</output>

<gadget id="calculator">70 / 160</gadget>
<output>7/16 = around 0.4375</output>
<result>7/16 = around 0.4375</result>

Choices:
A. 0.44
B. 0.55
C. 0.65
D. 0.75
E. 0.85

Explanation: "number of people whose age is less than 20 is given by 160 - 90 = 70 probability p that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer a"


Question: an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 800 sculptures are not on display , how many pieces of art does the gallery have ?

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

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

<gadget id="calculator">800 / (2/3)</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / (2/3)</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 360
B. 1800
C. 540
D. 640
E. 720

divide(divide(800, subtract(1, divide(1, 3))), subtract(1, divide(1, 3)))

Explanation: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 800 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 800 - - > { not on display } = 1200 . according to ( i ) 2 / 3 * { total } = 1200 - - > { total } = 1800 . answer : b ."


Question: if x and y are integers and | x - y | = 10 , what is the minimum possible value of xy ?

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

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

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

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

Choices:
A. - 9
B. - 18
C. - 24
D. - 25
E. - 48

multiply(negate(add(const_2, const_3)), subtract(10, add(const_2, const_3)))

Explanation: "sometimes the answer choices to a given question provide a big ' hint ' as to how you can go about solving it . this prompt can also be solved without any complex math ideas - you just need to do a bit of ' brute force ' math and you ' ll have the answer relatively quickly . we ' re told that x and y are integers and | x - y | = 10 . we ' re asked for the minimum possible value of ( x ) ( y ) . since all of the answer choices are negative , this tells us that one of the two variables must be negative ( and the other must be positive ) , so we should restrict our work to those options . if . . . x = 9 , y = - 1 , then xy = - 9 x = 8 , y = - 2 , then xy = - 16 x = 7 , y = - 3 , then xy = - 21 x = 6 , y = - 4 , then xy = - 24 x = 5 , y = - 5 , then xy = - 25 x = 4 , y = - 6 , then xy = - 24 x = 3 , y = - 7 , then xy = - 21 from this , we can conclude the xy will start to get bigger as x continues to decrease down to 1 , so there ' s no need to do any additional work . final answer : d"


Question: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 25 hours and 16 hours respectively . the ratio of their speeds is ?

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

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

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

Choices:
A. 4 : 6
B. 4 : 3
C. 4 : 9
D. 4 : 5
E. 4 : 2

Explanation: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 16 : â ˆ š 25 = 4 : 5 . answer : d"


Question: at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years ?

<gadget id="calculator">1_348.32 * 100</gadget>
<output>134_832</output>

<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>

<gadget id="calculator">134_832 / 12</gadget>
<output>11_236</output>

<gadget id="calculator">11_236 ** (1/2)</gadget>
<output>106</output>

<gadget id="calculator">1_200 * 100</gadget>
<output>120_000</output>

<gadget id="calculator">120_000 / 12</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 ** (1/2)</gadget>
<output>100</output>

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

Choices:
A. 6 %
B. 6.5 %
C. 7 %
D. 7.5 %
E. 8 %

subtract(sqrt(divide(multiply(1348.32, const_100), divide(1200, const_100))), sqrt(divide(multiply(1200, const_100), divide(1200, const_100))))

Explanation: explanation : let the rate be r % p . a . then , 1200 x ( 1 + r / 100 ) 2 = 1348.32 = ( 1 + r / 100 ) 2 = 134832 / 120000 = 11236 / 10000 ( 1 + r / 100 ) 2 = ( 106 / 100 ) 2 = > 1 + r / 100 = 106 / 100 r = 6 % answer is a


Question: in the first 10 overs of a cricket game , the run rate was only 6.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?

<gadget id="calculator">10 * 6.2</gadget>
<output>62</output>

<gadget id="calculator">282 - 62</gadget>
<output>220</output>

<gadget id="calculator">220 / 40</gadget>
<output>11/2 = around 5.5</output>
<result>11/2 = around 5.5</result>

Choices:
A. 6.25
B. 5.5
C. 6.75
D. 7
E. 8

divide(subtract(282, multiply(10, 6.2)), 40)

Explanation: "10 overs - run rate = 6.2 runs scored in first 10 overs = 62 remaining overs 40 total runs to be scored = 282 62 runs already scored 282 - 62 = 220 220 runs to be scored in 40 overs let required runrate be x 40 * x = 220 x = 220 / 40 x = 5.5 the required runrate is 5.5 answer : b"


Question: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 135 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?

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

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

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

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

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

<gadget id="calculator">135 / (3/8)</gadget>
<output>360</output>
<result>360</result>

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

divide(135, subtract(1, add(divide(1, 2), multiply(divide(1, 2), divide(1, 4)))))

Explanation: easy 360 is the answer . 3 / 4 ( x / 2 ) = 135 x = 135 * 8 / 3 = 360 . answer c


Question: a and b go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?

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

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

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

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

<gadget id="calculator">600 / 5</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 120
B. 775
C. 555
D. 288
E. 278

divide(600, subtract(multiply(54, const_0_2778), multiply(36, const_0_2778)))

Explanation: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 36 * 5 / 18 ) , 600 / ( 54 * 5 / 18 ) } = lcm ( 60 , 40 ) = 120 sec . answer : a"


Question: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 132 . what is the number of frogs in the pond ?

<gadget id="calculator">37 + 39</gadget>
<output>76</output>

<gadget id="calculator">76 + 2</gadget>
<output>78</output>

<gadget id="calculator">78 / 2</gadget>
<output>39</output>

<gadget id="calculator">132 / 39</gadget>
<output>44/13 = around 3.384615</output>

<gadget id="calculator">39 * (44/13)</gadget>
<output>132</output>
<result>132</result>

Choices:
A. 148
B. 134
C. 156
D. 144
E. none

multiply(39, divide(132, divide(add(add(37, 39), const_2), const_2)))

Explanation: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 132 . so , total number of ducks and frogs in the pond , = 2 * 132 = 262 . therefore , number of frogs , = ( 262 * 39 ) / 76 = 134 . answer : option b"


Question: a certain car can travel 32 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )

<gadget id="calculator">32 * 3.8</gadget>
<output>121.6</output>

<gadget id="calculator">121.6 / 1.6</gadget>
<output>76</output>

<gadget id="calculator">76 * 3.9</gadget>
<output>296.4</output>

<gadget id="calculator">296.4 / 5.7</gadget>
<output>52</output>
<result>52</result>

Choices:
A. 52
B. 65
C. 78
D. 91
E. 104

divide(multiply(divide(multiply(32, 3.8), 1.6), 3.9), 5.7)

Explanation: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 32 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 32 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : a ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 32 x 3.9 x 3.8 / 5.7 x 1.6 = 52 a"


Question: the ratio of the number of females to males at a party was 1 : 2 but when 7 females and 7 males left , the ratio became 1 : 3 . how many people were at the party originally ?

<gadget id="calculator">7 * 2</gadget>
<output>14</output>

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

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

<gadget id="calculator">28 / 2</gadget>
<output>14</output>

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

Choices:
A. 28
B. 32
C. 36
D. 42
E. 50

add(divide(subtract(multiply(multiply(7, 2), 3), multiply(7, 2)), const_2), subtract(multiply(multiply(7, 2), 3), multiply(7, 2)))

Explanation: the total number of people are x females + 2 x males . 3 * ( x - 7 ) = 2 x - 7 x = 14 there were 3 x = 42 people at the party originally . the answer is d .


Question: the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 is ?

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

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

<gadget id="calculator">15 / 12</gadget>
<output>5/4 = around 1.25</output>

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

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

<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(5/4) / (6/5)</gadget>
<output>25/24 = around 1.041667</output>
<result>25/24 = around 1.041667</result>

Choices:
A. 3 : 5
B. 2 : 7
C. 1 : 1
D. 1 : 4
E. none

divide(divide(multiply(5, 3), multiply(6, 2)), divide(multiply(3, 4), multiply(2, 5)))

Explanation: "answer : option c 5 / 6 : 3 / 2 : 4 / 5 = 1 : 1"


Question: a woman complete a journey in 20 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">20 * 24</gadget>
<output>480</output>

<gadget id="calculator">24 + 21</gadget>
<output>45</output>

<gadget id="calculator">480 / 45</gadget>
<output>32/3 = around 10.666667</output>

<gadget id="calculator">(32/3) * 21</gadget>
<output>224</output>

<gadget id="calculator">224 * 2</gadget>
<output>448</output>
<result>448</result>

Choices:
A. 334 km .
B. 216 km .
C. 314 km .
D. 448 km .
E. 544 km .

multiply(multiply(divide(multiply(20, 24), add(24, 21)), 21), const_2)

Explanation: "0.5 x / 21 + 0.5 x / 24 = 20 - - > x / 21 + x / 24 = 40 - - > x = 448 km . d"


Question: find the compound interest on $ 1200 for 6 years at 20 % p . a . if ci is component yearly ?

Choices:
A. $ 120
B. $ 150
C. $ 2383
D. $ 250
E. $ 300

subtract(multiply(1200, power(add(const_1, divide(20, const_100)), 6)), 1200)

Explanation: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 6 = $ 3583 ci = $ 2383 answer is c"


Question: you need to unlock a secret code using following clues , can you ? here you have the clues : clue - 1 : 0 7 9 ( one of the numbers is correct and is placed in its correct position ) clue - 2 : 0 3 2 ( nothing is correct ) clue - 3 : 1 0 8 ( two numbers are correct but not placed at its correct position . ) clue - 4 : 9 2 6 ( one number is correct but not placed at its correct position . ) clue - 5 : 6 7 8 ( one number is correct but not placed at its correct position . )

<gadget id="calculator">8 * 100</gadget>
<output>800</output>

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

<gadget id="calculator">800 + 10</gadget>
<output>810</output>

<gadget id="calculator">810 + 9</gadget>
<output>819</output>
<result>819</result>

Choices:
A. 819
B. 918
C. 198
D. 189
E. 891

add(add(multiply(8, const_100), multiply(1, const_10)), 9)

Explanation: 0 7 9 : 9 is placed correctly * 0 3 2 : none of the numbers is in the code * 1 0 8 : 1 and 8 are correct number of code but placed at wrong position * 9 2 6 : number 9 is there but placed at wrong position * 6 7 8 : number 8 is there but placed at wrong position correct answer is a ) 819


Question: set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 7 , while all other numbers remain the same , what is the new average of set s ?

<gadget id="calculator">10 * 6.2</gadget>
<output>62</output>

<gadget id="calculator">62 + 7</gadget>
<output>69</output>

<gadget id="calculator">69 / 10</gadget>
<output>69/10 = around 6.9</output>
<result>69/10 = around 6.9</result>

Choices:
A. 6.6
B. 6.7
C. 6.8
D. 6.85
E. 6.9

Explanation: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 7 then total increased to 62 + 7 = 69 new avg - 69 / 10 = 6.9 . hence answer is e ."


Question: if p ( a ) = 1 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .

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

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

<gadget id="calculator">(1/5) * (2/5)</gadget>
<output>2/25 = around 0.08</output>
<result>2/25 = around 0.08</result>

Choices:
A. 7 / 25
B. 3 / 25
C. 8 / 25
D. 2 / 25
E. 3 / 17

Explanation: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 1 / 5 . 2 / 5 p ( a n b ) = 2 / 25 . d"


Question: a train is 320 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?

<gadget id="calculator">320 + 140</gadget>
<output>460</output>

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

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

<gadget id="calculator">460 / (25/2)</gadget>
<output>184/5 = around 36.8</output>
<result>184/5 = around 36.8</result>

Choices:
A. 11 seconds
B. 38 seconds
C. 40 seconds
D. 88 seconds
E. 36.8 seconds

divide(add(320, 140), divide(multiply(45, const_1000), const_3600))

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 320 + 140 = 460 meter time = distance / speed = 460 * ( 2 / 25 ) = 36.8 seconds answer : e"


Question: by the how much is two - fifth of 300 greater than 3 - fifths of 125 ?

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

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

<gadget id="calculator">(2/5) * 300</gadget>
<output>120</output>

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

<gadget id="calculator">(3/5) * 125</gadget>
<output>75</output>

<gadget id="calculator">120 - 75</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 15
B. 3
C. 5
D. 45
E. none of these

subtract(multiply(divide(const_2, add(const_2, const_3)), 300), multiply(divide(3, add(const_2, const_3)), 125))

Explanation: reqd no . = 2 â  „ 5 ã — 300 - 3 â  „ 5 ã — 125 = 120 - 75 = 45 answer d


Question: excluding stoppages , the speed of a train is 60 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?

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

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

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

Choices:
A. 12
B. 14
C. 16
D. 18
E. 20

subtract(const_60, multiply(const_60, divide(40, 60)))

Explanation: "explanation : t = 20 / 60 * 60 = 20 answer : option e"


Question: an error 10 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?

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

<gadget id="calculator">110 ** 2</gadget>
<output>12_100</output>

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

<gadget id="calculator">12_100 - 10_000</gadget>
<output>2_100</output>

<gadget id="calculator">2_100 * 100</gadget>
<output>210_000</output>

<gadget id="calculator">210_000 / 10_000</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 6.64 %
B. 16.64 %
C. 15.64 %
D. 21 %
E. 10.64 %

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

Explanation: "percentage error in calculated area = ( 10 + 10 + ( 10 ã — 10 ) / 100 ) % = 21 % answer : d"


Question: if 2 a = 3 b and ab ≠ 0 , what is the ratio of a / 3 to b / 2 ?

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

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

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

Choices:
A. 27 / 8
B. 8 / 27
C. 1
D. 9 / 4
E. 81 / 64

Explanation: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 2 a = 3 b here ' s one pair : a = 3 and b = 2 what is the ratio of a / 3 to b / 3 ? in other words , what is the value of ( a / 3 ) / ( b / 2 ) ? plug in values to get : ( a / 3 ) / ( b / 2 ) = ( 3 / 3 ) / ( 2 / 2 ) = 1 / 1 = 1 c"


Question: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?

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

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

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

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

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

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

<gadget id="calculator">120 - 48</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 48
B. 66
C. 72
D. 78
E. 90

subtract(multiply(multiply(multiply(5, 4), 3), const_2), multiply(multiply(multiply(4, 3), const_2), const_2))

Explanation: total number of 5 digit numbers that can be formed = 5 ! = 120 . total number of 5 digit numbers in which 3 and 4 are adjacent = 48 . this can be calculated by taking 3 and 4 as a pair and considering positions where they can appear . number of 5 digit numbers in which 3 and 4 are not adjacent = total number of 5 digit numbers - total number of 5 digit numbers in which 3 and 4 are adjacent . ans = 120 - 48 = 72 c


Question: in a 200 m race , a beats b by 20 m and c by 38 m . in a race of 600 m b will beat c by

<gadget id="calculator">200 - 38</gadget>
<output>162</output>

<gadget id="calculator">200 / 162</gadget>
<output>100/81 = around 1.234568</output>

<gadget id="calculator">200 - 20</gadget>
<output>180</output>

<gadget id="calculator">180 / 200</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(100/81) * (9/10)</gadget>
<output>10/9 = around 1.111111</output>

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

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

<gadget id="calculator">600 - 540</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 20 m
B. 30 m
C. 25 m
D. 15 m
E. 60 m

subtract(600, multiply(inverse(multiply(divide(200, subtract(200, 38)), divide(subtract(200, 20), 200))), 600))

Explanation: "it means , when a covers 200 m , b covers only ( 200 - 20 ) = 180 m and c covers only ( 200 - 38 ) = 162 m = > when c covers 162 m , b covers 180 m = > when b covers 600 m , c covers 162 / 180 × 600 = 540 m hence , b beats c by 600 - 540 = 60 metre answer : e"


Question: in what time will a train 120 m long cross an electric pole , it its speed be 121 km / hr ?

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

<gadget id="calculator">121 * (5/18)</gadget>
<output>605/18 = around 33.611111</output>

<gadget id="calculator">120 / (605/18)</gadget>
<output>432/121 = around 3.570248</output>
<result>432/121 = around 3.570248</result>

Choices:
A. 2.5
B. 2.7
C. 2.9
D. 3.6
E. 2.1

Explanation: "speed = 121 * 5 / 18 = 33.6 m / sec time taken = 120 / 33.6 = 3.6 sec . answer : d"


Question: at a recent small town election for mayor a total of 963 votes were cast for the 4 candidates , the winner exceding his opponents by 53 , 79 and 105 votes , respectively . how many votes were cast for each candidate ?

<gadget id="calculator">963 + 53</gadget>
<output>1_016</output>

<gadget id="calculator">79 + 105</gadget>
<output>184</output>

<gadget id="calculator">1_016 + 184</gadget>
<output>1_200</output>

<gadget id="calculator">1_200 / 4</gadget>
<output>300</output>

<gadget id="calculator">300 - 105</gadget>
<output>195</output>
<result>195</result>

Choices:
A. 134
B. 178
C. 195
D. 166
E. 194

Explanation: c 195 the number of votes the winning candidate received was 963 + 53 + 79 + 105 / 4 = 300 . the second received 300 – 53 = 247 , the third received 300 – 105 = 195 .


Question: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 5 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?

<gadget id="calculator">5 / 50</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">50 / (1/10)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 400
B. 500
C. 1,250
D. 2,500
E. 10,000

Explanation: "total fish = x percentage of second catch = ( 5 / 50 ) * 100 = 10 % so , x * 10 % = 50 x = 500 ans b ."


Question: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many q hours would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?

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

<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/4) + (1/11)</gadget>
<output>15/44 = around 0.340909</output>

<gadget id="calculator">(15/44) / 15</gadget>
<output>1/44 = around 0.022727</output>

<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 22 hours
B. 30 hours
C. 44 hours
D. 60 hours
E. it can not be determined from the information above .

divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))

Explanation: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job q in 44 hours . answer : c ."


Question: rectangular floors x and y have equal area . if floor x is 10 feet by 18 feet and floor y is 9 feet wide , what is the length of floor y , in feet ?

<gadget id="calculator">10 * 18</gadget>
<output>180</output>

<gadget id="calculator">180 / 9</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 13 1 / 2
B. 20
C. 18 3 / 4
D. 21
E. 24

Explanation: the area of a rectangle is : area = length x width we are given that floor x is 10 feet by 18 feet and that floor y is 9 feet wide . so we can say : length of x = 10 width of x = 18 width of y = 9 length of y = n we also can say : area of floor x = area of floor y ( length of x ) ( width of x ) = ( length of y ) ( width of y ) ( 10 ) ( 18 ) = 9 n ( 10 ) ( 2 ) = n 20 = n answer b .


Question: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 18 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?

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

<gadget id="calculator">(1/5) * 18</gadget>
<output>18/5 = around 3.6</output>

<gadget id="calculator">(18/5) + 18</gadget>
<output>108/5 = around 21.6</output>

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

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

<gadget id="calculator">(108/5) / (4/5)</gadget>
<output>27</output>
<result>27</result>

Choices:
A. $ 25
B. $ 26
C. $ 27
D. $ 28
E. $ 29

divide(add(multiply(divide(20, const_100), 18), 18), divide(subtract(const_100, 20), const_100))

Explanation: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 18 ) = 0.8 x x = 1.2 ( 18 ) / 0.8 = 1.5 ( 18 ) = $ 27 the answer is c ."


Question: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 47 kg , then the weight of b is :

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

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

<gadget id="calculator">80 + 94</gadget>
<output>174</output>

<gadget id="calculator">45 * 3</gadget>
<output>135</output>

<gadget id="calculator">174 - 135</gadget>
<output>39</output>
<result>39</result>

Choices:
A. 39 kg
B. 32 kg
C. 33 kg
D. 34 kg
E. none of these

subtract(add(multiply(40, const_2), multiply(47, const_2)), multiply(45, const_3))

Explanation: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 47 x 2 ) = 94 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 174 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 39 . b ’ s weight = 39 kg . answer : a"


Question: 6 women can do 75 units of work in 8 days by working 5 hrs / day . in how many days can 4 women do 30 units of work by working 8 hrs / day ?

<gadget id="calculator">6 * 8</gadget>
<output>48</output>

<gadget id="calculator">48 * 5</gadget>
<output>240</output>

<gadget id="calculator">240 / 75</gadget>
<output>16/5 = around 3.2</output>

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

<gadget id="calculator">32 / 30</gadget>
<output>16/15 = around 1.066667</output>

<gadget id="calculator">(16/5) / (16/15)</gadget>
<output>3</output>
<result>3</result>

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

divide(divide(multiply(multiply(6, 8), 5), 75), divide(multiply(4, 8), 30))

Explanation: 6 x 8 x 5 / 75 = 4 x 8 xa / 30 solve this for a then we get a = 3 days answer : a


Question: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 18 minutes is :

<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">20 + 5</gadget>
<output>25</output>

<gadget id="calculator">(3/10) * 25</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>

Choices:
A. 9.5
B. 5.5
C. 7.5
D. 6.5
E. 5.1

multiply(divide(18, const_60), add(20, 5))

Explanation: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 18 / 60 ) ) km = 7.5 km . answer : c"


Question: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 14 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?

Choices:
A. 117 %
B. 120 %
C. 121 %
D. 138 %
E. 145 %

multiply(power(add(1, divide(divide(14, const_100), const_2)), add(const_2, const_3)), const_100)

Explanation: "since michelle earns 14 % interest compounded semiannually , then she earns 7 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 7 % * 5 = 35 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 35 % , only answer choice d fits . answer : d"


Question: the average of the marks of 30 students in a class is 45 . if the marks of each student are doubled , find the new average ?

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

Choices:
A. 85
B. 77
C. 33
D. 90
E. 75

Explanation: "sum of the marks for the 30 students = 30 * 45 = 1350 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1350 * 2 = 2700 . so , the new average = 2700 / 30 = 90 . answer : d"


Question: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 25 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?

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

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

<gadget id="calculator">(1/2) - (1/4)</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">(1/4) / (3/4)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>

Choices:
A. 10 %
B. 12 %
C. 15 %
D. 17 %
E. 33 %

multiply(divide(subtract(divide(50, const_100), divide(25, const_100)), subtract(const_1, divide(25, const_100))), const_100)

Explanation: "lets assume that candidate got 25 % votes and total votes is 100 . candidate won = 25 remaining = 75 to get 50 % , candidate requires 25 votes from 100 which is 25 % and 25 votes from 75 . 25 / 75 = 33.33 % which is approx 33 % . hence the answer is e"


Question: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 100 shares of the company ' s stock ?

<gadget id="calculator">0.8 / 2</gadget>
<output>0.4</output>

<gadget id="calculator">1.1 - 0.8</gadget>
<output>0.3</output>

<gadget id="calculator">0.3 * 10</gadget>
<output>3</output>

<gadget id="calculator">3 * 0.04</gadget>
<output>0.12</output>

<gadget id="calculator">0.4 + 0.12</gadget>
<output>0.52</output>

<gadget id="calculator">0.52 * 100</gadget>
<output>52</output>
<result>52</result>

Choices:
A. $ 92
B. $ 96
C. $ 52
D. $ 120
E. $ 240

multiply(add(divide(0.80, const_2), multiply(multiply(subtract(1.10, 0.80), const_10), 0.04)), 100)

Explanation: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 100 - - > $ 52 answer is c"


Question: the price of precious stone is directly proportional to square of its weight . what will be the loss incurred if a stone weighing 28 gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15 : 13 ?

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

<gadget id="calculator">28 * 1_000</gadget>
<output>28_000</output>

<gadget id="calculator">28 * 28</gadget>
<output>784</output>

<gadget id="calculator">28_000 / 784</gadget>
<output>250/7 = around 35.714286</output>

<gadget id="calculator">13 * 13</gadget>
<output>169</output>

<gadget id="calculator">(250/7) * 169</gadget>
<output>42_250/7 = around 6_035.714286</output>

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

<gadget id="calculator">(250/7) * 225</gadget>
<output>56_250/7 = around 8_035.714286</output>

<gadget id="calculator">(42_250/7) + (56_250/7)</gadget>
<output>98_500/7 = around 14_071.428571</output>

<gadget id="calculator">28_000 - (98_500/7)</gadget>
<output>97_500/7 = around 13_928.571429</output>
<result>97_500/7 = around 13_928.571429</result>

Choices:
A. no loss
B. 10,000
C. 28,000
D. 9,500
E. 14,000

subtract(multiply(28, multiply(const_10, const_100)), add(multiply(divide(multiply(28, multiply(const_10, const_100)), multiply(28, 28)), multiply(13, 13)), multiply(divide(multiply(28, multiply(const_10, const_100)), multiply(28, 28)), multiply(15, 15))))

Explanation: x = 28000 / 28 ^ 2 = 35.71 cost of 15 g = 35.71 * 15 ^ 2 = 8035.714 cost of 13 g = 35.71 * 13 ^ 2 = 6035.714 total cost = 14071.428 loss = 28000 - 14071.428 = 13928.5 = 14000 answer : e


Question: roy is now 6 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy ’ s age multiplied by kelly ’ s age ?

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

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

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

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

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

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

<gadget id="calculator">12 * 9</gadget>
<output>108</output>
<result>108</result>

Choices:
A. 72
B. 84
C. 90
D. 96
E. 108

multiply(add(add(6, subtract(6, 4)), 4), add(subtract(add(6, subtract(6, 4)), divide(6, const_2)), 4))

Explanation: r = j + 6 = k + 3 r + 4 = 2 ( j + 4 ) ( j + 6 ) + 4 = 2 j + 8 j = 2 r = 8 k = 5 in 4 years ( r + 4 ) ( k + 4 ) = 12 * 9 = 108 the answer is e .


Question: the mean of 50 observations was 36 . it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :

<gadget id="calculator">36 * 50</gadget>
<output>1_800</output>

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

<gadget id="calculator">48 - 23</gadget>
<output>25</output>

<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>

<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>73/2 = around 36.5</result>

Choices:
A. 35.2
B. 36.1
C. 36.5
D. 39.1
E. none of these

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50)

Explanation: "solution correct sum = ( 36 × 50 + 48 - 23 ) = 1525 . ∴ correct mean = 1825 / 50 = 36.5 answer c"


Question: there are 750 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?

<gadget id="calculator">750 / 3</gadget>
<output>250</output>

<gadget id="calculator">250 * 4</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 750</gadget>
<output>250</output>

<gadget id="calculator">250 / 2</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 75
B. 100
C. 125
D. 175
E. 225

divide(subtract(multiply(divide(750, const_3), const_4), 750), const_2)

Explanation: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 750 . hence , we have m + f = 750 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 750 / 3 = 250 solving the three equations yields the solution f = 250 , m = 500 , and d = 250 . the number of female democratic participants equals half the female participants equals 250 / 2 = 125 . answer : c"


Question: in what ratio must water be mixed with milk to gain 16 2 / 3 % on selling the mixture at cost price ?

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

<gadget id="calculator">16 + (2/3)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) / 100</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

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

divide(add(16, divide(2, 3)), const_100)

Explanation: required ratio is cheaper quantity : dearer quantity = ( d - m ) : ( m - c ) answer with explanation : step i ) let c . p of 1 litre of mild be rs . 1 and s . p of 1 litre of mild be rs . 1 gain = 50 / 3 per cent  c . p of 1 litre of mixture =              1 3 50 100 100 x = re . 100 x 3 / 350 x 1 = 6 / 7 ( mean price ) step ( ii ) by the rule of allegation i . c . p of 1 liter of water = 0 ii . c . p of 1 liter of milk = 1 iii . mean price ( p ) = 6 / 7 iv . d – m = 1 – 6 / 7 = 1 / 7 v . m – c = 6 / 7 - 0 = 6 / 7  ratio of water and milk = 1 / 7 : 6 / 7 = 1 : 6 answer : d


Question: 9 friends decided to divide the hotel bill evenly . if the bill was $ 124.15 dollars , how much money did they pay if 1 cent is the smallest unit ?

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

<gadget id="calculator">124.15 - (1/25)</gadget>
<output>124.11</output>
<result>124.11</result>

Choices:
A. $ 124.11
B. $ 124.12
C. $ 124.13
D. $ 124.14
E. $ 124.15

Explanation: this is equivalent to finding the first number that is divisible by 9 that occurs after 12415 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 12415 = 13 and 9 is divisible by 9 . hence , we need to remove 4 to this number for it to be divisible by 9 correct option : a


Question: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 36 miles on saturday and sunday , how many miles did bill run on sunday ?

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

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

<gadget id="calculator">36 - 12</gadget>
<output>24</output>

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

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

Choices:
A. 5
B. 6
C. 7
D. 8
E. 10

add(divide(subtract(36, add(4, multiply(const_2, 4))), 4), 4)

Explanation: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 36 . . 4 x + 12 = 36 . . x = 6 . . ans = x + 4 = 6 + 4 = 10 answer e"


Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 2000 resolutions ?

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

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

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

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

<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>

<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>

<gadget id="calculator">140.8 * 2_000</gadget>
<output>281_600</output>

<gadget id="calculator">281_600 / 100</gadget>
<output>2_816</output>
<result>2_816</result>

Choices:
A. 1187 m
B. 1704 m
C. 2816 m
D. 2827 m
E. 2897 m

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 2000), const_100)

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2000 resolutions . = 2000 * 2 * 22 / 7 * 22.4 = 281600 cm = 2816 m answer : c"


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 300 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">300 / 60</gadget>
<output>5</output>
<result>5</result>

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

divide(300, 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 300 envelopes they will take 300 / 60 mins . i . e . , 5 mins . answer : b"


Question: the sum of first 45 natural numbers is ?

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

<gadget id="calculator">45 * 46</gadget>
<output>2_070</output>

<gadget id="calculator">2_070 / 2</gadget>
<output>1_035</output>
<result>1_035</result>

Choices:
A. 1030
B. 1034
C. 1035
D. 1037
E. 1040

divide(multiply(45, add(45, const_1)), const_2)

Explanation: "let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . c )"


Question: vehicle x is 22 miles ahead of vehicle y , which is traveling the same direction along the same route as vehicle x . if vehicle x is traveling at an average speed of 36 miles per hour and vehicle y is traveling at an average speed of 45 miles per hour , how long will it take vehicle y to overtake and drive 23 miles ahead of vehicle x ?

<gadget id="calculator">22 + 23</gadget>
<output>45</output>

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

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

Choices:
A. 5 hours
B. 7 hours 20 minutes
C. 4 hours
D. 3 hours 45 minutes
E. 2 hours 30 minutes

Explanation: relative speed = 45 - 36 = 9 miles per hour dist required = 22 + 23 = 45 miles time taken to overtake = 45 / 9 = 5 hours . a is the answer .


Question: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 5 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?

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

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

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

<gadget id="calculator">480 / 2</gadget>
<output>240</output>

<gadget id="calculator">10 * 240</gadget>
<output>2_400</output>

<gadget id="calculator">1 * 2_400</gadget>
<output>2_400</output>
<result>2_400</result>

Choices:
A. 600
B. 1200
C. 1500
D. 1600
E. 2400

multiply(divide(5, 5), multiply(10, divide(multiply(8, 60), subtract(10, 8))))

Explanation: "sugar : flour = 5 : 5 = 10 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 10 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 10 x = 2400 answer : e ."


Question: the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?

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

<gadget id="calculator">24 + 70</gadget>
<output>94</output>
<result>94</result>

Choices:
A. 94 kg
B. 85 kg
C. 90 kg
D. 100 kg
E. 110 kg

Explanation: "total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 70 + 24 ) kg = 94 kg . answer : a"


Question: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 10 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?

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

<gadget id="calculator">15 + 25</gadget>
<output>40</output>

<gadget id="calculator">24 * 40</gadget>
<output>960</output>

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

<gadget id="calculator">960 - 18</gadget>
<output>942</output>

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

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

<gadget id="calculator">942 - 36</gadget>
<output>906</output>

<gadget id="calculator">906 * 10</gadget>
<output>9_060</output>
<result>9_060</result>

Choices:
A. s . 9060
B. s . 4520
C. s . 4527
D. s . 4530
E. s . 4521

multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 10)

Explanation: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 10 = rs . 9060 answer : a"


Question: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 7 days . b can do the work alone in ?

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

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

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

Choices:
A. 19
B. 12
C. 11
D. 42
E. 114

multiply(add(add(const_1, const_2), const_3), 7)

Explanation: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 7 6 / x = 1 / 7 = > x = 42 so , b takes 21 hours to finish the work . answer : d"


Question: a man can swim in still water at 4.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?

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

Choices:
A. 1.0
B. 1.9
C. 1.6
D. 1.5
E. 1.1

Explanation: "m = 4.5 s = x ds = 4.5 + x us = 4.5 + x 4.5 + x = ( 4.5 - x ) 2 4.5 + x = 9 - 2 x 3 x = 4.5 x = 1.5 answer : d"


Question: ifaequals the sum of the even integers from 2 to 120 , inclusive , andbequals the sum of the odd integers from 1 to 119 , inclusive , what is the value of a - b ?

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

<gadget id="calculator">60 + 1</gadget>
<output>61</output>

<gadget id="calculator">60 * 61</gadget>
<output>3_660</output>

<gadget id="calculator">119 + 1</gadget>
<output>120</output>

<gadget id="calculator">119 - 1</gadget>
<output>118</output>

<gadget id="calculator">118 / 2</gadget>
<output>59</output>

<gadget id="calculator">59 + 1</gadget>
<output>60</output>

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

<gadget id="calculator">3_660 - 3_600</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 60
B. 10
C. 19
D. 20
E. 21

subtract(multiply(divide(120, 2), add(divide(120, 2), 1)), multiply(divide(add(119, 1), 2), add(divide(subtract(119, 1), 2), 1)))

Explanation: "this is a solution from beatthegmat : even numbers : ( 120 - 2 ) / 2 + 1 = 60 even integers . ( 120 + 2 ) / 2 = 61 is the average of the even set . sum = avg * ( # of elements ) = 61 * 60 = 3660 = a odd numbers : ( 119 - 1 ) / 2 + 1 = 60 odd integers . ( 119 + 1 ) / 2 = 60 is the average of the odd set . sum = avg * ( # of elements ) = 60 * 60 = 3600 = b a - b = 3660 - 3600 = 60 . answer : a"


Question: at what price must an article costing rs . 47.50 be marked in order that after deducting 7 % from the list price . it may be sold at a profit of 25 % on the cost price ?

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

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

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

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

<gadget id="calculator">100 - 7</gadget>
<output>93</output>

<gadget id="calculator">5_937.5 / 93</gadget>
<output>63.844086</output>
<result>63.844086</result>

Choices:
A. 63.84
B. 62.6
C. 62.1
D. 62.7
E. 62.2

divide(multiply(add(47.50, divide(multiply(47.50, 25), const_100)), const_100), subtract(const_100, 7))

Explanation: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 93 / 100 ) = 59.375 mp = 63.84 answer : a"


Question: in may mrs lee ' s earnings were 50 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?

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

<gadget id="calculator">120 + 100</gadget>
<output>220</output>

<gadget id="calculator">120 / 220</gadget>
<output>6/11 = around 0.545455</output>

<gadget id="calculator">(6/11) * 100</gadget>
<output>600/11 = around 54.545455</output>
<result>600/11 = around 54.545455</result>

Choices:
A. 55
B. 56
C. 34
D. 78
E. 23

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

Explanation: lets say the family income is 100 in may , lee earned 50 family income is 50 in june , lee earned 20 % more than may , so it is ( 50 + 20 * 50 / 100 = 60 ) family income is same 50 in june lee ' s income percent is 60 * 100 / 110 ~ 55 ans is a


Question: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 69 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

<gadget id="calculator">75 - 69</gadget>
<output>6</output>

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

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

<gadget id="calculator">6 / (1/5)</gadget>
<output>30</output>
<result>30</result>

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

divide(subtract(75, 69), subtract(const_1, divide(80, const_100)))

Explanation: "there are 6 books less ( 75 - 69 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 30 answer b"


Question: if an object travels 300 feet in 6 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )

<gadget id="calculator">300 / 5_280</gadget>
<output>5/88 = around 0.056818</output>

<gadget id="calculator">1 / 3_600</gadget>
<output>1/3_600 = around 0.000278</output>

<gadget id="calculator">6 * (1/3_600)</gadget>
<output>1/600 = around 0.001667</output>

<gadget id="calculator">(5/88) / (1/600)</gadget>
<output>375/11 = around 34.090909</output>
<result>375/11 = around 34.090909</result>

Choices:
A. 30
B. 31
C. 32
D. 33
E. 34

divide(divide(300, 5280), multiply(6, divide(1, const_3600)))

Explanation: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 300 feet in 6 sec then it travels 300 / 6 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 50 feet in 1 hour = 180000 feet in 1 hr = 180000 / 5280 miles in 1 hour = 18000 / 528 miles / hr ~ 34 miles / hr answer - e"


Question: in a sports club with 80 members , 48 play badminton and 46 play tennis and 7 do not play either . how many members play both badminton and tennis ?

<gadget id="calculator">48 + 46</gadget>
<output>94</output>

<gadget id="calculator">94 + 7</gadget>
<output>101</output>

<gadget id="calculator">101 - 80</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 23
B. 21
C. 20
D. 26
E. 27

Explanation: 48 + 46 = 94 but where as total number is 80 - 7 = 73 therefore answer is 94 - 73 = 21 hence answer is b


Question: in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.60 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?

<gadget id="calculator">120 * 65</gadget>
<output>7_800</output>

<gadget id="calculator">7_800 / 100</gadget>
<output>78</output>

<gadget id="calculator">78 + 65</gadget>
<output>143</output>

<gadget id="calculator">143 * 2</gadget>
<output>286</output>

<gadget id="calculator">286 * 0.6</gadget>
<output>171.6</output>

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

<gadget id="calculator">195 * 0.6</gadget>
<output>117</output>

<gadget id="calculator">171.6 + 117</gadget>
<output>288.6</output>

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

<gadget id="calculator">2.1 * 5</gadget>
<output>10.5</output>

<gadget id="calculator">288.6 + 10.5</gadget>
<output>299.1</output>
<result>299.1</result>

Choices:
A. $ 287.50
B. $ 290.40
C. $ 293.30
D. $ 296.20
E. $ 299.10

add(add(multiply(multiply(add(divide(multiply(120, 65), const_100), 65), 2), 0.60), multiply(multiply(3, 65), 0.60)), multiply(2.10, add(3, 2)))

Explanation: "the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.6 = $ 288.60 the total cost is $ 288.60 + $ 10.50 = $ 299.10 the answer is e ."


Question: half a number plus 7 is 17 . what is the number ?

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

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

Choices:
A. 8
B. 9
C. 10
D. 11
E. 20

Explanation: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 7 = 17 ( 1 / 2 ) x = 17 - 7 ( 1 / 2 ) x = 20 x = 20 correct answer is e"


Question: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 343 , what is the common ratio of the g . p ?

<gadget id="calculator">343 - 1</gadget>
<output>342</output>

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

<gadget id="calculator">342 ** (1/3)</gadget>
<output>342**(1/3) = around 6.993191</output>
<result>342**(1/3) = around 6.993191</result>

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

power(subtract(343, const_1), divide(const_1, 3))

Explanation: "343 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 343 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 343 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 342 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 342 = r ^ 3 r = 7 d"


Question: bert and rebecca were looking at the price of a condominium . the price of the condominium was 50 % more than bert had in savings , and separately , the same price was also 25 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .

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

<gadget id="calculator">100 / 150</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">100 / 125</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(2/3) / (4/5)</gadget>
<output>5/6 = around 0.833333</output>
<result>5/6 = around 0.833333</result>

Choices:
A. 1 : 6
B. 1 : 3
C. 1 : 2
D. 3 : 4
E. 5 : 6

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

Explanation: "suppose bert had 100 so price becomes 150 , this 150 = 1.25 times r ' s saving . . so r ' s saving becomes 120 so required ratio is 100 : 120 = 5 : 6 answer : e"


Question: a shopkeeper sells 500 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?

<gadget id="calculator">18_000 / 500</gadget>
<output>36</output>

<gadget id="calculator">36 + 5</gadget>
<output>41</output>
<result>41</result>

Choices:
A. 12
B. 27
C. 29
D. 50
E. 41

Explanation: sp per metre = 18000 / 500 = rs . 36 loss per metre = rs . 5 cp per metre = 36 + 5 = rs . 41 . answer : e


Question: the difference of two numbers is 1565 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?

<gadget id="calculator">1_565 + 15</gadget>
<output>1_580</output>

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

<gadget id="calculator">1_580 / 5</gadget>
<output>316</output>
<result>316</result>

Choices:
A. 270
B. 280
C. 290
D. 300
E. 310

divide(add(1565, 15), subtract(6, const_1))

Explanation: "let the smaller number be x . then larger number = ( x + 1565 ) . x + 1565 = 6 x + 15 5 x = 1550 x = 310 smaller number = 310 . e )"


Question: how many even number in the range between 15 to 100 inclusive are not divisible by 3

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

<gadget id="calculator">85 - 2</gadget>
<output>83</output>

<gadget id="calculator">83 / 2</gadget>
<output>83/2 = around 41.5</output>

<gadget id="calculator">100 - 2</gadget>
<output>98</output>

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

<gadget id="calculator">98 - 12</gadget>
<output>86</output>

<gadget id="calculator">86 - 3</gadget>
<output>83</output>

<gadget id="calculator">83 - 3</gadget>
<output>80</output>

<gadget id="calculator">80 / 3</gadget>
<output>80/3 = around 26.666667</output>

<gadget id="calculator">(80/3) / 2</gadget>
<output>40/3 = around 13.333333</output>

<gadget id="calculator">(83/2) - (40/3)</gadget>
<output>169/6 = around 28.166667</output>
<result>169/6 = around 28.166667</result>

Choices:
A. 29
B. 30
C. 31
D. 33
E. 46

subtract(divide(subtract(subtract(100, 15), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(100, const_2), multiply(3, const_4)), 3), 3), 3), const_2))

Explanation: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 16,18 . . . 100 using ap formula , we can say 100 = 16 + ( n - 1 ) * 2 or n = 43 . for 6 , 18 , . . . 96 using ap formula , we can say 96 = 18 + ( n - 1 ) * 6 or n = 14 . hence , only divisible by 2 but not 3 = 43 - 14 = 29 . hence , answer a"


Question: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 7 per metre approximately

Choices:
A. 4457
B. 10400
C. 4235
D. 4547
E. 4675

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 7)

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 7 ) = rs . 10400 . answer : option b"


Question: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 2 m + n ?

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

<gadget id="calculator">4 * 9</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 11
B. 18
C. 20
D. 25
E. 35

Explanation: k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 2 * 10 + 15 = 35 answer : e


Question: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 7 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?

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

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

Choices:
A. 8 mph
B. 5.25 mph
C. 3.5 mph
D. 4 mph
E. 0.5 mph

Explanation: "( 1 mph + 7 mph ) / 2 = 4 mph correct option is : d"


Question: a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.0 km long ?

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

<gadget id="calculator">26 * 60</gadget>
<output>1_560</output>

<gadget id="calculator">1_560 / 1_000</gadget>
<output>39/25 = around 1.56</output>

<gadget id="calculator">(39/25) + 1</gadget>
<output>64/25 = around 2.56</output>
<result>64/25 = around 2.56</result>

Choices:
A. 2.5
B. 3
C. 5
D. 7
E. 9

add(divide(multiply(add(25, const_1), 60), const_1000), 1.0)

Explanation: "d = 25 * 60 + 1000 = 2500 m t = 2500 / 60 * 18 / 5 = 150 sec = 2.5 mins answer : a"


Question: find the principle on a certain sum of money at 9 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?

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

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

<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(12/5) * 9</gadget>
<output>108/5 = around 21.6</output>

<gadget id="calculator">(108/5) / 100</gadget>
<output>27/125 = around 0.216</output>

<gadget id="calculator">(27/125) + 1</gadget>
<output>152/125 = around 1.216</output>

<gadget id="calculator">1_120 / (152/125)</gadget>
<output>17_500/19 = around 921.052632</output>
<result>17_500/19 = around 921.052632</result>

Choices:
A. 1000
B. 912.88
C. 927.78
D. 926.82
E. 921.05

divide(1120, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 9), const_100), const_1))

Explanation: 1120 = p [ 1 + ( 9 * 12 / 5 ) / 100 ] p = 921.05 answer : e


Question: a man whose bowling average is 12.4 , takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?

<gadget id="calculator">floor(12.4)</gadget>
<output>12</output>

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

<gadget id="calculator">60 - 26</gadget>
<output>34</output>

<gadget id="calculator">12.4 - 12</gadget>
<output>0.4</output>

<gadget id="calculator">34 / 0.4</gadget>
<output>85</output>
<result>85</result>

Choices:
A. 82
B. 83
C. 84
D. 85
E. 86

divide(subtract(multiply(floor(12.4), 5), 26), subtract(12.4, floor(12.4)))

Explanation: "12.4 x + 26 / ( 5 + x ) = 12 12.4 x + 26 = 60 + 12 x x = 34 / 0.4 = 85 answer : d"


Question: anand finishes a work in 7 days , bittu finishes the same job in 8 days and chandu in 6 days . they take turns to finish the work . anand on the first day , bittu on the second and chandu on the third day and then anand again and so on . on which day will the work get over ?

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

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

<gadget id="calculator">(1/7) + (1/8)</gadget>
<output>15/56 = around 0.267857</output>

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

<gadget id="calculator">(15/56) + (1/6)</gadget>
<output>73/168 = around 0.434524</output>

<gadget id="calculator">1 / (73/168)</gadget>
<output>168/73 = around 2.30137</output>

<gadget id="calculator">(168/73) * 3</gadget>
<output>504/73 = around 6.90411</output>

<gadget id="calculator">floor(504/73)</gadget>
<output>6</output>

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

Choices:
A. 3 rd
B. 6 th
C. 9 th
D. 7 th
E. 8 th

add(floor(multiply(inverse(add(add(divide(const_1, 7), divide(const_1, 8)), divide(const_1, 6))), const_3)), const_1)

Explanation: they completed 146 / 168 work in 6 days working one by one on eacg day . on 7 th day , 22 / 168 work is left which will be completed by anand on 7 th day . answer : d


Question: if the product of two numbers is 45276 and their h . c . f . is 22 , find their l . c . m .

<gadget id="calculator">45_276 / 22</gadget>
<output>2_058</output>
<result>2_058</result>

Choices:
A. 2574
B. 2500
C. 2100
D. 2058
E. none of these

Explanation: explanation : hcf * lcm = 45276 , because we know product of two numbers = product of hcf and lcm lcm = 45276 / 22 = 2058 option d


Question: okeydokey paid 5 apples at the apple investment booth for an unopened box of earthworms . artichokey paid 7 apples towards the same lot . the booth pays off earthworms proportional to the apples invested . the box turned out to contain 60 earthworms . how many of them should okeydokey receive ?

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

<gadget id="calculator">5 + 7</gadget>
<output>12</output>

<gadget id="calculator">300 / 12</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 25
B. 27
C. 28
D. 29
E. 30

Explanation: i 1 = 5 i 2 = 7 i 1 share 5 parts & i 2 share 7 parts total 12 parts - - - - - > 60 - - - - > 1 part - - - - - - - > 5 i 1 share = 5 parts - - - - - > 25 a


Question: a glass was filled with 10 ounces of water , and 0.01 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?

<gadget id="calculator">0.01 * 20</gadget>
<output>0.2</output>

<gadget id="calculator">0.2 / 10</gadget>
<output>0.02</output>

<gadget id="calculator">0.02 * 100</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 0.002 %
B. 0.02 %
C. 0.2 %
D. 2 %
E. 20 %

multiply(divide(multiply(0.01, 20), 10), const_100)

Explanation: "in 20 days 20 * 0.01 = 0.2 ounces of water evaporated , which is 0.2 / 10 ∗ 100 = 2 of the original amount of water . answer : d ."


Question: a 64 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?

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

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

<gadget id="calculator">128 / 8</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 8
B. 12
C. 13
D. 14
E. 16

divide(multiply(64, subtract(10, 8)), 8)

Explanation: amount of salt = 6.4 assume x gallons of water are added . 6.4 / 64 + x = 8 / 100 640 = 8 x + 512 8 x = 128 x = 16 correct option : e


Question: there are 200 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?

<gadget id="calculator">99 / 100</gadget>
<output>99/100 = around 0.99</output>

<gadget id="calculator">200 * (99/100)</gadget>
<output>198</output>

<gadget id="calculator">98 / 100</gadget>
<output>49/50 = around 0.98</output>

<gadget id="calculator">200 * (49/50)</gadget>
<output>196</output>

<gadget id="calculator">198 - 196</gadget>
<output>2</output>

<gadget id="calculator">1 - (49/50)</gadget>
<output>1/50 = around 0.02</output>

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

Choices:
A. 150
B. 100
C. 99
D. 50
E. 25

divide(subtract(multiply(200, divide(99, const_100)), multiply(200, divide(98, const_100))), subtract(const_1, divide(98, const_100)))

Explanation: "there are 198 managers and 2 others . the 2 others would compose 2 % of the total number of people if there were 100 people in the room . thus 100 managers must leave . the answer is b ."


Question: if a and b are the roots of the equation x 2 - 9 x + 9 = 0 , then the value of a 2 + b 2 is :

<gadget id="calculator">9 ** 2</gadget>
<output>81</output>

<gadget id="calculator">4 * 9</gadget>
<output>36</output>

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

<gadget id="calculator">45 ** (1/2)</gadget>
<output>3*sqrt(5) = around 6.708204</output>

<gadget id="calculator">9 - (3*sqrt(5))</gadget>
<output>9 - 3*sqrt(5) = around 2.291796</output>

<gadget id="calculator">(9 - 3*sqrt(5)) / 2</gadget>
<output>9/2 - 3*sqrt(5)/2 = around 1.145898</output>

<gadget id="calculator">(9/2 - 3*sqrt(5)/2) ** 2</gadget>
<output>(9/2 - 3*sqrt(5)/2)**2 = around 1.313082</output>

<gadget id="calculator">9 + (3*sqrt(5))</gadget>
<output>3*sqrt(5) + 9 = around 15.708204</output>

<gadget id="calculator">(3*sqrt(5) + 9) / 2</gadget>
<output>3*sqrt(5)/2 + 9/2 = around 7.854102</output>

<gadget id="calculator">(3*sqrt(5)/2 + 9/2) ** 2</gadget>
<output>(3*sqrt(5)/2 + 9/2)**2 = around 61.686918</output>

<gadget id="calculator">((9/2 - 3*sqrt(5)/2)**2) + ((3*sqrt(5)/2 + 9/2)**2)</gadget>
<output>(9/2 - 3*sqrt(5)/2)**2 + (3*sqrt(5)/2 + 9/2)**2 = around 63</output>
<result>(9/2 - 3*sqrt(5)/2)**2 + (3*sqrt(5)/2 + 9/2)**2 = around 63</result>

Choices:
A. 63
B. 24
C. 17
D. 6
E. 5

add(power(divide(subtract(9, sqrt(subtract(power(9, 2), multiply(const_4, 9)))), 2), 2), power(divide(add(9, sqrt(subtract(power(9, 2), multiply(const_4, 9)))), 2), 2))

Explanation: "sol . ( b ) the sum of roots = a + b = 9 product of roots = ab = 9 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 81 - 18 = 63 answer a"


Question: a light has a rating of 80 watts , it is replaced with a new light that has 25 % higher wattage . how many watts does the new light have ?

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

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

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

Choices:
A. 105
B. 95
C. 80
D. 60
E. 100

multiply(80, add(const_1, divide(25, const_100)))

Explanation: "final number = initial number + 25 % ( original number ) = 80 + 25 % ( 80 ) = 80 + 20 = 100 . answer e"


Question: in the class of 40 students , 30 speak hindi and 20 speak english . what is the lowest possible number of students who speak both the languages ?

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

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

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

Explanation: let the student who speaks hindi - x let the student who speaks english - y as ( xuy ) - ( xny ) = total 30 + 20 - ( xny ) = 40 = 10 a )


Question: if k is an integer and 0.00010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?

<gadget id="calculator">100 / 0.000101</gadget>
<output>990_099.009901</output>

<gadget id="calculator">log(990_099.009901)</gadget>
<output>13.80556</output>

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

<gadget id="calculator">13.80556 / log(10)</gadget>
<output>13.80556/log(10) = around 5.995679</output>
<result>13.80556/log(10) = around 5.995679</result>

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

Explanation: 0.00010101 * 10 ^ k > 100 we need to move the decimal point to the right 6 places to get 101.01 this is equivalent to multiplying by 10 ^ 6 . the answer is d .


Question: how many numbers from 10 to 50 are exactly divisible by 3 .

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

<gadget id="calculator">floor(50/3)</gadget>
<output>16</output>

<gadget id="calculator">16 * 3</gadget>
<output>48</output>

<gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>

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

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

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

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

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

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

Choices:
A. 13
B. 14
C. 16
D. 17
E. 19

add(divide(subtract(multiply(floor(divide(50, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1)

Explanation: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits . a )"


Question: the ratio of laxmi ' s age to the age of her mother is 3 : 11 . the difference of their ages is 24 years . the ratio of their ages after 3 years will be ?

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

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

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

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

<gadget id="calculator">11 * 3</gadget>
<output>33</output>

<gadget id="calculator">33 + 3</gadget>
<output>36</output>

<gadget id="calculator">12 / 36</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>

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

divide(add(multiply(3, divide(24, subtract(11, 3))), 3), add(multiply(11, divide(24, subtract(11, 3))), 3))

Explanation: suppose age of laxmi is x years . the difference of their ages \ inline \ therefore ratio of their ages after 3 years = = = 12 : 36 = 1 : 3 answer : b


Question: solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 6 kilograms of solution y and 2 kilograms of solution y are added to the remaining 4 kilograms of liquid , what percent of this new solution is liquid x ?

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

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

<gadget id="calculator">2 * (3/10)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(9/5) + (3/5)</gadget>
<output>12/5 = around 2.4</output>

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

<gadget id="calculator">6 * (7/10)</gadget>
<output>21/5 = around 4.2</output>

<gadget id="calculator">(21/5) - 2</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">2 * (7/10)</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">(11/5) + (7/5)</gadget>
<output>18/5 = around 3.6</output>

<gadget id="calculator">(12/5) + (18/5)</gadget>
<output>6</output>

<gadget id="calculator">(12/5) / 6</gadget>
<output>2/5 = around 0.4</output>

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

Choices:
A. 33 %
B. 35 1 / 2 %
C. 37 %
D. 40 %
E. 42 %

multiply(const_100, divide(add(multiply(6, divide(30, const_100)), multiply(2, divide(30, const_100))), add(add(multiply(6, divide(30, const_100)), multiply(2, divide(30, const_100))), add(subtract(multiply(6, divide(70, const_100)), 2), multiply(2, divide(70, const_100))))))

Explanation: "in 8 kilograms of solution y there are 0.3 * 6 = 1.8 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 1.8 kilograms of solution x , 0.3 * 2 = 0.6 kilograms of solution x are added , so in the new solution of 6 kilograms there are 1.8 + 0.6 = 2.4 kilograms of solution x , which is 2.4 / 6 * 100 = 40 % of this new solution . answer : d ."


Question: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3312 , how much was it in the beginning ?

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

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

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

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

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

<gadget id="calculator">3_312 / (18/25)</gadget>
<output>4_600</output>

<gadget id="calculator">floor(4_600)</gadget>
<output>4_600</output>
<result>4_600</result>

Choices:
A. 3800
B. 4200
C. 4400
D. 4500
E. 4600

floor(divide(3312, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100))))

Explanation: "x * ( 90 / 100 ) * ( 80 / 100 ) = 3312 x = 4600 answer : e"


Question: a is twice as good a workman as b and they took 11 days together to do the work b alone can do it in .

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

<gadget id="calculator">11 * 3</gadget>
<output>33</output>

<gadget id="calculator">33 / 2</gadget>
<output>33/2 = around 16.5</output>

<gadget id="calculator">(33/2) * 2</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 17 days
B. 12 days
C. 29 days
D. 25 days
E. 33 days

multiply(divide(multiply(11, add(const_2, const_1)), const_2), const_2)

Explanation: "wc = 2 : 1 2 x + x = 1 / 11 x = 1 / 33 = > 33 days answer : e"


Question: if the price of 357 apples is rs . 1517.25 , what will be the approximate price of 49 dozens of such apples ?

<gadget id="calculator">49 * 12</gadget>
<output>588</output>

<gadget id="calculator">1_517.25 / 357</gadget>
<output>4.25</output>

<gadget id="calculator">588 * 4.25</gadget>
<output>2_499</output>
<result>2_499</result>

Choices:
A. rs . 2500
B. rs . 2300
C. rs . 2200
D. rs . 1400
E. rs . 1600

multiply(multiply(49, const_12), divide(1517.25, 357))

Explanation: explanation : price of 357 apples = rs . 1517.25 price of 1 apple = rs . 1517.25 / 357 price of 49 dozens apples = rs ( 49 × 12 × 1517.25 / 357 ) ≈ rs . 2500 answer : option a


Question: in the first 10 overs of a cricket game , the run rate was only 3.8 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?

<gadget id="calculator">10 * 3.8</gadget>
<output>38</output>

<gadget id="calculator">282 - 38</gadget>
<output>244</output>

<gadget id="calculator">244 / 40</gadget>
<output>61/10 = around 6.1</output>
<result>61/10 = around 6.1</result>

Choices:
A. 6.25
B. 6.5
C. 6.75
D. 6.1
E. 8

divide(subtract(282, multiply(10, 3.8)), 40)

Explanation: "10 overs - run rate = 3.8 runs scored in first 10 overs = 38 remaining overs 40 total runs to be scored = 282 38 runs already scored 282 - 38 = 244 244 runs to be scored in 40 overs let required runrate be x 40 * x = 244 x = 244 / 40 x = 6.1 the required runrate is 6.1 answer : d"


Question: a person buys an article at rs . 480 . at what price should he sell the article so as to make a profit of 24 % ?

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">480 * (6/25)</gadget>
<output>576/5 = around 115.2</output>

<gadget id="calculator">480 + (576/5)</gadget>
<output>2_976/5 = around 595.2</output>
<result>2_976/5 = around 595.2</result>

Choices:
A. 595
B. 882
C. 772
D. 662
E. 521

add(480, multiply(480, divide(24, const_100)))

Explanation: "cost price = rs . 480 profit = 24 % of 480 = rs . 115 selling price = cost price + profit = 480 + 115 = 595 answer : a"


Question: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 110 ?

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

Choices:
A. 10
B. 25
C. 55
D. 75
E. 100

Explanation: surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 110 / 2 = 55 answer is c


Question: roses can be purchased individually for $ 6.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?

<gadget id="calculator">680 / 50</gadget>
<output>68/5 = around 13.6</output>

<gadget id="calculator">floor(68/5)</gadget>
<output>13</output>

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

<gadget id="calculator">13 * 24</gadget>
<output>312</output>

<gadget id="calculator">13 * 50</gadget>
<output>650</output>

<gadget id="calculator">680 - 650</gadget>
<output>30</output>

<gadget id="calculator">30 / 6.3</gadget>
<output>4.761905</output>

<gadget id="calculator">floor(4.761905)</gadget>
<output>4</output>

<gadget id="calculator">312 + 4</gadget>
<output>316</output>
<result>316</result>

Choices:
A. 156
B. 162
C. 316
D. 324
E. 325

add(multiply(floor(divide(680, 50)), multiply(const_12, const_2)), floor(divide(subtract(680, multiply(floor(divide(680, 50)), 50)), 6.30)))

Explanation: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 6.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c ."


Question: the sub - duplicate ratio of 25 : 49 is

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

<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>

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

Choices:
A. 4 : 3
B. 5 : 7
C. 6 : 4
D. 1 : 4
E. 2 : 3

Explanation: "root ( 25 ) : root ( 49 ) = 5 : 7 answer : b"


Question: a man walking at a rate of 10 km / hr crosses a bridge in 24 minutes . the length of the bridge is ?

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

<gadget id="calculator">10_000 / 60</gadget>
<output>500/3 = around 166.666667</output>

<gadget id="calculator">(500/3) * 24</gadget>
<output>4_000</output>
<result>4_000</result>

Choices:
A. 1521
B. 1492
C. 1667
D. 4000
E. 1112

multiply(divide(multiply(10, const_1000), const_60), 24)

Explanation: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 24 minutes = 50 / 18 * 24 * 60 = 4000 m answer is d"


Question: find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?

<gadget id="calculator">6.3 - 5.7</gadget>
<output>0.6</output>

<gadget id="calculator">7.1 - 6.3</gadget>
<output>0.8</output>

<gadget id="calculator">0.6 / 0.8</gadget>
<output>0.75</output>
<result>0.75</result>

Choices:
A. 1 : 3
B. 2 : 3
C. 3 : 4
D. 4 : 5
E. none of these

Explanation: "solution required ratio = 60 : 80 = 3 : 4 answer c"


Question: a class consists of 15 biology students and 10 chemistry students . if you pick two students at the same time , what ' s the probability that one is maths and one is chemistry ?

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

<gadget id="calculator">15 / 25</gadget>
<output>3/5 = around 0.6</output>

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

<gadget id="calculator">10 / 24</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">(3/5) * (5/12)</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">15 / 24</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">10 / 25</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(5/8) * (2/5)</gadget>
<output>1/4 = around 0.25</output>

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

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

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

Explanation: p ( 1 st b , 2 nd c ) = 15 / 25 * 10 / 24 = 150 / 600 = 1 / 4 ; p ( 1 st c , 2 nd b ) = 10 / 25 * 15 / 24 = 150 / 600 = 1 / 4 . p = 1 / 4 + 1 / 4 = 1 / 2 . answer : c .


Question: an aeroplane covers a certain distance of 420 kmph in 6 hours . to cover the same distance in 4 2 / 3 hours , it must travel at a speed of

<gadget id="calculator">420 * 6</gadget>
<output>2_520</output>

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

<gadget id="calculator">12 + 2</gadget>
<output>14</output>

<gadget id="calculator">14 / 3</gadget>
<output>14/3 = around 4.666667</output>

<gadget id="calculator">2_520 / (14/3)</gadget>
<output>540</output>
<result>540</result>

Choices:
A. 440
B. 540
C. 640
D. 740
E. 250

divide(multiply(420, 6), divide(add(multiply(3, 4), 2), 3))

Explanation: "speed of aeroplane = 420 kmph distance travelled in 6 hours = 420 * 6 = 2520 km speed of aeroplane to acver 2520 km in 14 / 3 = 2520 * 3 / 14 = 540 km answer b ."


Question: the average mark of the students of a class in a particular exam is 80 . if 8 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .

<gadget id="calculator">90 * 8</gadget>
<output>720</output>

<gadget id="calculator">8 * 20</gadget>
<output>160</output>

<gadget id="calculator">720 - 160</gadget>
<output>560</output>

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

<gadget id="calculator">560 / 10</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 15
B. 25
C. 35
D. 45
E. 56

divide(subtract(multiply(90, 8), multiply(8, 20)), subtract(90, 80))

Explanation: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 8 ) students = 90 ( x - 8 ) 80 x - ( 8 * 20 ) = 90 ( x - 8 ) 560 = 10 x = > x = 56 answer : e"


Question: what is the smallest integer k for which 64 ^ k > 4 ^ 17 ?

<gadget id="calculator">17 / 3</gadget>
<output>17/3 = around 5.666667</output>

<gadget id="calculator">floor(17/3)</gadget>
<output>5</output>

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

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

Explanation: "64 ^ k > 4 ^ 17 4 ^ ( 3 k ) > 4 ^ 17 3 k > 17 k = 6 the answer is c ."


Question: one side of a rectangular field is 14 m and one of its diagonal is 17 m . find the area of the field .

<gadget id="calculator">17 ** 2</gadget>
<output>289</output>

<gadget id="calculator">14 ** 2</gadget>
<output>196</output>

<gadget id="calculator">289 - 196</gadget>
<output>93</output>

<gadget id="calculator">93 ** (1/2)</gadget>
<output>sqrt(93) = around 9.643651</output>

<gadget id="calculator">14 * (sqrt(93))</gadget>
<output>14*sqrt(93) = around 135.011111</output>
<result>14*sqrt(93) = around 135.011111</result>

Choices:
A. 134.4
B. 120
C. 150
D. 180
E. none

rectangle_area(14, sqrt(subtract(power(17, const_2), power(14, const_2))))

Explanation: "solution other side = √ ( 17 ) 2 - ( 14 ) 2 = √ 289 - 196 = √ 93 = 9.6 m . ∴ area = ( 14 x 9.6 ) m 2 = 134.4 m 2 . answer a"


Question: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 24 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?

<gadget id="calculator">5 / 60</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">24 * (1/12)</gadget>
<output>2</output>

<gadget id="calculator">4 * (1/12)</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">(5/3) / 4</gadget>
<output>5/12 = around 0.416667</output>

<gadget id="calculator">(5/12) * 60</gadget>
<output>25</output>
<result>25</result>

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

multiply(divide(subtract(multiply(24, divide(5, const_60)), multiply(4, divide(5, const_60))), 4), const_60)

Explanation: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 24 = 2 km . the time it takes the hiker to complete this distance is 2 / 4 hours = 30 minutes the cyclist needs to wait 30 - 5 = 25 minutes the answer is d ."


Question: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.1 kg . the weight of the new student is

<gadget id="calculator">29 + 1</gadget>
<output>30</output>

<gadget id="calculator">30 * 27.1</gadget>
<output>813</output>

<gadget id="calculator">29 * 28</gadget>
<output>812</output>

<gadget id="calculator">813 - 812</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 22 kg
B. 1 kg
C. 22.4 kg
D. 21 kg
E. none of these

subtract(multiply(add(29, const_1), 27.1), multiply(29, 28))

Explanation: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.1 weight of the new student = ( 30 * 27.1 – 29 * 28 ) = 813 - 812 = 1 answer : b"


Question: what will be in unit ' s place digit of 3 to the power 34 .

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

Choices:
A. 1
B. 6
C. 3
D. 0
E. 9

Explanation: as the unit place digit of 3 to the power of 1 is 3 , to the power of 2 is 9 . to the power of 3 is 7 , to the power of 4 is 1 and it ' ll be repeated again in the same order . . . . so the unit place digit of 3 to the power of 34 is 9 . . answer : e


Question: a group of 8 friends want to play doubles tennis . how many different ways can the group be divided into 4 teams of 2 people ?

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

<gadget id="calculator">32 * 2</gadget>
<output>64</output>

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

<gadget id="calculator">128 - 10</gadget>
<output>118</output>

<gadget id="calculator">118 - 10</gadget>
<output>108</output>
<result>108</result>

Choices:
A. 420
B. 2520
C. 168
D. 90
E. 105

subtract(subtract(multiply(multiply(multiply(8, 4), 2), 2), const_10), const_10)

Explanation: c 28 ∗ c 26 ∗ c 24 ∗ c 22 / 4 ! = 105 , we are dividing by 4 ! ( factorial of the # of teams ) as the order of the teams does not matter . if 8 people are - 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , then ( 12 ) ( 34 ) ( 56 ) ( 78 ) would be the same 4 teams as ( 56 ) ( 78 ) ( 12 ) ( 34 ) , as we do n ' t have team # 1 , team # 2 , . . . you can think about this in another way . for the first person we can pick a pair in 7 ways ; for the second one in 5 ways ( as two are already chosen ) ; for the third one in 3 ways ( as 4 people are already chosen ) ; for the fourth one there is only one left . so we have 7 * 5 * 3 * 1 = 105 answer : e


Question: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 10 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?

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

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

<gadget id="calculator">200 + 40</gadget>
<output>240</output>

<gadget id="calculator">240 / 100</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">(12/5) * 10</gadget>
<output>24</output>

<gadget id="calculator">240 - 24</gadget>
<output>216</output>
<result>216</result>

Choices:
A. $ 198
B. $ 216
C. $ 220
D. $ 230
E. $ 240

subtract(add(200, multiply(divide(200, const_100), 20)), multiply(divide(add(200, multiply(divide(200, const_100), 20)), const_100), 10))

Explanation: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 10 employee paid = . 9 * 240 = 216 $ answer b"


Question: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,455 , what was the total number of pairs of contact lenses that she sold ?

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

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

<gadget id="calculator">400 + 50</gadget>
<output>450</output>

<gadget id="calculator">450 + 5</gadget>
<output>455</output>

<gadget id="calculator">455 + 1_000</gadget>
<output>1_455</output>

<gadget id="calculator">150 * 5</gadget>
<output>750</output>

<gadget id="calculator">1_455 - 750</gadget>
<output>705</output>

<gadget id="calculator">150 + 85</gadget>
<output>235</output>

<gadget id="calculator">705 / 235</gadget>
<output>3</output>

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

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

Choices:
A. 11
B. 13
C. 15
D. 17
E. 19

add(multiply(divide(subtract(add(add(add(multiply(const_4, const_100), multiply(5, const_10)), 5), const_1000), multiply(150, 5)), add(150, 85)), const_2), 5)

Explanation: ( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a


Question: it costs $ 5 for the first 1 / 3 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 2 hours and 30 minutes , how much will it cost him ?

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

<gadget id="calculator">24 + 5</gadget>
<output>29</output>

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

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

<gadget id="calculator">(1/5) * 10</gadget>
<output>2</output>

<gadget id="calculator">29 + 2</gadget>
<output>31</output>
<result>31</result>

Choices:
A. $ 27 .
B. $ 29 .
C. $ 31 .
D. $ 33 .
E. $ 35 .

add(add(multiply(12, 2), 5), multiply(divide(12, const_60), divide(30, 3)))

Explanation: 2 hrs 30 min = 150 min first 20 min - - - - - - > $ 5 time left is 130 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 150 min costs $ 12 / 60 * 130 = > $ 26.00 so , total cost will be $ 26 + $ 5 = > $ 31 hence answer will be c