Question: it costs $ 2 for the first 15 minutes to use the bumper cars at a fair ground . after the first 15 minutes it costs $ 6 per hour . if a certain customer uses the bumper cars for 3 hours and 25 minutes , how much will it cost him ?

<gadget id="calculator">6 / 60</gadget>
<output>1/10 = around 0.1</output>

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

<gadget id="calculator">180 + 25</gadget>
<output>205</output>

<gadget id="calculator">205 - 15</gadget>
<output>190</output>

<gadget id="calculator">(1/10) * 190</gadget>
<output>19</output>

<gadget id="calculator">19 + 2</gadget>
<output>21</output>
<result>21</result>

Choices:
A. $ 22
B. $ 3
C. $ 15
D. $ 21
E. $ 30

add(multiply(divide(6, const_60), subtract(add(multiply(3, const_60), 25), 15)), 2)

Explanation: 3 hrs 25 min = 205 min first 15 min - - - - - - > $ 2 time left is 190 min . . . now , 60 min costs $ 6 1 min costs $ 6 / 60 190 min costs $ 6 / 60 * 190 = > $ 19 so , total cost will be $ 19 + $ 2 = > $ 21 the answer will be ( d ) $ 21


Question: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 30 paise per sq . metre

<gadget id="calculator">110 * 65</gadget>
<output>7_150</output>

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

<gadget id="calculator">110 - 5</gadget>
<output>105</output>

<gadget id="calculator">65 - 5</gadget>
<output>60</output>

<gadget id="calculator">105 * 60</gadget>
<output>6_300</output>

<gadget id="calculator">7_150 - 6_300</gadget>
<output>850</output>

<gadget id="calculator">850 * 30</gadget>
<output>25_500</output>

<gadget id="calculator">25_500 / 100</gadget>
<output>255</output>
<result>255</result>

Choices:
A. s 255
B. s 780
C. s 880
D. s 480
E. s 980

divide(multiply(subtract(multiply(110, 65), multiply(subtract(110, multiply(2.5, const_2)), subtract(65, multiply(2.5, const_2)))), 30), const_100)

Explanation: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 30 = 25500 p in rs = 25500 / 100 = rs 255 answer : a"


Question: john and andrew can finish the work 9 days if they work together . they worked together for 6 days and then andrew left . john finished the remaining work in another 6 days . in how many days john alone can finish the work ?

<gadget id="calculator">6 / 9</gadget>
<output>2/3 = around 0.666667</output>

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

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

Choices:
A. 30 days
B. 60 days
C. 18 days
D. 80 days
E. 90 days

divide(6, subtract(const_1, divide(6, 9)))

Explanation: amount of work done by john and andrew in 1 day = 1 / 9 amount of work done by john and andrew in 6 days = 6 ã — ( 1 / 9 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 6 days amount of work john can do in 1 day = ( 1 / 3 ) / 6 = 1 / 18 = > john can complete the work in 18 days answer : c


Question: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 160 runs and his average excluding these two innings is 58 runs , find his highest score .

<gadget id="calculator">60 * 46</gadget>
<output>2_760</output>

<gadget id="calculator">46 - 2</gadget>
<output>44</output>

<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>

<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>

<gadget id="calculator">160 + 208</gadget>
<output>368</output>

<gadget id="calculator">368 / 2</gadget>
<output>184</output>
<result>184</result>

Choices:
A. 184
B. 367
C. 269
D. 177
E. 191

divide(add(160, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

Explanation: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 160 x + ( x - 160 ) = 208 2 x = 368 x = 184 runs answer : a"


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

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

Choices:
A. 11
B. 12
C. 13
D. 14
E. 15

Explanation: "explanation : given that a + b = 14 + b + c = > a ? c = 14 + b ? b = 14 = > c is younger than a by 14 years answer : option d"


Question: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m , what is its area ?

<gadget id="calculator">2 * 23</gadget>
<output>46</output>

<gadget id="calculator">206 - 46</gadget>
<output>160</output>

<gadget id="calculator">160 / 4</gadget>
<output>40</output>

<gadget id="calculator">40 + 23</gadget>
<output>63</output>

<gadget id="calculator">63 * 40</gadget>
<output>2_520</output>
<result>2_520</result>

Choices:
A. 2520
B. 2510
C. 2525
D. 2025
E. 2020

rectangle_area(add(divide(subtract(206, multiply(const_2, 23)), const_4), 23), divide(subtract(206, multiply(const_2, 23)), const_4))

Explanation: l - b = 23 . . . ( 1 ) perimeter = 206 2 ( l = b ) = 206 l + b = 103 . . . ( 2 ) ( 1 ) + ( 2 ) 2 l = 23 + 103 = 126 l = 126 / 2 = 63 metre substituting the value of l in ( 1 ) , we get 63 - b = 23 b = 63 - 23 = 40 metre area = lb = 63 ã — 40 = 2520 m 2 answer : a


Question: a boat having a length 5 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

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

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

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

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

Choices:
A. 100 kg
B. 60 kg
C. 72 kg
D. 96 kg
E. none of these

multiply(multiply(multiply(5, 2), divide(1, const_100)), const_1000)

Explanation: "explanation : volume of water displaced = ( 5 x 2 x 0.01 ) m 3 = 0.10 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.10 x 1000 ) kg = 100 kg . answer : a"


Question: if 100 cats kill 100 mice in 100 days , then 4 cats would kill 4 mice in how many days ?

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

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

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

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

Choices:
A. 1 day
B. 4 days
C. 40 days
D. 100 days
E. 50 days

divide(multiply(multiply(4, 100), 100), multiply(100, 4))

Explanation: as 100 cats kill 100 mice in 100 days 1 cats kill 1 mouse in 100 days then 4 cats kill 4 mice in 100 days answer : d


Question: of the 55 cars on a car lot , 40 have air - conditioning , 25 have power windows , and 12 have both air - conditioning and power windows . how many of the cars on the lot have neither air - conditioning nor power windows ?

<gadget id="calculator">40 + 25</gadget>
<output>65</output>

<gadget id="calculator">65 - 12</gadget>
<output>53</output>

<gadget id="calculator">55 - 53</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 15
B. 8
C. 10
D. 2
E. 18

Explanation: total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d


Question: a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 420 less than the sum lent . what was the sum lent ?

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

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

<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">420 / (3/5)</gadget>
<output>700</output>
<result>700</result>

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

divide(420, subtract(const_1, divide(multiply(5, 8), const_100)))

Explanation: "p - 420 = ( p * 5 * 8 ) / 100 p = 700 the answer is c ."


Question: 30 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?

<gadget id="calculator">18 * 30</gadget>
<output>540</output>

<gadget id="calculator">540 / 27</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20
B. 77
C. 36
D. 25
E. 13

Explanation: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 30 : : 18 : x [ please pay attention , we have written 27 : 30 rather than 30 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 30 \ times 18 } { 27 } } x = 20 so 20 days will be required to get work done by 27 men . answer : a"


Question: if n is a positive integer and n ^ 2 is divisible by 200 , then what is the largest positive integer that must divide n ?

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

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

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

Choices:
A. 10
B. 15
C. 20
D. 36
E. 50

Explanation: 200 = 2 ^ 3 * 5 ^ 2 if 200 divides n ^ 2 , then n must be divisible by 2 ^ 2 * 5 = 20 the answer is c .


Question: john paid a sum of money for purchasing 20 pens , which he recovered in full when he sold 10 of them . what was his percentage of profit or loss per pen ?

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

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

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

Choices:
A. 100 %
B. 150 %
C. 90 %
D. 80 %
E. 95 %

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

Explanation: a 100 % if the sum he paid whilst purchasing 20 pens = a , then the cost price of each pen = a / 20 . since the amount he got whilst selling 10 pens is also = a then the selling price of each pen = a / 10 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 10 - a / 20 = a / 20 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 20 ) / ( a / 20 ) x 100 = 100 %


Question: find the smallest number of 6 digits exactly divisible by 25 , 3545 and 15 .

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

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

Choices:
A. 100555
B. 100775
C. 100885
D. 100995
E. 100665

Explanation: smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b .


Question: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?

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

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

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

Choices:
A. 25 %
B. 15 %
C. 20 %
D. 40 %
E. 45 %

multiply(divide(const_1, add(const_3, const_1)), const_100)

Explanation: ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a


Question: if two - third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be .

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

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

Choices:
A. 90 seconds
B. 70 seconds
C. 60 seconds
D. 9 minutes
E. 120 seconds

Explanation: "2 / 3 filled in 6 mint 1 / 3 filled in 3 mint thn 2 / 3 + 1 / 3 = 6 + 3 = 9 minutes answer : d"


Question: a batsman makes a score of 76 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .

<gadget id="calculator">17 * 3</gadget>
<output>51</output>

<gadget id="calculator">76 - 51</gadget>
<output>25</output>

<gadget id="calculator">25 + 3</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 36
B. 28
C. 42
D. 45
E. none of the above

Explanation: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 76 = 17 x or x = ( 76 – 48 ) = 28 . answer b"


Question: find the remainder of the division ( 2 ^ 14 ) / 7 .

<gadget id="calculator">2 ** 14</gadget>
<output>16_384</output>

<gadget id="calculator">16_384 % 7</gadget>
<output>4</output>
<result>4</result>

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

Explanation: "find the pattern of the remainders after each power : ( 2 ^ 1 ) / 7 remainder 2 ( 2 ^ 2 ) / 7 remainder 4 ( 2 ^ 3 ) / 7 remainder 1 - - > this is where the cycle ends ( 2 ^ 4 ) / 7 remainder 2 - - > this is where the cycle begins again ( 2 ^ 5 ) / 7 remainder 4 continuing the pattern to ( 2 ^ 14 ) / 7 gives us a remainder of 4 final answer : d ) 4"


Question: barbata invests $ 2600 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">(3/50) * 2_600</gadget>
<output>156</output>

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

<gadget id="calculator">2_600 * (1/20)</gadget>
<output>130</output>

<gadget id="calculator">156 - 130</gadget>
<output>26</output>

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

<gadget id="calculator">(2/25) - (3/50)</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">26 / (1/50)</gadget>
<output>1_300</output>
<result>1_300</result>

Choices:
A. 1200
B. 3000
C. 1300
D. 3600
E. 2400

divide(subtract(multiply(divide(6, const_100), 2600), multiply(2600, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100)))

Explanation: "let the additional invested amount for 8 % interest be x ; equation will be ; 2600 + 0.05 * 2600 + x + 0.08 x = 2600 + x + 0.06 ( 2600 + x ) 0.05 * 2600 + 0.08 x = 0.06 x + 0.06 * 2600 0.02 x = 2600 ( 0.06 - 0.05 ) x = 2600 * 0.01 / 0.02 = 1300 ans : ` ` c ' '"


Question: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses w at the restaurant ? ( assume that all boxes are filled to capacity . )

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

<gadget id="calculator">32 * 15</gadget>
<output>480</output>
<result>480</result>

Choices:
A. 96
B. 240
C. w = 256
D. w = 384
E. w = 480

Explanation: "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"


Question: if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?

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

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

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

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

<gadget id="calculator">45 * 11</gadget>
<output>495</output>

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

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

<gadget id="calculator">495 + 6</gadget>
<output>501</output>
<result>501</result>

Choices:
A. 171
B. 281
C. 391
D. 501
E. 613

add(multiply(divide(add(40, 50), const_2), add(subtract(50, 40), const_1)), add(divide(subtract(50, 40), const_2), const_1))

Explanation: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 40 + ( 11 - 1 ) * 1 } = 11 * 45 = 495 = x number of even number = ( 50 - 40 ) / 2 + 1 = 6 = y x + y = 495 + 6 = 501 d"


Question: a man swims downstream 28 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?

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

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

<gadget id="calculator">4 + 7</gadget>
<output>11</output>

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

Choices:
A. 6.5
B. 8.6
C. 7.5
D. 9.2
E. 5.5

divide(add(divide(16, 4), divide(28, 4)), const_2)

Explanation: "28 - - - 4 ds = 7 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : e"


Question: alice and bob drive at constant speeds toward each other on a highway . alice drives at a constant speed of 30 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if alice is 100 km away from bob at 7 am , and also 100 km away from bob at 11 am , then how fast is bob driving ( in kilometers per hour ) ?

<gadget id="calculator">100 + 100</gadget>
<output>200</output>

<gadget id="calculator">11 - 7</gadget>
<output>4</output>

<gadget id="calculator">200 / 4</gadget>
<output>50</output>

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

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

subtract(divide(add(100, 100), subtract(11, 7)), 30)

Explanation: alice and bob complete 200 km / 4 hours = 50 km / hour bob ' s speed is 50 - 30 = 20 km / hour the answer is a .


Question: the calendar of the year 2040 can be used again in the year ?

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

<gadget id="calculator">16 - 2</gadget>
<output>14</output>

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

<gadget id="calculator">28 + 2_040</gadget>
<output>2_068</output>
<result>2_068</result>

Choices:
A. 2063
B. 2061
C. 2111
D. 2191
E. 2068

add(multiply(subtract(multiply(const_4, const_4), const_2), const_2), 2040)

Explanation: "explanation : given year 2040 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2040 + 28 = 2068 answer : e"


Question: in what time will a train 100 metres long cross an electic pole , if its speed be 144 km / hr ?

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

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

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

Choices:
A. 2.5 sec
B. 4.25 sec
C. 5 sec
D. 12.5 sec
E. none

Explanation: "sol . speed = [ 144 x 5 / 18 ] m / sec = 40 m / sec . time taken = ( 100 / 40 ) sec = 2.5 sec . answer a"


Question: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back , how far is the place ?

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

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

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

<gadget id="calculator">96 * 25</gadget>
<output>2_400</output>

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

<gadget id="calculator">2_400 / 20</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 24 km
B. 30 km
C. 48 km
D. 120 km
E. 15 km

divide(multiply(multiply(subtract(10, 2), add(10, 2)), 25), add(subtract(10, 2), add(10, 2)))

Explanation: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 25 2 x + 3 x = 600 x = 120 km answer is d"


Question: from a group of 4 boys and 4 girls , 4 children are to be randomly selected . what is the probability that 2 boys and 2 girls will be selected ?

<gadget id="calculator">binomial(4, 2)</gadget>
<output>6</output>

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

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

<gadget id="calculator">binomial(8, 4)</gadget>
<output>70</output>

<gadget id="calculator">36 / 70</gadget>
<output>18/35 = around 0.514286</output>
<result>18/35 = around 0.514286</result>

Choices:
A. 12 / 29
B. 14 / 31
C. 16 / 33
D. 18 / 35
E. 20 / 37

divide(multiply(choose(4, const_2), choose(4, const_2)), choose(add(4, 4), 4))

Explanation: "the total number of ways to choose 4 children from 8 is 8 c 4 = 70 the number of ways to choose 2 boys and 2 girls is 4 c 2 * 4 c 2 = 6 * 6 = 36 p ( 2 boys and 2 girls ) = 36 / 70 = 18 / 35 the answer is d ."


Question: a can do a work in 8 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ?

<gadget id="calculator">8 * 24</gadget>
<output>192</output>

<gadget id="calculator">8 + 24</gadget>
<output>32</output>

<gadget id="calculator">192 / 32</gadget>
<output>6</output>
<result>6</result>

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

Explanation: "a rate = 1 / 8 b rate = 1 / 24 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 24 ) = 1 / 6 a & b finish the work in 6 days correct option is e"


Question: what is the remainder when 50 ! is divided by 16 ^ 8 ? ?

<gadget id="calculator">16 * 50</gadget>
<output>800</output>

<gadget id="calculator">800 % 8</gadget>
<output>0</output>
<result>0</result>

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

Explanation: "16 raise to 8 = 2 raise to 32 , now highest power of 2 divisible by 50 ! is 25 + 12 + 6 + 3 + 1 = 47 since 2 raise to 47 is divisible , 2 raise to 32 also will be divisible answer : a"


Question: if the cost price of 140 pencils is equal to the selling price of 100 pencils , the gain percent is

<gadget id="calculator">140 - 100</gadget>
<output>40</output>

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

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

Choices:
A. 36
B. 37
C. 38
D. 39
E. 40

divide(const_100, divide(100, subtract(140, 100)))

Explanation: "let c . p . of each pencil be re . 1 . then , c . p . of 100 pencils = rs . 100 ; s . p . of 100 pencils = rs . 140 . gain % = 40 / 100 * 100 = 40 % answer : e"


Question: mother , her daughter and her grand child weighs 140 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?

<gadget id="calculator">140 - 60</gadget>
<output>80</output>

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

<gadget id="calculator">60 - 16</gadget>
<output>44</output>
<result>44</result>

Choices:
A. 44
B. 47
C. 48
D. 49
E. 50

subtract(60, divide(subtract(140, 60), 5))

Explanation: "mother + daughter + child = 140 kg daughter + child = 60 kg mother = 140 - 60 = 80 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 80 = 16 kg so now daughter = 140 - ( mother + child ) = 140 - ( 80 + 16 ) = 44 kg answer : a"


Question: a mixture of sand and cement contains , 3 parts of sand and 5 parts of cement . how much of the mixture must be substituted with sand to make the mixture half sand and half cement ?

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

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

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

<gadget id="calculator">(8/5) / 8</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>

Choices:
A. 1 / 3
B. 1 / 4
C. 1 / 5
D. 1 / 7
E. 1 / 8

divide(add(const_1, divide(3, 5)), add(5, 3))

Explanation: we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c .


Question: a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 24.00 , how much did he pay for it ?

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

<gadget id="calculator">(1/5) * 24</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">24 - (24/5)</gadget>
<output>96/5 = around 19.2</output>
<result>96/5 = around 19.2</result>

Choices:
A. $ 14.40
B. $ 14.00
C. $ 10.00
D. $ 9.60
E. $ 20.00

subtract(24, multiply(divide(20, const_100), 24))

Explanation: let the cost price of book = x selling price of book = 24 $ markup % = 20 ( 120 / 100 ) x = 24 = > x = 20 answer e


Question: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 10 percent , but profits were 15 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?

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

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

<gadget id="calculator">15 * (9/10)</gadget>
<output>27/2 = around 13.5</output>

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

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

Choices:
A. 80 %
B. 105 %
C. 135 %
D. 124.2 %
E. 138 %

multiply(divide(multiply(15, subtract(const_1, divide(10, const_100))), 10), const_100)

Explanation: "the profit 0 f 2009 in terms of 2008 = 0.9 * 15 / 10 * 100 = 135 % c"


Question: find the simple interest on $ 10000 at 6 % per annum for 12 months ?

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

<gadget id="calculator">10_000 * (3/50)</gadget>
<output>600</output>
<result>600</result>

Choices:
A. $ 410
B. $ 500
C. $ 600
D. $ 710
E. $ 1000

Explanation: "p = $ 10000 r = 6 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 6 * 1 / 100 = $ 600 answer is c"


Question: of the 3,600 employees of company x , 12 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?

<gadget id="calculator">12 / 25</gadget>
<output>12/25 = around 0.48</output>

<gadget id="calculator">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">(12/25) * (3/4)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">1 - (12/25)</gadget>
<output>13/25 = around 0.52</output>

<gadget id="calculator">(9/25) + (13/25)</gadget>
<output>22/25 = around 0.88</output>

<gadget id="calculator">(9/25) / (22/25)</gadget>
<output>9/22 = around 0.409091</output>

<gadget id="calculator">(9/22) * 100</gadget>
<output>450/11 = around 40.909091</output>
<result>450/11 = around 40.909091</result>

Choices:
A. 40 %
B. 22.2 %
C. 20 %
D. 12.5 %
E. 11.1 %

multiply(divide(multiply(divide(12, 25), subtract(1, divide(1, 4))), add(multiply(divide(12, 25), subtract(1, divide(1, 4))), subtract(const_1, divide(12, 25)))), const_100)

Explanation: let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 %


Question: a man two flats for $ 675958 each . on one he gains 13 % while on the other he loses 13 % . how much does he gain or lose in the whole transaction ?

Choices:
A. 1.69 %
B. 2.56 %
C. 3.12 %
D. 4.65 %
E. 5.12 %

multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 13)), 675958), multiply(divide(const_100, subtract(const_100, 13)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 13)), 675958), multiply(divide(const_100, subtract(const_100, 13)), 675958))), const_100)

Explanation: "in such a case there is always a loss loss % = ( 13 / 10 ) ^ 2 = 120 / 71 = 1.69 % answer is a"


Question: what is the greatest of 3 consecutive integers whose sum is 30 ?

<gadget id="calculator">30 - 3</gadget>
<output>27</output>

<gadget id="calculator">27 / 3</gadget>
<output>9</output>

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

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

add(divide(subtract(30, 3), 3), const_2)

Explanation: "30 / 3 = 10 the three numbers are 9 , 10 , and 11 . the answer is d ."


Question: students of 3 different classes appeared in common examination . pass average of 10 students of first class was 45 % , pass average of 15 students of second class was 60 % and pass average of 25 students of third class was 80 % then what will be the pass average of all students of 3 classes ?

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

<gadget id="calculator">450 / 100</gadget>
<output>9/2 = around 4.5</output>

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

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

<gadget id="calculator">(9/2) + 9</gadget>
<output>27/2 = around 13.5</output>

<gadget id="calculator">25 * 80</gadget>
<output>2_000</output>

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

<gadget id="calculator">(27/2) + 20</gadget>
<output>67/2 = around 33.5</output>

<gadget id="calculator">(67/2) * 100</gadget>
<output>3_350</output>

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

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

<gadget id="calculator">3_350 / 50</gadget>
<output>67</output>
<result>67</result>

Choices:
A. 74 %
B. 75 %
C. 67 %
D. 72 %
E. none

divide(multiply(add(add(divide(multiply(10, 45), const_100), divide(multiply(15, 60), const_100)), divide(multiply(25, 80), const_100)), const_100), add(add(10, 15), 25))

Explanation: solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c


Question: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?

<gadget id="calculator">12 * 16</gadget>
<output>192</output>

<gadget id="calculator">192 / 2</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 70
B. 79
C. 85
D. 96
E. 92

Explanation: "the triangle with sides 20 cm , 12 cm and 16 cm is right angled , where the hypotenuse is 20 cm . area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"


Question: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

<gadget id="calculator">150 + 100</gadget>
<output>250</output>

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

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

<gadget id="calculator">250 / 10</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 2
B. 28
C. 25
D. 99
E. 12

Explanation: "d = 100 + 150 = 250 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 25 sec . answer : c"


Question: 34.94 + 240.016 + 23.98 = ?

<gadget id="calculator">34.94 + 240.016</gadget>
<output>274.956</output>

<gadget id="calculator">274.956 + 23.98</gadget>
<output>298.936</output>
<result>298.936</result>

Choices:
A. 298.936
B. 298.694
C. 289.496
D. 289.469
E. 298.964

Explanation: 34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a .


Question: meera purchased two 3 items from a shop . total price for 3 items is rs . 2000 / - she have given rs . 3000 / - what is the balance amount meera got ?

<gadget id="calculator">3_000 - 2_000</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 650
B. 1000
C. 1500
D. 800
E. 750

Explanation: total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b


Question: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 86 then find the correct average marks up to two decimal places .

<gadget id="calculator">35 * 72</gadget>
<output>2_520</output>

<gadget id="calculator">86 - 36</gadget>
<output>50</output>

<gadget id="calculator">2_520 - 50</gadget>
<output>2_470</output>

<gadget id="calculator">2_470 / 35</gadget>
<output>494/7 = around 70.571429</output>
<result>494/7 = around 70.571429</result>

Choices:
A. 73.41
B. 74.31
C. 72.43
D. 73.43
E. can not be determined

divide(subtract(multiply(35, 72), subtract(86, 36)), 35)

Explanation: "correct average = 35 x 72 + ( 86 - 36 ) / 35 ≈ 72 + 1.43 = 73.43 answer d"


Question: what is the smallest integer e greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?

<gadget id="calculator">lcm(6, 8)</gadget>
<output>24</output>

<gadget id="calculator">lcm(10, 24)</gadget>
<output>120</output>

<gadget id="calculator">120 + 1</gadget>
<output>121</output>
<result>121</result>

Choices:
A. 21
B. 41
C. e = 121
D. 241
E. 481

Explanation: or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c


Question: a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 30 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 40 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

<gadget id="calculator">(7/5) * 130</gadget>
<output>182</output>

<gadget id="calculator">182 - 100</gadget>
<output>82</output>
<result>82</result>

Choices:
A. 28 %
B. 82 %
C. 24.33 %
D. 29.109 %
E. 78 %

subtract(multiply(divide(add(const_100, 40), const_100), add(const_100, 30)), const_100)

Explanation: "anyways , one can infer that he ' steals ' 30 % from suppliers and then charges 40 % extra to customers so basically 1.3 * 1.4 = 1.82 given that 1 is start point , we get 21 % more hence answer is b"


Question: in a class of 37 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?

<gadget id="calculator">26 + 20</gadget>
<output>46</output>

<gadget id="calculator">46 - 17</gadget>
<output>29</output>

<gadget id="calculator">37 - 29</gadget>
<output>8</output>
<result>8</result>

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

Explanation: "26 + 20 - 17 = 29 37 - 29 = 8 play neither answer is b"


Question: a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 86 km downstream .

<gadget id="calculator">15 + 6</gadget>
<output>21</output>

<gadget id="calculator">86 / 21</gadget>
<output>86/21 = around 4.095238</output>
<result>86/21 = around 4.095238</result>

Choices:
A. 4.1 hr
B. 5.25 hr
C. 8.25 hr
D. 2.25 hr
E. 2.50 hr

Explanation: "speed of boat in still water = 15 km / hr speed of the stream = 6 km / hr speed downstream = ( 15 + 6 ) = 21 km / hr time taken to travel 86 km downstream = 86 â  „ 16 = 17 â  „ 4 = 4.1 hours answer is a"


Question: bhanu spends 30 % of his income on petrol on scooter 12 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?

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

<gadget id="calculator">300 / (3/10)</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 300</gadget>
<output>700</output>

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

<gadget id="calculator">700 * (3/25)</gadget>
<output>84</output>
<result>84</result>

Choices:
A. 62
B. 140
C. 84
D. 60
E. 123

multiply(subtract(divide(300, divide(30, const_100)), 300), divide(12, const_100))

Explanation: given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 12 % ( 700 ) = rs . 84 answer : c


Question: a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 370 - meter long platform ?

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

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

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

<gadget id="calculator">150 + 370</gadget>
<output>520</output>

<gadget id="calculator">520 / 10</gadget>
<output>52</output>
<result>52</result>

Choices:
A. 46
B. 48
C. 50
D. 52
E. 54

divide(add(multiply(multiply(36, const_0_2778), 15), 370), multiply(36, const_0_2778))

Explanation: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 370 ) / 10 = 52 seconds the answer is d ."


Question: a pump can fill a tank with water in 3 hours . because of a leak , it took 3 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?

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

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

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

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

<gadget id="calculator">1 / (10/3)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(1/3) - (3/10)</gadget>
<output>1/30 = around 0.033333</output>

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

Choices:
A. 17 hr
B. 19 hr
C. 30 hr
D. 14 hr
E. 16 hr

inverse(subtract(divide(1, 3), inverse(divide(add(multiply(3, 3), 1), 3))))

Explanation: "work done by the tank in 1 hour = ( 1 / 3 - 3 1 / 3 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : c"


Question: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 13 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?

<gadget id="calculator">100 + 13</gadget>
<output>113</output>

<gadget id="calculator">100 / 113</gadget>
<output>100/113 = around 0.884956</output>

<gadget id="calculator">(100/113) * 45</gadget>
<output>4_500/113 = around 39.823009</output>
<result>4_500/113 = around 39.823009</result>

Choices:
A. 38
B. 39
C. 40
D. 41
E. 42

multiply(divide(const_100, add(const_100, 13)), 45)

Explanation: "soln : - 13 x = 45 - - > 87 / 77 * x = 45 - - > x = 45 * 77 / 87 = 677 / 17 = ~ 40 . answer : c ."


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

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

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

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

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

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

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


Question: if ( a - b - c + d = 18 ) and ( a + b - c - d = 4 ) , what is the value of ( b - d ) ^ 2 ?

<gadget id="calculator">18 + 4</gadget>
<output>22</output>

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

<gadget id="calculator">4 - 11</gadget>
<output>-7</output>

<gadget id="calculator">(-7) ** 2</gadget>
<output>49</output>
<result>49</result>

Choices:
A. 49 .
B. 8 .
C. 12 .
D. 16 .
E. 64 .

power(subtract(4, divide(add(18, 4), 2)), 2)

Explanation: "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 4 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 4 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 14 ( 2 ) simplify - b + d = 7 b - d = - 7 ( b - d ) ^ 2 = ( - 7 ) ^ 2 = 49 my answer : a"


Question: john purchased some shirts and trousers for $ 800 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?

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

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

<gadget id="calculator">800 - 200</gadget>
<output>600</output>

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

<gadget id="calculator">600 / 60</gadget>
<output>10</output>
<result>10</result>

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

Explanation: given that the total purchase of two items cost 800 . so the average purchase of one item will cost 800 / 2 = 400 . its given as total shirt cost 400 $ less . hence total shirt cost = 400 - 200 and total trouser cost = 400 + 200 5 shirts = 200 $ = = > one shirt = 40 $ one trouser = 40 + 20 = 60 $ total trousers = 600 / 60 = 10 . e


Question: the average age of a class of 24 students is 23 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?

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

<gadget id="calculator">23 + 1</gadget>
<output>24</output>

<gadget id="calculator">25 * 24</gadget>
<output>600</output>

<gadget id="calculator">24 * 23</gadget>
<output>552</output>

<gadget id="calculator">600 - 552</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 40
B. 41
C. 48
D. 52
E. 43

subtract(multiply(add(24, 1), add(23, 1)), multiply(24, 23))

Explanation: "total age of all students = 24 ã — 23 total age of all students + age of the teacher = 25 ã — 24 age of the teacher = 25 ã — 24 â ˆ ’ 24 ã — 23 = 24 ( 25 â ˆ ’ 23 ) = 24 ã — 2 = 48 answer is c ."


Question: 45 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?

<gadget id="calculator">18 * 45</gadget>
<output>810</output>

<gadget id="calculator">810 / 27</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 24
B. 77
C. 30
D. 25
E. 13

Explanation: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 45 : : 18 : x [ please pay attention , we have written 27 : 45 rather than 45 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 45 \ times 18 } { 27 } } x = 30 so 30 days will be required to get work done by 27 men . answer : c"


Question: 27 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?

<gadget id="calculator">27 * 8</gadget>
<output>216</output>

<gadget id="calculator">216 / 30</gadget>
<output>36/5 = around 7.2</output>

<gadget id="calculator">(36/5) * 50</gadget>
<output>360</output>

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

<gadget id="calculator">60 - 27</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 33
B. 66
C. 88
D. 100
E. 281

subtract(divide(multiply(divide(multiply(27, 8), 30), 50), 6), 27)

Explanation: "( 27 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 60 60 – 27 = 33 answer : a"


Question: n and m are each 3 - digit integers . each of the numbers 2 , 3 , 4,5 , 6 , and 7 is a digit of either n or m . what is the smallest possible positive difference between n and m ?

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

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

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

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

Choices:
A. 59
B. 49
C. 58
D. 113
E. 131

subtract(subtract(const_100, multiply(subtract(7, 2), const_10)), const_1)

Explanation: "you have 6 digits : 2 , 3 , 4 , 5 , 6 , 7 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 7 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 376 and 425 ( difference is 49 ) or try and make a pair with ( 5 * * and 6 * * ) . make the 5 * * number as large as possible and make the 6 * * number as small as possible . we get 574 and 623 ( difference is 49 ) b"


Question: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 4 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?

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

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

<gadget id="calculator">21 * 4</gadget>
<output>84</output>

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

<gadget id="calculator">84 * (2/3)</gadget>
<output>56</output>

<gadget id="calculator">2_520 / 56</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 30
B. 20
C. 15
D. 25
E. 45

divide(multiply(multiply(15, 21), 8), multiply(multiply(21, 4), divide(2, 3)))

Explanation: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 4 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 4 * ( 2 / 3 ) ) days = > 45 days answer : e"


Question: on dividing 21 by a number , the quotient is 10 and the remainder is 1 . find the divisor .

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

<gadget id="calculator">floor(21/10)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 1
B. 2
C. 4
D. 6
E. 7

Explanation: "d = ( d - r ) / q = ( 21 - 1 ) / 10 = 20 / 10 = 2 b"


Question: if length of a rectangle is equal to side of a square and breadth of rectangle is half of length . if area of square is 36 sq . m . calculate the area of rectangle ?

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

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

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

Choices:
A. 18
B. 20
C. 27
D. 32
E. 25

Explanation: side of square = √ 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a


Question: the price of a t . v . set worth rs . 70000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?

<gadget id="calculator">70_000 - 1_000</gadget>
<output>69_000</output>
<result>69_000</result>

Choices:
A. 22678
B. 26699
C. 69000
D. 19000
E. 26711

Explanation: "money paid in cash = rs . 1000 balance payment = ( 70000 - 1000 ) = rs . 69000 answer : c"


Question: the original price of a suit is $ 200 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?

<gadget id="calculator">200 * 20</gadget>
<output>4_000</output>

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

<gadget id="calculator">200 + 40</gadget>
<output>240</output>

<gadget id="calculator">240 * 20</gadget>
<output>4_800</output>

<gadget id="calculator">4_800 / 100</gadget>
<output>48</output>

<gadget id="calculator">240 - 48</gadget>
<output>192</output>
<result>192</result>

Choices:
A. $ 192
B. $ 198
C. $ 200
D. $ 208
E. $ 216

subtract(add(200, divide(multiply(200, 20), const_100)), divide(multiply(add(200, divide(multiply(200, 20), const_100)), 20), const_100))

Explanation: "0.8 * ( 1.2 * 200 ) = $ 192 the answer is a ."


Question: in a basketball game , dhoni scored 30 points more than dravid , but only half as many points as shewag . if the 3 players scored a combined total of 150 points , how many points did dhoni score ?

<gadget id="calculator">150 + 30</gadget>
<output>180</output>

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

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

<gadget id="calculator">180 / 4</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 50
B. 52
C. 35
D. 40
E. 45

divide(add(150, 30), add(add(const_2, const_1), const_1))

Explanation: let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e


Question: on a partly cloudy day , milton decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?

<gadget id="calculator">2.8 + 2.8</gadget>
<output>5.6</output>

<gadget id="calculator">2.8 + 5.6</gadget>
<output>8.4</output>

<gadget id="calculator">8.4 + 5.6</gadget>
<output>14</output>

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

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

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

Explanation: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d


Question: if the sample interest on a sum of money 10 % per annum for 2 years is $ 1200 , find the compound interest on the same sum for the same period at the same rate ?

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

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

<gadget id="calculator">120_000 / 20</gadget>
<output>6_000</output>

<gadget id="calculator">6_000 * 10</gadget>
<output>60_000</output>

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

<gadget id="calculator">6_000 + 600</gadget>
<output>6_600</output>

<gadget id="calculator">6_600 * 10</gadget>
<output>66_000</output>

<gadget id="calculator">66_000 / 100</gadget>
<output>660</output>

<gadget id="calculator">660 + 6_600</gadget>
<output>7_260</output>

<gadget id="calculator">7_260 - 6_000</gadget>
<output>1_260</output>
<result>1_260</result>

Choices:
A. $ 1260
B. $ 1520
C. $ 1356
D. $ 1440
E. $ 1210

subtract(add(divide(multiply(add(divide(multiply(1200, const_100), multiply(10, 2)), divide(multiply(divide(multiply(1200, const_100), multiply(10, 2)), 10), const_100)), 10), const_100), add(divide(multiply(1200, const_100), multiply(10, 2)), divide(multiply(divide(multiply(1200, const_100), multiply(10, 2)), 10), const_100))), divide(multiply(1200, const_100), multiply(10, 2)))

Explanation: rate = 10 % time = 2 years s . i . = $ 1200 principal = 100 * 1200 / 10 * 2 = $ 6000 amount = 6000 ( 1 + 10 / 100 ) ^ 2 = $ 7260 c . i . = 7260 - 6000 = $ 1260 answer is a


Question: if 35 % of a number is 12 less than 50 % of that number , then the number is ?

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

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

<gadget id="calculator">12 / (3/20)</gadget>
<output>80</output>
<result>80</result>

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

divide(12, divide(subtract(50, 35), const_100))

Explanation: "let the number be x . then , 50 % of x - 35 % of x = 12 50 / 100 x - 35 / 100 x = 12 x = ( 12 * 100 ) / 15 = 80 . answer : d"


Question: rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ?

<gadget id="calculator">50_000 * 20</gadget>
<output>1_000_000</output>

<gadget id="calculator">1_000_000 / 100</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 - 8_000</gadget>
<output>2_000</output>

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

<gadget id="calculator">2_000 / (1/10)</gadget>
<output>20_000</output>
<result>20_000</result>

Choices:
A. 20000
B. 40000
C. 50000
D. 60000
E. 70000

divide(subtract(divide(multiply(50000, 20), const_100), 8000), divide(10, const_100))

Explanation: let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 50000 + y so y = 30000 then x = 50000 - 30000 = 20000 first part = 20000 answer : a


Question: a number when divided by a certain divisor left remainder 245 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?

<gadget id="calculator">245 * 2</gadget>
<output>490</output>

<gadget id="calculator">490 - 112</gadget>
<output>378</output>
<result>378</result>

Choices:
A. 378
B. 365
C. 380
D. 456
E. 460

Explanation: "easy solution : n = dq 1 + 245 2 n = 2 dq 1 + 490 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 378 d * some integer = 378 checking all options only ( a ) syncs with it . answer a"


Question: 85 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?

<gadget id="calculator">85 - 10</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 75
B. 80
C. 85
D. 90
E. 95

Explanation: "answer = a please refer diagram below 85 - 10 = 75"


Question: the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places

<gadget id="calculator">2 * (16 + 14)</gadget>
<output>60</output>

<gadget id="calculator">60 / 4</gadget>
<output>15</output>

<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">2 * pi * (15/2)</gadget>
<output>15*pi = around 47.12389</output>

<gadget id="calculator">(15*pi) / 2</gadget>
<output>15*pi/2 = around 23.561945</output>
<result>15*pi/2 = around 23.561945</result>

Choices:
A. 34
B. 35
C. 56
D. 67
E. 23.57

divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(16, 14)), const_2)), const_2)

Explanation: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e"


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

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

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

Choices:
A. 10 m
B. 12.5 m
C. 17.5 m
D. 21.25 m
E. none

Explanation: "let height of the building be x meters 40.25 : 28.75 : : 17.5 < = > 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : option b"


Question: x can do a piece of work in 4 hours ; y and z together can do it in 3 hours , while x and z together can do it in 2 hours . how long will y 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. 5 hours
B. 10 hours
C. 12 hours
D. 24 hours
E. 15 hours

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

Explanation: x 1 hour ' s work = 1 / 4 ; y + z ' s hour ' s work = 1 / 3 x + y + z ' s 1 hour ' s work = 1 / 4 + 1 / 3 = 7 / 12 y ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 . y alone will take 12 hours to do the work . c


Question: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 40 % of all the employees are men . what % of all the employee went to the picnic ?

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

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

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

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

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

<gadget id="calculator">(3/5) * (2/5)</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">(2/25) + (6/25)</gadget>
<output>8/25 = around 0.32</output>

<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 32 %
B. 34 %
C. 35 %
D. 36 %
E. 37 %

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

Explanation: "total men in company 40 % means total women in company 60 % ( assume total people in company 100 % ) no of men employees attended picnic = 40 x ( 20 / 100 ) = 8 no of women employees attended picnic = 60 x ( 40 / 100 ) = 24 total percentage of employees attended the picnic = 8 + 24 = 32 % answer : a"


Question: excluding stoppages , the speed of a bus is 84 kmph and including stoppages , it is 70 kmph . for how many minutes does the bus stop per hour ?

<gadget id="calculator">84 - 70</gadget>
<output>14</output>

<gadget id="calculator">14 / 84</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">60 * (1/6)</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 12 min
B. 10 min
C. 15 min
D. 14 min
E. 13 min

multiply(const_60, divide(subtract(84, 70), 84))

Explanation: "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( 14 / 84 x 60 ) min = 10 min answer : b"


Question: 40 is what percent of 160 ?

<gadget id="calculator">40 / 160</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 35 %
B. 40 %
C. 45 %
D. 50 %
E. 25 %

Explanation: 40 / 160 × 100 = 25 % answer : e


Question: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty , how much money total will it cost to fuel all cars ?

<gadget id="calculator">0.65 * 57</gadget>
<output>37.05</output>

<gadget id="calculator">37.05 * 12</gadget>
<output>444.6</output>
<result>444.6</result>

Choices:
A. 320.50 $
B. 380.50 $
C. 425.50 $
D. 450.50 $
E. 465.60 $

Explanation: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 57 ) = 465.60 hence answer will be ( e )"


Question: the l . c . m of 22 , 54 , 108 , 135 and 198 is

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

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

<gadget id="calculator">9 * 3</gadget>
<output>27</output>

<gadget id="calculator">4 * 27</gadget>
<output>108</output>

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

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

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

<gadget id="calculator">108 * 5</gadget>
<output>540</output>

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

<gadget id="calculator">540 * 11</gadget>
<output>5_940</output>
<result>5_940</result>

Choices:
A. 5942
B. 2887
C. 5940
D. 2888
E. 28881

multiply(multiply(multiply(multiply(const_2, const_2), multiply(multiply(const_3, const_3), const_3)), divide(divide(divide(135, const_3), const_3), const_3)), divide(22, const_2))

Explanation: answer : c ) 5940


Question: the sale price sarees listed for rs . 280 after successive discount is 12 % and 8 % is ?

<gadget id="calculator">280 * 12</gadget>
<output>3_360</output>

<gadget id="calculator">3_360 / 100</gadget>
<output>168/5 = around 33.6</output>

<gadget id="calculator">280 - (168/5)</gadget>
<output>1_232/5 = around 246.4</output>

<gadget id="calculator">(1_232/5) * 8</gadget>
<output>9_856/5 = around 1_971.2</output>

<gadget id="calculator">(9_856/5) / 100</gadget>
<output>2_464/125 = around 19.712</output>

<gadget id="calculator">(1_232/5) - (2_464/125)</gadget>
<output>28_336/125 = around 226.688</output>
<result>28_336/125 = around 226.688</result>

Choices:
A. 288
B. 226
C. 250
D. 230
E. 262

subtract(subtract(280, divide(multiply(280, 12), const_100)), divide(multiply(subtract(280, divide(multiply(280, 12), const_100)), 8), const_100))

Explanation: "280 * ( 88 / 100 ) * ( 92 / 100 ) = 226 answer : b"


Question: a girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction , takes 12 seconds to pass him . if the goods train is 1120 m long , find its speed .

<gadget id="calculator">1_120 / 12</gadget>
<output>280/3 = around 93.333333</output>

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

<gadget id="calculator">(280/3) / (5/18)</gadget>
<output>336</output>

<gadget id="calculator">336 - 40</gadget>
<output>296</output>
<result>296</result>

Choices:
A. 295
B. 296
C. 297
D. 298
E. 299

subtract(divide(divide(1120, 12), const_0_2778), 40)

Explanation: relative speed = ( 1120 / 12 ) m / s = ( 1120 / 12 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 40 = 296 kmph answer is b


Question: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ?

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

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

<gadget id="calculator">5 + 21</gadget>
<output>26</output>

<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>

<gadget id="calculator">(13/2) * 2</gadget>
<output>13</output>

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

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

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

Choices:
A. 1 / 20
B. 1 / 6
C. 1 / 5
D. 4 / 21
E. 5 / 21

divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))

Explanation: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b"


Question: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 66 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480

<gadget id="calculator">66 / 3</gadget>
<output>22</output>

<gadget id="calculator">22 * 100</gadget>
<output>2_200</output>
<result>2_200</result>

Choices:
A. 2000
B. 2100
C. 2200
D. 2300
E. 2400

Explanation: "1 percent for 3 years = 66 1 percent for 1 year = 22 = > 100 percent = 2200 answer : c"


Question: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.82 . what is the median gasoline price ?

<gadget id="calculator">1.75 + 1.61</gadget>
<output>3.36</output>

<gadget id="calculator">3.36 + 1.79</gadget>
<output>5.15</output>

<gadget id="calculator">5.15 + 2.11</gadget>
<output>7.26</output>

<gadget id="calculator">7.26 + 1.96</gadget>
<output>9.22</output>

<gadget id="calculator">9.22 + 2.09</gadget>
<output>11.31</output>

<gadget id="calculator">11.31 + 1.82</gadget>
<output>13.13</output>

<gadget id="calculator">13.13 / 7</gadget>
<output>1.875714</output>

<gadget id="calculator">min(1.875714, 1.82)</gadget>
<output>1.82</output>
<result>1.82</result>

Choices:
A. $ 1
B. $ 1.82
C. $ 1.92
D. $ 2.13
E. $ 2.15

Explanation: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.82 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.82 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b


Question: if 625 ( 5 ^ x ) = 1 then x =

<gadget id="calculator">1 / 625</gadget>
<output>1/625 = around 0.0016</output>

<gadget id="calculator">log(1/625)</gadget>
<output>-log(625) = around -6.437752</output>

<gadget id="calculator">log(5)</gadget>
<output>log(5) = around 1.609438</output>

<gadget id="calculator">(-log(625)) / log(5)</gadget>
<output>-log(625)/log(5) = around -4</output>
<result>-log(625)/log(5) = around -4</result>

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

Explanation: "5 ^ x = 1 / 625 5 ^ x = 1 / 5 ^ 4 5 ^ x = 5 ^ - 4 x = - 4 b"


Question: find the least number of complete years in which a sum of money put out at 45 % compound interest will be more than double of itself ?

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">1 + (9/20)</gadget>
<output>29/20 = around 1.45</output>

<gadget id="calculator">log(29/20)</gadget>
<output>log(29/20) = around 0.371564</output>

<gadget id="calculator">log(2) / log(29/20)</gadget>
<output>log(2)/log(29/20) = around 1.865488</output>

<gadget id="calculator">(log(2)/log(29/20)) + 1</gadget>
<output>1 + log(2)/log(29/20) = around 2.865488</output>

<gadget id="calculator">floor(1 + log(2)/log(29/20))</gadget>
<output>2</output>
<result>2</result>

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

floor(add(divide(log(const_2), log(add(const_1, divide(45, const_100)))), const_1))

Explanation: "2 years answer : a"


Question: the speed of the boat in still water in 12 kmph . it can travel downstream through 45 kms in 3 hrs . in what time would it cover the same distance upstream ?

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

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

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

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

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

divide(45, subtract(12, subtract(divide(45, 3), 12)))

Explanation: still water = 12 km / hr downstream = 45 / 3 = 15 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 15 / 2 = 9 km / hr so time taken in upstream = 45 / 9 = 5 hrs answer : d


Question: the avg weight of a , b & c is 55 kg . if d joins the group , the avg weight of the group becomes 60 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 58 kg . what is the weight of a ?

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

<gadget id="calculator">58 * 4</gadget>
<output>232</output>

<gadget id="calculator">55 * 3</gadget>
<output>165</output>

<gadget id="calculator">240 - 165</gadget>
<output>75</output>

<gadget id="calculator">3 + 75</gadget>
<output>78</output>

<gadget id="calculator">232 - 78</gadget>
<output>154</output>

<gadget id="calculator">240 - 154</gadget>
<output>86</output>
<result>86</result>

Choices:
A. 56
B. 65
C. 75
D. 86
E. 90

subtract(multiply(60, const_4), subtract(multiply(58, const_4), add(3, subtract(multiply(60, const_4), multiply(55, 3)))))

Explanation: "a + b + c = 3 * 55 = 165 a + b + c + d = 4 * 60 = 240 - - - - ( i ) so , d = 75 & e = 75 + 3 = 78 b + c + d + e = 58 * 4 = 232 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 240 – 232 = 8 a = e + 8 = 78 + 8 = 86 answer : d"


Question: if ' a ' completes a piece of work in 3 days , which ' b ' completes it in 5 days and ' c ' takes 10 days to complete the same work . how long will they take to complete the work , if they work together ?

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

<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. 1.5 days
B. 4.5 days
C. 7 days
D. 9.8 days
E. 9 days

add(subtract(3, const_2), divide(5, 10))

Explanation: explanation : hint : a ' s one day work = 1 / 3 b ' s one day work = 1 / 5 c ' s one day work = 1 / 10 ( a + b + c ) ' s one day work = 1 / 3 + 1 / 5 + 1 / 10 = 1 / 1.5 hence , a , b & c together will take 1.5 days to complete the work . answer is a


Question: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 105 liters of drink a to convert it to drink b ?

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

<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>

<gadget id="calculator">(4/7) * 105</gadget>
<output>60</output>

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

<gadget id="calculator">240 / 3</gadget>
<output>80</output>

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

<gadget id="calculator">(3/7) * 105</gadget>
<output>45</output>

<gadget id="calculator">80 - 45</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 14
B. 21
C. 28
D. 35
E. 42

subtract(divide(multiply(multiply(divide(4, add(4, 3)), 105), 4), 3), multiply(divide(3, add(4, 3)), 105))

Explanation: "in 105 liters of drink a , there are 60 liters of milk and 45 liters of juice . with 60 liters of milk , we need a total of 80 liters of juice to make drink b . we need to add 35 liters of juice . the answer is d ."


Question: at what rate percent per annum will a sum of money double in 9 years .

<gadget id="calculator">100 / 9</gadget>
<output>100/9 = around 11.111111</output>
<result>100/9 = around 11.111111</result>

Choices:
A. 12.5 %
B. 13.5 %
C. 11.5 %
D. 11.1 %
E. 21.5 %

Explanation: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 9 ) ] % = 11.1 % per annum . answer : d"


Question: if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to :

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

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

<gadget id="calculator">6 + 15</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 22
B. 37
C. 38
D. 398
E. 72

Explanation: "explanation : 3 * 5 + 5 * 3 = ( 2 * 3 - 3 * 5 + 3 * 5 ) + ( 2 * 5 - 3 * 3 + 5 * 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer : a ) 22"


Question: noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 4 kilometers per hour ?

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

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

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

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

Choices:
A. 5.75
B. 6
C. 7.25
D. 7.5
E. 7.75

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

Explanation: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 4 = 2 * 3 * x / 3 + x x = 6 b is the answer"


Question: the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ?

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">100 / 140</gadget>
<output>5/7 = around 0.714286</output>

<gadget id="calculator">1 - (5/7)</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>

Choices:
A. 34 %
B. 36 %
C. 28.57 %
D. 30 %
E. 32 %

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

Explanation: x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.4 x ( 140 ) i . e . 140 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 140 = 71.43 i . e . y decreases from 100 to 71.43 i . e . decrease of 28.57 % c


Question: if a and b are the roots of the equation x 2 - 6 x + 6 = 0 , then the value of a 2 + b 2 is :

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

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

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

<gadget id="calculator">12 ** (1/2)</gadget>
<output>2*sqrt(3) = around 3.464102</output>

<gadget id="calculator">6 - (2*sqrt(3))</gadget>
<output>6 - 2*sqrt(3) = around 2.535898</output>

<gadget id="calculator">(6 - 2*sqrt(3)) / 2</gadget>
<output>3 - sqrt(3) = around 1.267949</output>

<gadget id="calculator">(3 - sqrt(3)) ** 2</gadget>
<output>(3 - sqrt(3))**2 = around 1.607695</output>

<gadget id="calculator">6 + (2*sqrt(3))</gadget>
<output>2*sqrt(3) + 6 = around 9.464102</output>

<gadget id="calculator">(2*sqrt(3) + 6) / 2</gadget>
<output>sqrt(3) + 3 = around 4.732051</output>

<gadget id="calculator">(sqrt(3) + 3) ** 2</gadget>
<output>(sqrt(3) + 3)**2 = around 22.392305</output>

<gadget id="calculator">((3 - sqrt(3))**2) + ((sqrt(3) + 3)**2)</gadget>
<output>(3 - sqrt(3))**2 + (sqrt(3) + 3)**2 = around 24</output>
<result>(3 - sqrt(3))**2 + (sqrt(3) + 3)**2 = around 24</result>

Choices:
A. 36
B. 24
C. 17
D. 6
E. 5

add(power(divide(subtract(6, sqrt(subtract(power(6, 2), multiply(const_4, 6)))), 2), 2), power(divide(add(6, sqrt(subtract(power(6, 2), multiply(const_4, 6)))), 2), 2))

Explanation: "sol . ( b ) the sum of roots = a + b = 6 product of roots = ab = 6 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 36 - 12 = 24 answer b"


Question: 6 persons in an organization including x and y were to be divided in two groups of 3 members each . the total number of groups containing both x and y is what fraction of the total number of groups which can be formed ?

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>

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

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

<gadget id="calculator">6 / 20</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>

Choices:
A. 1 / 4
B. 1 / 70
C. 3 / 14
D. 3 / 10
E. 11 / 14

divide(factorial(3), multiply(subtract(6, const_1), const_4))

Explanation: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose x and y and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : d


Question: having scored 94 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?

<gadget id="calculator">19 * 4</gadget>
<output>76</output>

<gadget id="calculator">94 - 76</gadget>
<output>18</output>

<gadget id="calculator">18 + 4</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 28
B. 27
C. 26
D. 22
E. 24

Explanation: "explanation : let the average score of the first 18 innings be n 18 n + 94 = 19 ( n + 4 ) = > n = 18 so , average score after 19 th innings = x + 4 = 22 . answer : d"


Question: a train 150 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?

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

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

<gadget id="calculator">25 * 20</gadget>
<output>500</output>

<gadget id="calculator">500 - 150</gadget>
<output>350</output>
<result>350</result>

Choices:
A. 288
B. 236
C. 350
D. 299
E. 266

subtract(multiply(25, multiply(72, const_0_2778)), 150)

Explanation: d = 72 * 5 / 18 = 25 = 500 – 150 = 299 . answer : c


Question: the present worth of a certain bill due sometime hence is rs . 1296 and the true discount is rs . 72 . what is the banker ' s discount ?

<gadget id="calculator">72 ** 2</gadget>
<output>5_184</output>

<gadget id="calculator">5_184 / 1_296</gadget>
<output>4</output>

<gadget id="calculator">72 + 4</gadget>
<output>76</output>
<result>76</result>

Choices:
A. rs . 76
B. rs . 72
C. rs . 74
D. rs . 4
E. none of these

add(72, divide(power(72, const_2), 1296))

Explanation: explanation : bg = ( td ) 2 / pw = 722 / 1296 = 72 × 72 / 1296 = 12 × 12 / 36 = 12 / 3 = rs . 4 bg = bd – td = > 4 = bd - 72 = > bd = 72 + 4 = rs . 76 answer : option a


Question: the grade point average of the entire class is 88 . if the average of one third of the class is 94 , what is the average of the rest of the class ?

<gadget id="calculator">88 * 4</gadget>
<output>352</output>

<gadget id="calculator">352 - 94</gadget>
<output>258</output>

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

<gadget id="calculator">258 / 3</gadget>
<output>86</output>
<result>86</result>

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

divide(subtract(multiply(88, const_4), 94), subtract(const_4, const_1))

Explanation: "let x be the number of students in the class . let p be the average of the rest of the class . 88 x = ( 1 / 3 ) 94 x + ( 2 / 3 ) ( p ) x 264 = 94 + 2 p 2 p = 170 p = 85 . the answer is d ."


Question: a truck covers a distance of 376 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?

<gadget id="calculator">376 + 14</gadget>
<output>390</output>

<gadget id="calculator">376 / 8</gadget>
<output>47</output>

<gadget id="calculator">47 + 18</gadget>
<output>65</output>

<gadget id="calculator">390 / 65</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6 hours
B. 5 hours
C. 7 hours
D. 8 hours
E. none

Explanation: "explanation : speed of the truck = distance / time = 376 / 8 = 47 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 47 + 18 ) = 65 kmph distance travelled by car = 376 + 14 = 390 km time taken by car = distance / speed = 390 / 65 = 6 hours . answer – a"


Question: the ratio of the ages of maala and kala is 3 : 5 . the total of their ages is 3.2 decades . the proportion of their ages after 0.8 decades will be [ 1 decade = 10 years ]

<gadget id="calculator">3.2 * 10</gadget>
<output>32</output>

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

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

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

<gadget id="calculator">0.8 * 10</gadget>
<output>8</output>

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

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

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

<gadget id="calculator">20 / 28</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>

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

divide(add(multiply(divide(multiply(3.2, 10), add(3, 5)), 3), multiply(0.8, 10)), add(multiply(5, divide(multiply(3.2, 10), add(3, 5))), multiply(0.8, 10)))

Explanation: let , maala ’ s age = 3 a and kala ’ s age = 5 a then 3 a + 5 a = 32 a = 4 maala ’ s age = 12 years and kala ’ s age = 20 years proportion of their ages after 8 is = ( 12 + 8 ) : ( 20 + 8 ) = 20 : 28 = 5 : 7 answer : b


Question: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 18 miles , how many miles was mike ' s ride ?

<gadget id="calculator">2.5 + 5</gadget>
<output>7.5</output>

<gadget id="calculator">0.25 * 18</gadget>
<output>4.5</output>

<gadget id="calculator">7.5 + 4.5</gadget>
<output>12</output>

<gadget id="calculator">12 - 2.5</gadget>
<output>9.5</output>

<gadget id="calculator">9.5 / 0.25</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 30
B. 34
C. 38
D. 42
E. 48

Explanation: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 18 ) = $ 12 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 12 0.25 * x = 9.5 x = 38 miles the answer is c ."


Question: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 55 percent .

<gadget id="calculator">55 / 20</gadget>
<output>11/4 = around 2.75</output>

<gadget id="calculator">(11/4) * 60</gadget>
<output>165</output>
<result>165</result>

Choices:
A. 145
B. 150
C. 175
D. 165
E. 130

Explanation: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 55 percent 165 min . answer : d


Question: in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

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

<gadget id="calculator">8 / 11</gadget>
<output>8/11 = around 0.727273</output>

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

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

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

<gadget id="calculator">(8/11) * (7/10)</gadget>
<output>28/55 = around 0.509091</output>
<result>28/55 = around 0.509091</result>

Choices:
A. 28 / 55
B. 19 / 33
C. 7 / 11
D. 4 / 7
E. 3 / 5

multiply(divide(subtract(11, 3), 11), divide(subtract(subtract(11, 3), const_1), subtract(11, const_1)))

Explanation: "p ( neither pen is defective ) = 8 / 11 * 7 / 10 = 28 / 55 the answer is a ."


Question: a rectangular box measures internally 1.6 m long , 1 m broad and 60 cm deep . the number of cubical box each of edge 20 cm that can be packed inside the box is :

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

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

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

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

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

<gadget id="calculator">8 * 5 * 3</gadget>
<output>120</output>
<result>120</result>

Choices:
A. 30
B. 60
C. 90
D. 120
E. 140

volume_rectangular_prism(divide(1.6, divide(20, const_100)), divide(1, divide(20, const_100)), divide(divide(60, const_100), divide(20, const_100)))

Explanation: "explanation : number of blocks = ( 160 x 100 x 60 / 20 x 20 x 20 ) = 120 answer : d"


Question: bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p & q , having each turn together to fill the empty drum ?

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>

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

<gadget id="calculator">1 / 180</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(1/60) + (1/180)</gadget>
<output>1/45 = around 0.022222</output>

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

Choices:
A. 45
B. 53
C. 54
D. 46
E. 63

divide(const_1, add(divide(const_1, 60), divide(const_1, multiply(60, const_3))))

Explanation: if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a


Question: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 40 now , the son age 5 years back was

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

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

Choices:
A. 14
B. 17
C. 15
D. 19
E. 99

Explanation: "let the son ' s present age be x years . then , ( 40 - x ) = x x = 20 . son ' s age 5 years back = ( 20 - 5 ) = 15 years answer : c"


Question: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

<gadget id="calculator">30 * 14</gadget>
<output>420</output>
<result>420</result>

Choices:
A. 276
B. 299
C. 420
D. 345
E. 365

Explanation: "clearly , the numbers are ( 30 x 13 ) and ( 30 x 14 ) . larger number = ( 30 x 14 ) = 420 . answer : option c"


Question: find compound interest on rs . 7500 at 4 % per year for 2 years , compounded annually .

<gadget id="calculator">7_500 * 4</gadget>
<output>30_000</output>

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

<gadget id="calculator">7_500 + 300</gadget>
<output>7_800</output>

<gadget id="calculator">7_800 * 4</gadget>
<output>31_200</output>

<gadget id="calculator">31_200 / 100</gadget>
<output>312</output>

<gadget id="calculator">7_800 + 312</gadget>
<output>8_112</output>

<gadget id="calculator">8_112 - 7_500</gadget>
<output>612</output>
<result>612</result>

Choices:
A. 812
B. 712
C. 412
D. 512
E. 612

subtract(add(add(7500, divide(multiply(7500, 4), const_100)), divide(multiply(add(7500, divide(multiply(7500, 4), const_100)), 4), const_100)), 7500)

Explanation: "amount = rs [ 7500 * ( 1 + ( 4 / 100 ) 2 ] = rs ( 7500 * ( 26 / 25 ) * ( 26 / 25 ) ) = rs . 8112 . therefore , compound interest = rs . ( 8112 - 7500 ) = rs . 612 . answer is e ."


Question: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 178 votes . find the total number of valid votes ?

<gadget id="calculator">100 - 70</gadget>
<output>30</output>

<gadget id="calculator">70 - 30</gadget>
<output>40</output>

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

<gadget id="calculator">178 / (2/5)</gadget>
<output>445</output>
<result>445</result>

Choices:
A. 445
B. 570
C. 480
D. 520
E. 550

divide(178, divide(subtract(70, subtract(const_100, 70)), const_100))

Explanation: let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 178 = > 4 x / 10 = 178 = > 4 x = 1780 = > x = 445 . answer : a


Question: 6 computers , each working at the same constant rate , together can process a certain amount of data in 9 days . how many additional computers , each working at the same constant rate , will be needed to process the same amount of data in 6 days ?

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

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

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

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

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

Choices:
A. 3
B. 5
C. 6
D. 9
E. 12

subtract(divide(multiply(6, divide(const_1, 6)), divide(const_1, 9)), 6)

Explanation: explanation : if six computers require 9 days to process the data , thats a total of 54 computer - days the product of 6 and 9 . if you change the number of computers or the number of days , 54 will have to remain the product , whether that means 54 days of one computer or one day with 54 computers . in 6 days , the number of computers is : 6 c = 54 c = 9 9 computers is 3 more than the 6 that it took to do the job in 9 days , so the correct choice is ( a ) .


Question: the radius of a cylindrical vessel is 7 cm and height is 4 cm . find the whole surface of the cylinder ?

<gadget id="calculator">2 * pi * 7 * (7 + 4)</gadget>
<output>154*pi = around 483.805269</output>
<result>154*pi = around 483.805269</result>

Choices:
A. 484
B. 771
C. 440
D. 767
E. 1981

Explanation: "r = 7 h = 4 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 11 ) = 484 answer : a"


Question: mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.00 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?

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

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

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

<gadget id="calculator">15 * 0.25</gadget>
<output>3.75</output>

<gadget id="calculator">8 - 3.75</gadget>
<output>4.25</output>

<gadget id="calculator">4.25 / 6</gadget>
<output>0.708333</output>

<gadget id="calculator">5 * 0.25</gadget>
<output>1.25</output>

<gadget id="calculator">0.708333 + 1.25</gadget>
<output>1.958333</output>
<result>1.958333</result>

Choices:
A. $ 1.75
B. $ 1.96
C. $ 2.00
D. $ 2.15
E. $ 2.30

add(divide(subtract(8.00, multiply(divide(multiply(subtract(6, const_1), 6), const_2), 0.25)), 6), multiply(subtract(6, const_1), 0.25))

Explanation: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.00 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.958 0.708 0.958 1.208 1.458 1.708 1.958 total = $ 8.00 so this must be the answer . b"


Question: a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt

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

<gadget id="calculator">110 * 65</gadget>
<output>7_150</output>

<gadget id="calculator">110 - 5</gadget>
<output>105</output>

<gadget id="calculator">65 - 5</gadget>
<output>60</output>

<gadget id="calculator">105 * 60</gadget>
<output>6_300</output>

<gadget id="calculator">7_150 - 6_300</gadget>
<output>850</output>

<gadget id="calculator">(4/5) * 850</gadget>
<output>680</output>
<result>680</result>

Choices:
A. 680
B. 378
C. 267
D. 299
E. 271

multiply(divide(80, const_100), subtract(multiply(110, 65), multiply(subtract(110, 5), subtract(65, 5))))

Explanation: "explanation : area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a ) 680 rs"


Question: in a dairy farm , 16 cows eat 16 bags of husk in 16 days . in how many days one cow will eat one bag of husk ?

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

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

Choices:
A. 16
B. 40
C. 20
D. 26
E. 30

Explanation: explanation : one bag of husk = 16 cows per day ⇒ 16 × 1 × 16 = 1 × 16 × x for one cow = 16 days answer : a


Question: in 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each , how many pumps will raise 2030 tons of water in 12 days of 11 hrs each ?

<gadget id="calculator">12 * 11</gadget>
<output>132</output>

<gadget id="calculator">132 * 9</gadget>
<output>1_188</output>

<gadget id="calculator">1_188 * 2_030</gadget>
<output>2_411_640</output>

<gadget id="calculator">132 * 1_218</gadget>
<output>160_776</output>

<gadget id="calculator">2_411_640 / 160_776</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 12
B. 15
C. 18
D. 21
E. 22

divide(multiply(multiply(multiply(12, 11), 9), 2030), multiply(multiply(12, 11), 1218))

Explanation: explanation : pumps work time 12 1218 99 x 2030 132 = > 1218 / ( 912 * 99 ) = 2020 / ( x × 132 ) = > x = 15 pumps answer : option b


Question: 32.32 / 2000 is equal to :

<gadget id="calculator">32.32 / 2_000</gadget>
<output>0.01616</output>
<result>0.01616</result>

Choices:
A. 1.012526
B. 0.012625
C. 0.12526
D. 0.01616
E. 0.12725

Explanation: "25.25 / 2000 = 2525 / 200000 = 0.01616 answer : d"


Question: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 5 % of the money for taxi fare and buys 25 mangoes . how many oranges can he buy ?

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

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

<gadget id="calculator">25 / 50</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(19/20) - (1/2)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(9/20) * 50</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>

Choices:
A. 25
B. 30
C. 20
D. 22.5
E. 12

multiply(subtract(subtract(const_1, divide(5, const_100)), divide(25, 50)), 50)

Explanation: let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 5 % of 200 = 10 for taxi fare , so he is left with 190 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 90 ( 190 - 100 ) no of oranges he can buy = 90 / 4 = > 22,5 so , george can buy 20 oranges . d


Question: if 4 spiders make 4 webs in 4 days , then 1 spider will make 1 web in how many days ?

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

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

Explanation: "explanation : let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 4 | | : : 4 : 1 webs 4 : 1 | = > 1 * 4 * x = 4 * 1 * 4 = > x = 4 answer : d"