Question: john and beth each drove from smallville to crown city by different routes . john drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than john to complete the trip . how many miles per hour was beth ' s average speed on this trip ?

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

<gadget id="calculator">40 * (1/2)</gadget>
<output>20</output>

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

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

<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">25 / (5/6)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 24
B. 30
C. 48
D. 54
E. 75

divide(add(multiply(40, divide(30, const_60)), 5), divide(add(30, 20), const_60))

Explanation: speed = distance / time distance for john = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for john + 5 = 20 + 5 = 25 miles time taken by beth = time taken by john + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer .


Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 180 only . men â € ™ s wages are ?

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

<gadget id="calculator">180 / 15</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 6 rs
B. 2 rs
C. 4 rs
D. 9 rs
E. 12 rs

Explanation: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 180 rs . 5 m + 5 m + 5 m - - - - - 180 rs . 15 m - - - - - - 180 rs . = > 1 m = 12 rs . answer : e"


Question: a train is 250 meter long is running at a speed of 36 km / hour . in what time will it pass a station of 200 meter length ?

<gadget id="calculator">250 + 200</gadget>
<output>450</output>

<gadget id="calculator">36 * 1_000</gadget>
<output>36_000</output>

<gadget id="calculator">36_000 / 3_600</gadget>
<output>10</output>

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

Choices:
A. 28 seconds
B. 27 seconds
C. 45 seconds
D. 26 seconds
E. 18 seconds

divide(add(250, 200), divide(multiply(36, const_1000), const_3600))

Explanation: "speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 250 + 200 = 450 meter time = distance / speed = 450 * ( 10 ) = 45 seconds answer : c"


Question: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 72.25 , the number of the member is the group is :

<gadget id="calculator">72.25 * 100</gadget>
<output>7_225</output>

<gadget id="calculator">7_225 ** (1/2)</gadget>
<output>85</output>
<result>85</result>

Choices:
A. 57
B. 67
C. 77
D. 85
E. 97

Explanation: "explanation : money collected = ( 72.25 x 100 ) paise = 7225 paise . ∴ number of members = √ ( 7225 ) = 85 . answer : d"


Question: triangle atriangle b are similar triangles with areas 2023 units square and 1792 units square respectively . the ratio of there corresponding height would be

<gadget id="calculator">2_023 / 1_792</gadget>
<output>289/256 = around 1.128906</output>

<gadget id="calculator">(289/256) ** (1/2)</gadget>
<output>17/16 = around 1.0625</output>
<result>17/16 = around 1.0625</result>

Choices:
A. 9 : 10
B. 17 : 16
C. 23 : 27
D. 13 : 17
E. 15 : 23

Explanation: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 2023 / 1792 ( x ^ 2 / y ^ 2 ) = ( 17 * 17 * 7 ) / ( 16 * 16 * 7 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 16 ^ 2 x / y = 17 / 16 ans = b you need to take a hint from given options to find factors of 2013 and 2527 ."


Question: the length of a rectangle is reduced by 20 % . by what % would the width have to be increased to maintainthe original area ?

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

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

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

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

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

Choices:
A. 14 %
B. 15 %
C. 25 %
D. 30 %
E. 35 %

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

Explanation: "sol . required change = ( 20 * 100 ) / ( 100 - 20 ) = 25 % c"


Question: find the area of a parallelogram with base 10 cm and height 20 cm .

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

Choices:
A. 200
B. 384
C. 200
D. 244
E. 242

Explanation: "area of a parallelogram = base * height = 10 * 20 = 200 cm 2 answer : option c"


Question: a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be .

<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">48 * (5/6)</gadget>
<output>40</output>

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

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

Choices:
A. 60 kmph
B. 63 kmph
C. 57 kmph
D. 70 kmph
E. 61 kmph

divide(multiply(48, divide(50, const_60)), divide(40, const_60))

Explanation: time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer is a .


Question: if y > 0 , ( 2 y ) / 10 + ( 3 y ) / 10 is what percent of y ?

<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>

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

<gadget id="calculator">(1/5) + (3/10)</gadget>
<output>1/2 = around 0.5</output>

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

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

multiply(const_100, add(divide(2, 10), divide(3, 10)))

Explanation: "can be reduced to y / 5 + 3 y / 10 = 2 y / 5 = 50 % b"


Question: 200 pupil total , out of 125 like pizza , 115 like burger , then how many like both ?

<gadget id="calculator">125 + 115</gadget>
<output>240</output>

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

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

Explanation: n ( a u b ) = n ( a ) + n ( b ) - n ( a intersection b ) 200 = 125 + 115 - both both = 240 - 200 = 40 . answer : a


Question: the area of a rectangular plot is 15 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?

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

Choices:
A. 10 metres
B. 5 metres
C. 7.5 metres
D. data inadequate
E. none of these

Explanation: "l × b = 15 × b ∴ l = 15 m and l – b = 10 ∴ b = 15 – 10 = 5 m answer b"


Question: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 10 % p . a . was rs . 420 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .

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

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

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">(121/100) - 1</gadget>
<output>21/100 = around 0.21</output>

<gadget id="calculator">420 / (21/100)</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 + 420</gadget>
<output>2_420</output>
<result>2_420</result>

Choices:
A. rs . 2530
B. rs . 2430
C. rs . 2420
D. rs . 2410
E. rs . 2440

add(divide(420, subtract(power(add(const_1, divide(10, const_100)), const_2), const_1)), 420)

Explanation: "let the sum be rs . p p { [ 1 + 10 / 100 ] 2 - 1 } = 420 p ( 10 / 100 ) ( 2 + 10 / 100 ) = 420 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 420 / ( 0.1 ) ( 2.1 ) = 2000 . amount = 2000 + 420 = rs . 2420 answer : c"


Question: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 25 meters . what distance is she from the starting point and in which direction ?

<gadget id="calculator">20 + 25</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 35 m east
B. 35 m north
C. 30 m west
D. 45 m west
E. 45 m east

Explanation: the net distance is 20 + 25 = 45 meters to the east . the answer is e .


Question: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 4 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?

<gadget id="calculator">7 / 4</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">1 + (7/4)</gadget>
<output>11/4 = around 2.75</output>

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

<gadget id="calculator">(7/4) + (3/4)</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">(11/4) / (5/2)</gadget>
<output>11/10 = around 1.1</output>
<result>11/10 = around 1.1</result>

Choices:
A. 5 : 4
B. 7 : 6
C. 9 : 8
D. 11 : 10
E. 13 : 12

divide(add(1, divide(7, 4)), add(divide(7, 4), divide(3, 4)))

Explanation: "3 b = 7 c and so b = 7 c / 3 7 a = 4 b and so a = 4 b / 7 = 4 c / 3 a + b = 4 c / 3 + 7 c / 3 = 11 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 11 : 10 the answer is d ."


Question: a man can swim in still water at 3 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?

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

Choices:
A. 1.7
B. 1.4
C. 1.1
D. 1.5
E. 1

Explanation: "m = 3 s = x ds = 3 + x us = 3 + x 3 + x = ( 3 - x ) 2 3 + x = 6 - 2 x 3 x = 3 x = 1 answer : e"


Question: a man gains 30 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .

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

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

<gadget id="calculator">(13/10) * 2</gadget>
<output>13/5 = around 2.6</output>

<gadget id="calculator">(13/5) - 1</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(8/5) * 100</gadget>
<output>160</output>

<gadget id="calculator">160 + 100</gadget>
<output>260</output>
<result>260</result>

Choices:
A. 130 %
B. 140 %
C. 150 %
D. 260 %
E. 170 %

add(multiply(subtract(multiply(add(const_1, divide(30, const_100)), const_2), const_1), const_100), const_100)

Explanation: "explanation : let the c . p . = x , then s . p . = ( 130 / 100 ) x = 13 x / 10 new s . p . = 2 ( 13 x / 10 ) = 26 x / 10 profit = 26 x / 10 - x = 26 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 26 x / 10 ) * ( 1 / x ) * 100 = 260 % option d"


Question: 2 persons can finish a job in 8 days . first person alone can finish the work in 24 days . how many days does the second person take to finish the job ?

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

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">(1/8) - (1/24)</gadget>
<output>1/12 = around 0.083333</output>

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

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

inverse(subtract(divide(const_1, 8), divide(const_1, 24)))

Explanation: 2 persons can do work in 1 day = 1 / 8 first person can do work in 1 day = 1 / 24 second person can do work in 1 day = 1 / 8 - 1 / 24 = 1 / 12 so second person can finish work in 12 days answer : b


Question: a cistern is filled by pipe a in 12 hours and the full cistern can be leaked out by an exhaust pipe b in 18 hours . if both the pipes are opened , in what time the cistern is full ?

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

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>

<gadget id="calculator">(1/12) - (1/18)</gadget>
<output>1/36 = around 0.027778</output>

<gadget id="calculator">1 / (1/36)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 50 hrs
B. 60 hrs
C. 36 hrs
D. 80 hrs
E. 90 hrs

divide(const_1, subtract(divide(const_1, 12), divide(const_1, 18)))

Explanation: "time taken to full the cistern = ( 1 / 12 - 1 / 18 ) hrs = 1 / 36 = 36 hrs answer : c"


Question: a number x is multiplied by 3 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?

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

Choices:
A. 25 / 9
B. 3 / 7
C. 5 / 3
D. 3 / 5
E. 9 / 25

Explanation: "sqrt ( 3 x / 7 ) to be perfect square x has to 3 / 7 ans : b"


Question: the list price of an article is rs . 70 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

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

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

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

<gadget id="calculator">63 - 56.16</gadget>
<output>6.84</output>

<gadget id="calculator">6.84 / 63</gadget>
<output>0.108571</output>

<gadget id="calculator">0.108571 * 100</gadget>
<output>10.8571</output>
<result>10.8571</result>

Choices:
A. 10.85 %
B. 14.85 %
C. 15.85 %
D. 16.85 %
E. 17.85 %

multiply(divide(subtract(subtract(70, multiply(70, divide(10, const_100))), 56.16), subtract(70, multiply(70, divide(10, const_100)))), const_100)

Explanation: "70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 10.85 % answer : a"


Question: a man swims downstream 42 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?

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

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

<gadget id="calculator">6 + 14</gadget>
<output>20</output>

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

Choices:
A. 2
B. 8
C. 9
D. 6
E. 10

divide(add(divide(18, 3), divide(42, 3)), const_2)

Explanation: "42 - - - 3 ds = 14 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 14 + 6 ) / 2 = 10 answer : e"


Question: a starts business with rs . 3500 and after 8 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?

<gadget id="calculator">3_500 * 12</gadget>
<output>42_000</output>

<gadget id="calculator">42_000 * 3</gadget>
<output>126_000</output>

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

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

<gadget id="calculator">126_000 / 8</gadget>
<output>15_750</output>
<result>15_750</result>

Choices:
A. 24887
B. 20778
C. 23788
D. 15750
E. 2811

divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 8), 2))

Explanation: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 8 = 4 months . so there profit ratio = ( 3500 ã — 12 ) : ( 4 x ) = 2 : 3 â ‡ ’ x = 15750 answer : d"


Question: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 914800 , how many months will it take joan to pay back her mortgage ?

<gadget id="calculator">914_800 * 2</gadget>
<output>1_829_600</output>

<gadget id="calculator">1_829_600 / 100</gadget>
<output>18_296</output>

<gadget id="calculator">18_296 + 1</gadget>
<output>18_297</output>

<gadget id="calculator">log(18_297)</gadget>
<output>log(18297) = around 9.814492</output>

<gadget id="calculator">log(3)</gadget>
<output>log(3) = around 1.098612</output>

<gadget id="calculator">log(18297) / log(3)</gadget>
<output>log(18297)/log(3) = around 8.933536</output>
<result>log(18297)/log(3) = around 8.933536</result>

Choices:
A. 6
B. 8
C. 10
D. 9
E. 13

divide(log(add(divide(multiply(914800, const_2), 100), const_1)), log(const_3))

Explanation: joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 914800 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 9148 so we have 1 , 3 , 9 , 27 . . . . . 914800 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 9148 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 9148 x - 2 = 1 - 3 ^ n - 19682 = 1 - 3 ^ n - 19682 = - 3 ^ n 19683 = 3 ^ n ( negatives cancel out ) 19863 can also be re written as 3 ^ 9 therefore ; 3 ^ 9 = 3 ^ n thus n = 9 ( d )


Question: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?

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

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

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

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

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

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

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

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

<gadget id="calculator">906 * 7</gadget>
<output>6_342</output>
<result>6_342</result>

Choices:
A. s . 4538
B. s . 6342
C. s . 4518
D. s . 4530
E. s . 4517

multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 7)

Explanation: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 7 = rs . 6342 answer : b"


Question: the grade point average of the entire class is 80 . if the average of one fourth of the class is 92 , what is the average of the rest of the class ?

<gadget id="calculator">80 * 4</gadget>
<output>320</output>

<gadget id="calculator">320 - 92</gadget>
<output>228</output>

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

<gadget id="calculator">228 / 3</gadget>
<output>76</output>
<result>76</result>

Choices:
A. 73
B. 74
C. 75
D. 76
E. 77

divide(subtract(multiply(80, const_4), 92), 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 . 80 x = ( 1 / 4 ) 92 x + ( 3 / 4 ) ( p ) x 320 = 92 + 3 p 3 p = 228 p = 76 . the answer is d .


Question: the compound interest earned on a sum for the second and the third years are $ 1200 and $ 1260 respectively . what is the rate of interest ?

<gadget id="calculator">1_260 - 1_200</gadget>
<output>60</output>

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

<gadget id="calculator">6_000 / 1_200</gadget>
<output>5</output>
<result>5</result>

Choices:
A. 5 %
B. 8 %
C. 11 %
D. 14 %
E. 18 %

divide(multiply(subtract(1260, 1200), const_100), 1200)

Explanation: "1260 - 1200 = 60 is the rate of interest on $ 1200 for one year . the rate of interest = ( 100 * 60 ) / ( 1200 ) = 5 % the answer is a ."


Question: a fair 2 sided coin is flipped 7 times . what is the probability that tails will be the result at least twice , but not more than 7 times ?

<gadget id="calculator">2 ** 7</gadget>
<output>128</output>

<gadget id="calculator">1 / 128</gadget>
<output>1/128 = around 0.007812</output>

<gadget id="calculator">(1/128) * 7</gadget>
<output>7/128 = around 0.054688</output>

<gadget id="calculator">(1/128) + (1/128)</gadget>
<output>1/64 = around 0.015625</output>

<gadget id="calculator">(7/128) + (1/64)</gadget>
<output>9/128 = around 0.070312</output>

<gadget id="calculator">1 - (9/128)</gadget>
<output>119/128 = around 0.929688</output>
<result>119/128 = around 0.929688</result>

Choices:
A. 119 / 128
B. 120 / 113
C. 114 / 210
D. 121 / 141
E. 104 / 117

subtract(const_1, add(multiply(inverse(power(2, 7)), 7), add(inverse(power(2, 7)), inverse(power(2, 7)))))

Explanation: "at least twice , but not more than 7 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 7 c 2 / 2 ^ 7 + 7 c 3 / 2 ^ 7 + 7 c 4 / 2 ^ 7 + 7 c 5 / 2 ^ 7 + 7 c 6 / 2 ^ 7 = 119 / 128 option : a"


Question: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent q of his family ’ s total income ?

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

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

<gadget id="calculator">(1/4) * (2/5)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(2/5) - (1/10)</gadget>
<output>3/10 = around 0.3</output>

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

<gadget id="calculator">(3/10) / (9/10)</gadget>
<output>1/3 = around 0.333333</output>

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

Choices:
A. 15 %
B. 17 %
C. 24 %
D. 30 %
E. 33 %

multiply(divide(subtract(divide(40, const_100), multiply(divide(25, const_100), divide(40, const_100))), subtract(const_1, multiply(divide(25, const_100), divide(40, const_100)))), const_100)

Explanation: lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march q = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e


Question: the s . i . on a certain sum of money for 2 years at 4 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?

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

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

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>

<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>

<gadget id="calculator">840 / 2</gadget>
<output>420</output>

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

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

<gadget id="calculator">420 / (2/25)</gadget>
<output>5_250</output>
<result>5_250</result>

Choices:
A. 5250
B. 1267
C. 5750
D. 2267
E. 5262

divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(4, const_100)))

Explanation: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 5250 answer : a"


Question: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 181 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?

<gadget id="calculator">181 / 2</gadget>
<output>181/2 = around 90.5</output>

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

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

<gadget id="calculator">(181/2) + (1/2)</gadget>
<output>91</output>

<gadget id="calculator">91 ** 2</gadget>
<output>8_281</output>
<result>8_281</result>

Choices:
A. 6564
B. 7372
C. 8281
D. 9331
E. can not be determined

power(add(divide(181, const_2), add(const_0_25, const_0_25)), const_2)

Explanation: let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 181 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 181 ( x + y ) ( x - y ) = 181 181 is a prime number and thus it will be ( 91 + 90 ) * ( 91 - 90 ) . thus x = 91 and y = 90 x ^ 2 = 91 ^ 2 = 8281 the answer is c .


Question: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 9.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?

<gadget id="calculator">3.5 - 3</gadget>
<output>0.5</output>

<gadget id="calculator">9.5 - 3</gadget>
<output>6.5</output>

<gadget id="calculator">0.5 / 6.5</gadget>
<output>0.076923</output>

<gadget id="calculator">0.076923 * 100</gadget>
<output>7.6923</output>
<result>7.6923</result>

Choices:
A. 16.5 %
B. 8 %
C. 35 %
D. 55 %
E. 65 %

multiply(divide(subtract(3.5, 3), subtract(9.5, 3)), const_100)

Explanation: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.095 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 95 f - - > s = f - - > f / s = 1 / 12 - - > f / ( s + f ) = 1 / ( 1 + 12 ) = 1 / 13 = 0.08 . answer : b ."


Question: ( p / q - q / p ) = 21 / 10 . then find 4 p / q + 4 q / p ?

<gadget id="calculator">21 + 10</gadget>
<output>31</output>

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

<gadget id="calculator">31 + 16</gadget>
<output>47</output>

<gadget id="calculator">47 + 1</gadget>
<output>48</output>

<gadget id="calculator">48 + 10</gadget>
<output>58</output>

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

<gadget id="calculator">58 / 5</gadget>
<output>58/5 = around 11.6</output>
<result>58/5 = around 11.6</result>

Choices:
A. 58 / 9
B. 58 / 5
C. 58 / 7
D. 58 / 2
E. 58 / 1

divide(add(add(add(add(21, 10), multiply(4, 4)), const_1), const_10), add(4, const_1))

Explanation: let p / q = a , then ( a - 1 / a ) = 21 / 10 ⇒ a 2 − 1 = a . 2110 ⇒ a 2 − 1 = a . 2110 ⇒ 10 a 2 − 21 a − 10 ⇒ 10 a 2 − 21 a − 10 = 0 roots of the equation = − b ± b 2 − 4 ac − − − − − − − √ 2 a − b ± b 2 − 4 ac 2 a a = 21 ± 441 + 400 − − − − − − − − √ 2021 ± 441 + 40020 a = 21 ± 292021 ± 2920 = 5 / 2 or - 2 / 5 for a = 5 / 2 , 4 p / q + 4 q / p = 58 / 5 for a = - 2 / 5 , 4 p / q + 4 q / p = - 58 / 5 answer : b


Question: a jar was full with honey . a person used to draw out 20 % of the honey from the jar and replaced it with sugar solution . he has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar , the rest part of the jar was filled with the sugar solution . the initial amount of honey in the jar was filled with the sugar solution . the initial amount of honey in the jar was :

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

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

<gadget id="calculator">(4/5) ** 4</gadget>
<output>256/625 = around 0.4096</output>

<gadget id="calculator">512 / (256/625)</gadget>
<output>1_250</output>

<gadget id="calculator">1_250 / 1_000</gadget>
<output>5/4 = around 1.25</output>
<result>5/4 = around 1.25</result>

Choices:
A. 1.25 kg
B. 1.29 kg
C. 1.85 kg
D. 3.25 kg
E. 1.23 kg

divide(divide(512, power(divide(4, divide(20, 4)), 4)), const_1000)

Explanation: answer : a ) 1.25 kg


Question: a pupil ' s marks were wrongly entered as 85 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :

<gadget id="calculator">85 - 45</gadget>
<output>40</output>

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

Choices:
A. 30
B. 80
C. 20
D. 25
E. 26

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 45 ) = > x / 2 = 40 = > x = 80 . answer : b"


Question: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

<gadget id="calculator">20 * 14</gadget>
<output>280</output>
<result>280</result>

Choices:
A. 276
B. 280
C. 322
D. 345
E. 354

Explanation: "clearly , the numbers are ( 20 x 13 ) and ( 20 x 14 ) . larger number = ( 20 x 14 ) = 280 . answer : option b"


Question: two cubes of their volumes in the ratio 64 : 125 . the ratio of their surface area is :

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

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

<gadget id="calculator">125 ** (1/3)</gadget>
<output>5</output>

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

Choices:
A. 1.5 : 5
B. 2 : 5
C. 3 : 5
D. 1 : 5
E. 4 : 5

divide(power(64, const_0_33), power(125, const_0_33))

Explanation: "the ratio of their surface area is 64 : 125 4 : 5 answer is e ."


Question: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22 , what is the value of r - p ?

<gadget id="calculator">22 * 2</gadget>
<output>44</output>

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

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

Choices:
A. 20
B. 10
C. 30
D. 24
E. 5

subtract(multiply(22, const_2), multiply(10, const_2))

Explanation: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 44 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 24 hence , the correct answer is d"


Question: a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?

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

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

<gadget id="calculator">28 - 2</gadget>
<output>26</output>

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

<gadget id="calculator">26 / 1</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 16
B. 19
C. 15
D. 26
E. 10

divide(subtract(28, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))

Explanation: "let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . ( x + 28 ) + 2 = 2 ( x + 2 ) x + 30 = 2 x + 4 = > x = 26 . answer : d"


Question: in an examination , 30 % of total students failed in hindi , 42 % failed in english and 28 % in both . the percentage of these who passed in both the subjects is :

<gadget id="calculator">30 + 42</gadget>
<output>72</output>

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

<gadget id="calculator">100 - 44</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 23
B. 37
C. 56
D. 40
E. 81

subtract(const_100, subtract(add(30, 42), 28))

Explanation: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 30 + 42 â € “ 28 = 44 therefore students who passed = 100 â € “ 44 = 56 . answer : c"


Question: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is : ?

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

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

<gadget id="calculator">40 * (11/10)</gadget>
<output>44</output>

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

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

<gadget id="calculator">50 * (6/5)</gadget>
<output>60</output>

<gadget id="calculator">44 + 60</gadget>
<output>104</output>

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

<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">90 * (23/20)</gadget>
<output>207/2 = around 103.5</output>

<gadget id="calculator">104 - (207/2)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">40 / (1/2)</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 40
B. 60
C. 80
D. 67
E. 30

divide(40, subtract(add(multiply(40, add(const_1, divide(10, const_100))), multiply(50, add(const_1, divide(20, const_100)))), multiply(90, add(const_1, divide(15, const_100)))))

Explanation: "let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c"


Question: two trains travelling in the same direction at 50 and 40 kmph completely pass off another in 1 1 / 2 minute . if the length of the first train is 125 m , what is the length of the second train ?

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

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

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

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

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

<gadget id="calculator">10 * (5/18)</gadget>
<output>25/9 = around 2.777778</output>

<gadget id="calculator">90 * (25/9)</gadget>
<output>250</output>

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

Choices:
A. 300 m
B. 287 m
C. 125 m
D. 250 m
E. 167 m

subtract(multiply(add(multiply(1, const_60), divide(multiply(1, const_60), 2)), multiply(subtract(50, 40), const_0_2778)), 125)

Explanation: rs = 50 â € “ 40 = 10 * 5 / 18 = 25 / 9 mps t = 90 sec d = 25 / 9 * 90 = 250 m 125 - - - - - - - - 125 m answer : c


Question: a man can row upstream at 25 kmph and downstream at 31 kmph , and then find the speed of the man in still water ?

<gadget id="calculator">25 + 31</gadget>
<output>56</output>

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

Choices:
A. 22
B. 28
C. 30
D. 27
E. 18

Explanation: "us = 25 ds = 31 m = ( 31 + 25 ) / 2 = 28 answer : b"


Question: a cricket player whose bowling average was 23.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?

<gadget id="calculator">23.5 - 0.5</gadget>
<output>23</output>

<gadget id="calculator">23 * 5</gadget>
<output>115</output>

<gadget id="calculator">115 - 52</gadget>
<output>63</output>

<gadget id="calculator">63 / 0.5</gadget>
<output>126</output>
<result>126</result>

Choices:
A. 64
B. 72
C. 131
D. 456
E. 108

divide(subtract(multiply(subtract(23.50, 0.50), 5), 52), 0.50)

Explanation: "average = total runs / total wickets total runs after last match = 23.5 w + 52 total wickets after last match = w + 5 ( 23.5 w + 52 ) / ( w + 5 ) = 23.5 - 0.5 = 23 w = 126 so total wickets aftr last match = w + 5 = 131 answer : c"


Question: on dividing 52 by a number , the quotient is 16 and the remainder is 4 . find the divisor ?

<gadget id="calculator">52 / 16</gadget>
<output>13/4 = around 3.25</output>

<gadget id="calculator">floor(13/4)</gadget>
<output>3</output>
<result>3</result>

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

Explanation: "d = ( d - r ) / q = ( 52 - 4 ) / 16 = 48 / 16 = 3 b )"


Question: jim â € ™ s taxi service charges an initial fee of $ 2.5 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?

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

<gadget id="calculator">3.6 / (2/5)</gadget>
<output>9</output>

<gadget id="calculator">9 * 0.35</gadget>
<output>3.15</output>

<gadget id="calculator">3.15 + 2.5</gadget>
<output>5.65</output>
<result>5.65</result>

Choices:
A. $ 3.15
B. $ 4.45
C. $ 4.80
D. $ 5.65
E. $ 5.40

Explanation: "let the fixed charge of jim â € ™ s taxi service = 2.5 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.5 + ( 3.6 / . 4 ) * . 35 = 2.5 + 9 * . 35 = 5.65 $ answer d"


Question: if the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches , then the face of greatest area is of what area ?

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

Choices:
A. 225 square inches
B. 45 square inches
C. 25 square inches
D. 15 square inches
E. 10 square inches

Explanation: definitely ( d ) 5 * 3 = 15 sq inches the question asks to find the greatest area of the faces of a cuboid the possible area of the faces are - length * breadth , breadth * height & height * length the possible areas are - 6 , 10 & 15 thus 15 is the greatest possible area . . . . answer : d


Question: at a certain university , 66 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?

<gadget id="calculator">100 - 66</gadget>
<output>34</output>

<gadget id="calculator">90 - 66</gadget>
<output>24</output>

<gadget id="calculator">34 + 24</gadget>
<output>58</output>
<result>58</result>

Choices:
A. 25
B. 37.5
C. 60
D. 62.5
E. 75

add(subtract(const_100, 66), subtract(90, 66))

Explanation: "answer is 75 % total women = 66 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 24 % but question wants to know the percent of men that are tenured 24 % / 40 % = 60 % c"


Question: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 50 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?

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

<gadget id="calculator">35 * (2/5)</gadget>
<output>14</output>

<gadget id="calculator">14 + 35</gadget>
<output>49</output>
<result>49</result>

Choices:
A. $ 37.80
B. $ 49
C. $ 39.20
D. $ 39.50
E. $ 40.60

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

Explanation: a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.5 = $ 14 - - > x = $ 28 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 28 + 21 = $ 49 . answer : b .


Question: excluding stoppages , the speed of a bus is 58 kmph and including stoppages , it is 40 kmph . for how many minutes does the bus stop per hour ?

<gadget id="calculator">58 - 40</gadget>
<output>18</output>

<gadget id="calculator">18 / 58</gadget>
<output>9/29 = around 0.310345</output>

<gadget id="calculator">60 * (9/29)</gadget>
<output>540/29 = around 18.62069</output>
<result>540/29 = around 18.62069</result>

Choices:
A. 19
B. 19.13
C. 10.5
D. 11.35
E. none of these

multiply(const_60, divide(subtract(58, 40), 58))

Explanation: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( ( 18 / 58 ) ã — 60 ) = 19 min . option ( a ) is correct"


Question: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 430 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .

<gadget id="calculator">15 * 430</gadget>
<output>6_450</output>

<gadget id="calculator">15 * 120</gadget>
<output>1_800</output>

<gadget id="calculator">6_450 - 1_800</gadget>
<output>4_650</output>

<gadget id="calculator">120 - 110</gadget>
<output>10</output>

<gadget id="calculator">4_650 / 10</gadget>
<output>465</output>
<result>465</result>

Choices:
A. 400
B. 465
C. 430
D. 450
E. 510

divide(subtract(multiply(15, 430), multiply(15, 120)), subtract(120, 110))

Explanation: "let no . of non - officers be x 15 * 430 + x * 110 = ( x + 15 ) 120 x = 465 b"


Question: the salary of a person was reduced by 14 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?

<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">100 * (7/50)</gadget>
<output>14</output>

<gadget id="calculator">100 - 14</gadget>
<output>86</output>

<gadget id="calculator">14 / 86</gadget>
<output>7/43 = around 0.162791</output>

<gadget id="calculator">(7/43) * 100</gadget>
<output>700/43 = around 16.27907</output>
<result>700/43 = around 16.27907</result>

Choices:
A. 10 %
B. 16.3 %
C. 13.7 %
D. 15.1 %
E. 12.3 %

multiply(divide(multiply(const_100, divide(14, const_100)), subtract(const_100, multiply(const_100, divide(14, const_100)))), const_100)

Explanation: let the original salary be $ 100 new salary = $ 86 increase on 86 = 14 increase on 100 = 14 / 86 * 100 = 16.3 % answer is b


Question: a bullet train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the bullet train must run to reduce the time of journey to 40 min will be .

<gadget id="calculator">50 * 48</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 / 40</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 80 kmph
B. 40 kmph
C. 60 kmph
D. 90 kmph
E. 30 kmph

Explanation: c 60 kmph time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph


Question: the area of a triangle is with base 12 m and height 5 m ?

<gadget id="calculator">(12 * 5) / 2</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 88 m 2
B. 30 m 2
C. 66 m 2
D. 77 m 2
E. 31 m 2

Explanation: "1 / 2 * 12 * 5 = 30 m 2 answer : b"


Question: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ?

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

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

<gadget id="calculator">70 / 2</gadget>
<output>35</output>

<gadget id="calculator">10 / 35</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>

Choices:
A. 3 / 10
B. 2 / 5
C. 2 / 7
D. 10 / 21
E. 5 / 11

divide(10, divide(multiply(10, subtract(10, const_3)), const_2))

Explanation: from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 7 . the answer is c .


Question: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 360 per week . how much does she earn in dollars per hour ?

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

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

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

<gadget id="calculator">360 / 36</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 11
B. 10
C. 9
D. 8
E. 7

divide(360, add(multiply(8, const_3), multiply(6, const_2)))

Explanation: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 360 per week 36 x = 360 x = 10 correct option : b"


Question: dacid obtained 90 , 92 , 85 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?

<gadget id="calculator">90 + 92</gadget>
<output>182</output>

<gadget id="calculator">182 + 85</gadget>
<output>267</output>

<gadget id="calculator">267 + 87</gadget>
<output>354</output>

<gadget id="calculator">354 + 85</gadget>
<output>439</output>

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

<gadget id="calculator">439 / 5</gadget>
<output>439/5 = around 87.8</output>
<result>439/5 = around 87.8</result>

Choices:
A. 67
B. 26
C. 88
D. 90
E. 75

divide(add(add(add(add(90, 92), 85), 87), 85), divide(const_10, const_2))

Explanation: "average = ( 90 + 92 + 85 + 87 + 85 ) / 5 = 439 / 5 = 87.8 . answer : c"


Question: in a group of 6 boys and 4 girls , four children are to be selected . in how many different ways can they be selected ?

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

<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>

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

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

<gadget id="calculator">24 * 720</gadget>
<output>17_280</output>

<gadget id="calculator">3_628_800 / 17_280</gadget>
<output>210</output>
<result>210</result>

Choices:
A. 159
B. 194
C. 210
D. 209
E. 166

divide(factorial(add(6, 4)), multiply(factorial(4), factorial(6)))

Explanation: "out of 10 students 4 children should to be selected . so the combination will be 10 c 4 . 10 c 4 = 10 ! / 6 ! * 4 ! = 10 * 9 * 8 * 7 * 6 ! / 6 ! * ( 4 * 3 * 2 * 1 ) 10 c 4 = 210 there are 210 differect possible ways to select 4 children out of 10 students ."


Question: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 360 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?

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

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

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

<gadget id="calculator">360 / 15</gadget>
<output>24</output>

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

Choices:
A. 96
B. 108
C. 120
D. 132
E. 140

multiply(divide(360, add(add(multiply(3, 2), 4), 5)), 4)

Explanation: the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 360 = 96 the answer is a .


Question: the sum of ages of 5 children born at the intervals of 3 years each is 55 years . what is the age of the youngest child ?

<gadget id="calculator">55 / 5</gadget>
<output>11</output>

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

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

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

Explanation: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . age of the youngest child = x = 5 years . a )"


Question: a man invested rs . 14,400 in rs . 100 shares of a company at 25 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?

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

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

<gadget id="calculator">10_000 + 4_000</gadget>
<output>14_000</output>

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

<gadget id="calculator">14_000 + 400</gadget>
<output>14_400</output>

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

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

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

<gadget id="calculator">14_400 / 125</gadget>
<output>576/5 = around 115.2</output>

<gadget id="calculator">100 * (576/5)</gadget>
<output>11_520</output>

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

<gadget id="calculator">11_520 * (1/20)</gadget>
<output>576</output>
<result>576</result>

Choices:
A. rs . 576
B. rs . 600
C. rs . 650
D. rs . 720
E. none

multiply(multiply(100, divide(add(add(multiply(const_10, const_1000), multiply(const_4, const_1000)), multiply(const_4, 100)), add(100, multiply(100, divide(25, 100))))), divide(5, 100))

Explanation: "solution number of shares = ( 14400 / 125 ) = 115.2 . face value = rs . ( 100 x 115.2 ) = rs . 11520 . annual income = rs . ( 5 / 100 x 11520 ) = rs . 576 . answer a"


Question: a ladder 22 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 7 feet from the base of the wall . if the top of the ladder slips down 3 feet , how many feet will the bottom of the ladder slip ?

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

<gadget id="calculator">7 ** 2</gadget>
<output>49</output>

<gadget id="calculator">484 - 49</gadget>
<output>435</output>

<gadget id="calculator">435 ** (1/2)</gadget>
<output>sqrt(435) = around 20.856654</output>

<gadget id="calculator">(sqrt(435)) - 3</gadget>
<output>-3 + sqrt(435) = around 17.856654</output>

<gadget id="calculator">(-3 + sqrt(435)) ** 2</gadget>
<output>(-3 + sqrt(435))**2 = around 318.860078</output>

<gadget id="calculator">484 - ((-3 + sqrt(435))**2)</gadget>
<output>484 - (-3 + sqrt(435))**2 = around 165.139922</output>

<gadget id="calculator">(484 - (-3 + sqrt(435))**2) ** (1/2)</gadget>
<output>sqrt(484 - (-3 + sqrt(435))**2) = around 12.850678</output>
<result>sqrt(484 - (-3 + sqrt(435))**2) = around 12.850678</result>

Choices:
A. 12.86
B. 15
C. 18
D. 19
E. 25

sqrt(subtract(power(22, const_2), power(subtract(sqrt(subtract(power(22, const_2), power(7, const_2))), 3), const_2)))

Explanation: "22 ^ 2 - 7 ^ 2 = 435 it means that the height is equal to 20.85 . since the top of the ladder slips down 4 feet , then the height of the wall = 20.85 - 3 = 17.85 the bottom = sqrt ( 22 ^ 2 - 17.85 ^ 2 ) = sqrt ( 484 - 318.62 ) = 12.86 ans is a"


Question: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 117 grams of water ?

<gadget id="calculator">2 + 16</gadget>
<output>18</output>

<gadget id="calculator">117 / 18</gadget>
<output>13/2 = around 6.5</output>

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

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

Explanation: ( 2 / 18 ) * 117 = 13 grams the answer is d .


Question: if a tire rotates at 400 revolutions per minute when the car is traveling 24 km / h , what is the circumference of the tire ?

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

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

<gadget id="calculator">60 * 400</gadget>
<output>24_000</output>

<gadget id="calculator">24 / 24_000</gadget>
<output>1/1_000 = around 0.001</output>

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

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

multiply(divide(24, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)

Explanation: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 24,000 m : c is the circumference c = 1 meters correct answer a"


Question: a can do a work in 15 days and b in 20 days . if they work on it together for 7 days , then the fraction of the work that is left is

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

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

<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">(7/60) * 7</gadget>
<output>49/60 = around 0.816667</output>

<gadget id="calculator">1 - (49/60)</gadget>
<output>11/60 = around 0.183333</output>
<result>11/60 = around 0.183333</result>

Choices:
A. 8 / 17
B. 7 / 15
C. 3 / 15
D. 8 / 15
E. 11 / 60

subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 7))

Explanation: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 7 = 245 remaining work is 300 - 245 = 55 remaining fraction of work is = 55 / 300 = 11 / 60 answer e"


Question: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.75 lacs . how many workers were they ?

<gadget id="calculator">3.75 - 3</gadget>
<output>0.75</output>

<gadget id="calculator">0.75 * 1_000</gadget>
<output>750</output>

<gadget id="calculator">750 * 100</gadget>
<output>75_000</output>

<gadget id="calculator">75_000 / 50</gadget>
<output>1_500</output>
<result>1_500</result>

Choices:
A. 220
B. 230
C. 500
D. 1500
E. 590

divide(multiply(multiply(subtract(3.75, 3), const_1000), const_100), 50)

Explanation: n * 50 = ( 375000 - 300000 ) = 75000 n = 75000 / 50 = 1500 d


Question: 40 % of a number is added to 60 , the result is the same number . find the number ?

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

<gadget id="calculator">60 / (3/5)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 300
B. 288
C. 270
D. 100
E. 281

Explanation: "( 40 / 100 ) * x + 60 = x 4 x + 600 = 10 x 6 x = 600 x = 100 answer : d"


Question: what is the smallest integer that is multiple of 5 , 711

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

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

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

<gadget id="calculator">77 * 5</gadget>
<output>385</output>
<result>385</result>

Choices:
A. 70
B. 35
C. 385
D. 280
E. 140

multiply(multiply(subtract(const_12, const_1), add(const_3, const_4)), 5)

Explanation: it is the lcm of 5 , 7 and 11 which is 385 . the answer is c .


Question: the average waight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .

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

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

<gadget id="calculator">43 * 2</gadget>
<output>86</output>

<gadget id="calculator">135 - 86</gadget>
<output>49</output>

<gadget id="calculator">80 - 49</gadget>
<output>31</output>
<result>31</result>

Choices:
A. 23 kg
B. 43 kg
C. 21 kg
D. 31 kg
E. 43 kg

subtract(multiply(40, const_2), subtract(multiply(45, const_3), multiply(43, const_2)))

Explanation: sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d


Question: a father is now 3 times as old as his son . 8 years back , he was 4 times as old as his son . the age of the son ( in years ) is

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

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

Choices:
A. 12
B. 24
C. 18
D. 27
E. 25

Explanation: if father ' s age is f and son ' s age is s , then f = 3 s and f - 8 = 4 * ( s - 8 ) 3 s - 5 = 4 s - 32 s = 24 f = 72 years answer : b


Question: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 40 per square m ?

<gadget id="calculator">20 * 15</gadget>
<output>300</output>

<gadget id="calculator">300 * 2</gadget>
<output>600</output>

<gadget id="calculator">600 * 40</gadget>
<output>24_000</output>

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

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

<gadget id="calculator">200 * 40</gadget>
<output>8_000</output>

<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>

<gadget id="calculator">15 * 5</gadget>
<output>75</output>

<gadget id="calculator">75 * 2</gadget>
<output>150</output>

<gadget id="calculator">150 * 40</gadget>
<output>6_000</output>

<gadget id="calculator">32_000 + 6_000</gadget>
<output>38_000</output>
<result>38_000</result>

Choices:
A. s . 43000
B. s . 50000
C. s . 57000
D. s . 38000
E. s . 62000

add(add(multiply(multiply(multiply(20, 15), const_2), 40), multiply(multiply(multiply(20, 5), const_2), 40)), multiply(multiply(multiply(15, 5), const_2), 40))

Explanation: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 40 * 950 = rs . 38000 d"


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 e 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. e = 256
D. e = 384
E. e = 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: a sum of money becomes 7 / 6 of itself in 7 years at a certain rate of simple interest . the rate per annum is ?

<gadget id="calculator">7 / 6</gadget>
<output>7/6 = around 1.166667</output>

<gadget id="calculator">(7/6) - 1</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) / 7</gadget>
<output>1/42 = around 0.02381</output>

<gadget id="calculator">(1/42) * 100</gadget>
<output>50/21 = around 2.380952</output>
<result>50/21 = around 2.380952</result>

Choices:
A. 50 / 13
B. 50 / 17
C. 50 / 19
D. 50 / 21
E. 50 / 23

multiply(divide(subtract(divide(7, 6), const_1), 7), const_100)

Explanation: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 7 years . rate = ( 100 * x ) / ( x * 6 * 7 ) = 50 / 21 % . answer : d"


Question: a ship 77 km from the shore , springs a leak which admits to 9 / 4 tonnes of water in 11 / 2 minutes . 92 tonnes of water would sink it . but the pumps can throw out 12 tonnes of water per hour . find the average rate of sailing so that the ship may just reach the shore as it begins to sink .

<gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>

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

<gadget id="calculator">(11/2) / 60</gadget>
<output>11/120 = around 0.091667</output>

<gadget id="calculator">(9/4) / (11/120)</gadget>
<output>270/11 = around 24.545455</output>

<gadget id="calculator">(270/11) - 12</gadget>
<output>138/11 = around 12.545455</output>

<gadget id="calculator">92 / (138/11)</gadget>
<output>22/3 = around 7.333333</output>

<gadget id="calculator">77 / (22/3)</gadget>
<output>21/2 = around 10.5</output>
<result>21/2 = around 10.5</result>

Choices:
A. 10.5
B. 11
C. 12
D. 13
E. 15

divide(77, divide(92, subtract(divide(divide(9, 4), divide(divide(11, 2), const_60)), 12)))

Explanation: leak admits 9 / 4 tonnes water in 11 / 2 min = 11 / 2 * 4 / 9 = 22 / 9 leak admits 9 / 22 tonne of water in 5 min in 1 min in thrws 1 / 5 tonne of water = 9 / 22 - 1 / 5 = 23 / 110 92 / 23 / 11 min = 440 min 22 / 3 min = 7 / 22 / 22 / 3 = > 10.5 km / hr answer a


Question: a library has an average of 600 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :

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

<gadget id="calculator">30 / 7</gadget>
<output>30/7 = around 4.285714</output>

<gadget id="calculator">floor(30/7)</gadget>
<output>4</output>

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

<gadget id="calculator">5 * 600</gadget>
<output>3_000</output>

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

<gadget id="calculator">25 * 240</gadget>
<output>6_000</output>

<gadget id="calculator">3_000 + 6_000</gadget>
<output>9_000</output>

<gadget id="calculator">9_000 / 30</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 250
B. 260
C. 300
D. 285
E. none

divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 600), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30)

Explanation: "since the month begins with sunday , to there will be five sundays in the month average required = ( 600 x 5 + 240 x 25 ) / 30 ) = 300 answer : option c"


Question: the lcm of two numbers is 2310 and hcf is 30 . if one of the numbers is 210 . then what is the other number ?

<gadget id="calculator">2_310 * 30</gadget>
<output>69_300</output>

<gadget id="calculator">69_300 / 210</gadget>
<output>330</output>
<result>330</result>

Choices:
A. 715
B. 825
C. 330
D. 582
E. 465

Explanation: "first number * second number = lcm * hcf other number = 2310 * 30 / 210 = 11 * 30 = 330 answer : c"


Question: a small college reduced its faculty by approximately 15 percent to 195 professors . what was the original number of faculty members ?

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

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">195 / (17/20)</gadget>
<output>3_900/17 = around 229.411765</output>
<result>3_900/17 = around 229.411765</result>

Choices:
A. 182
B. 208
C. 224
D. 229
E. 302

divide(195, divide(subtract(const_100, 15), const_100))

Explanation: "if x is the original number of faculty members , then after 15 % reduction in faculty members number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of faculty members is 229 correct answer - d"


Question: if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?

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

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

<gadget id="calculator">(27/20) ** 2</gadget>
<output>729/400 = around 1.8225</output>

<gadget id="calculator">(729/400) - 1</gadget>
<output>329/400 = around 0.8225</output>

<gadget id="calculator">(329/400) * 100</gadget>
<output>329/4 = around 82.25</output>
<result>329/4 = around 82.25</result>

Choices:
A. 38.25 %
B. 40.25 %
C. 82.25 %
D. 50 %
E. 65 %

multiply(subtract(power(add(divide(35, const_100), const_1), const_2), const_1), const_100)

Explanation: if sides are a and b , after increase sides would be 1.35 a and 1.35 b . percentage increase in area = ( 1.35 a * 1.35 b - ab ) * 100 / ab = 82.25 answer : c


Question: the length of the bridge , which a train 120 m long and traveling at 45 km / hr can cross in 30 sec is ?

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

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

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

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

<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>

<gadget id="calculator">375 - 120</gadget>
<output>255</output>
<result>255</result>

Choices:
A. 235
B. 240
C. 245
D. 250
E. 255

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 120)

Explanation: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 x = 255 m . answer : option e"


Question: if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 40 km more . the actual distance traveled by him is ?

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

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

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

Choices:
A. 40 km
B. 76 km
C. 18 km
D. 16 km
E. 97 km

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

Explanation: "let the actual distance traveled be x km . then , x / 10 = ( x + 40 ) / 20 10 x - 400 = > x = 40 km . answer : a"


Question: there are 840 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?

<gadget id="calculator">840 / 3</gadget>
<output>280</output>

<gadget id="calculator">280 * 4</gadget>
<output>1_120</output>

<gadget id="calculator">1_120 - 840</gadget>
<output>280</output>

<gadget id="calculator">280 / 2</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 75
B. 100
C. 125
D. 140
E. 225

divide(subtract(multiply(divide(840, const_3), const_4), 840), const_2)

Explanation: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d"


Question: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?

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

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

<gadget id="calculator">(6/5) * (6/5)</gadget>
<output>36/25 = around 1.44</output>

<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>

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

Choices:
A. 44 %
B. 45 %
C. 50 %
D. 55 %
E. 60 %

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

Explanation: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . a )"


Question: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 40 degrees . find the temperature on friday ?

<gadget id="calculator">48 * 4</gadget>
<output>192</output>

<gadget id="calculator">46 * 4</gadget>
<output>184</output>

<gadget id="calculator">192 - 184</gadget>
<output>8</output>

<gadget id="calculator">40 - 8</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 65 degrees
B. 32 degrees
C. 37 degrees
D. 34 degrees
E. 74 degrees

subtract(40, subtract(multiply(48, const_4), multiply(46, const_4)))

Explanation: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 40 tu + w + th = 192 - 40 = 152 f = 184 – 152 = 32 answer : b"


Question: difference between the length & breadth of a rectangle is 30 m . if its perimeter is 300 m , then its area is ? ? we have : ( l - b ) = 30 and 2 ( l + b ) = 300 or ( l + b ) = 150 ?

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

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

Explanation: solving the two equations , we get : l = 90 and b = 60 . the ratio of length and breath is 90 : 60 = 3 : 2 e


Question: what is the maximum number e of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?

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

<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>

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

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

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

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

<gadget id="calculator">floor(8/3)</gadget>
<output>2</output>

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

Choices:
A. 36
B. 32
C. 24
D. 21
E. 15

multiply(multiply(divide(12, power(27, inverse(const_3))), divide(9, power(27, inverse(const_3)))), floor(divide(8, power(27, inverse(const_3)))))

Explanation: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get e = 24 cubes . ans . c


Question: find k if 64 / k = 4 .

<gadget id="calculator">64 / 4</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 16
B. 17
C. 18
D. 14
E. 13

Explanation: since 64 / k = 4 and 64 / 16 = 4 , then k = 16 correct answer a


Question: if 1 + 3 = 10 ; 3 + 5 = 52 ; 5 + 7 = 174 then 7 + 11 = ?

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

<gadget id="calculator">11 ** 2</gadget>
<output>121</output>

<gadget id="calculator">343 + 121</gadget>
<output>464</output>
<result>464</result>

Choices:
A. 354
B. 225
C. 654
D. 741
E. 464

Explanation: "1 ^ 3 + 3 ^ 2 = 1 + 9 = 10 3 ^ 3 + 5 ^ 2 = 27 + 25 = 52 5 ^ 3 + 7 ^ 2 = 125 + 49 = 174 and 7 ^ 3 + 11 ^ 2 = 343 + 121 = 464 answer : e"


Question: 10 play kabadi , 30 play kho kho only , 5 play both gmaes . then how many in total ?

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

<gadget id="calculator">10 + 35</gadget>
<output>45</output>

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

Choices:
A. 30
B. 35
C. 38
D. 40
E. 45

Explanation: 10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 30 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 30 + 5 = 35 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 35 - 5 = 40 answer : d


Question: 14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish

<gadget id="calculator">5 * 14</gadget>
<output>70</output>

<gadget id="calculator">1_400 / 5</gadget>
<output>280</output>

<gadget id="calculator">1_400 - 280</gadget>
<output>1_120</output>

<gadget id="calculator">70 * 1_120</gadget>
<output>78_400</output>

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

<gadget id="calculator">28 * 1_400</gadget>
<output>39_200</output>

<gadget id="calculator">78_400 / 39_200</gadget>
<output>2</output>
<result>2</result>

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

divide(multiply(multiply(5, 14), subtract(1400, divide(1400, 5))), multiply(multiply(const_2, 14), 1400))

Explanation: 14 men make toy in 5 days after 1 day 14 more worker join m 1 / m 2 = d 2 / d 1 14 / 28 = d 2 / 4 = 2 day answer : b


Question: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19.50 ?

<gadget id="calculator">25 - 19.5</gadget>
<output>5.5</output>

<gadget id="calculator">19.5 - 16</gadget>
<output>3.5</output>

<gadget id="calculator">5.5 / 3.5</gadget>
<output>1.571429</output>
<result>1.571429</result>

Choices:
A. 10 : 7
B. 9 : 8
C. 11 : 7
D. 13 : 11
E. 14 : 8

Explanation: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5.50 : 3.50 = 11 : 7"


Question: a sum of rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months , the total amount of rs 500 is received . find the rate of interest ?

<gadget id="calculator">500 - 468.75</gadget>
<output>31.25</output>

<gadget id="calculator">31.25 * 100</gadget>
<output>3_125</output>

<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">3_125 / (5/3)</gadget>
<output>1_875</output>

<gadget id="calculator">1_875 / 468.75</gadget>
<output>4</output>
<result>4</result>

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

divide(divide(multiply(subtract(500, 468.75), const_100), add(1, divide(8, const_12))), 468.75)

Explanation: here p = 468.75 which is the principle . amount = rs 500 amount = si + p 500 = [ 468.75 * ( 20 / 12 ) * r ] / 100 + 468.75 31.25 = 156.25 * 5 r / 100 r = 4 % answer : b


Question: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 110 . what was the number he chose ?

<gadget id="calculator">110 + 138</gadget>
<output>248</output>

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

Choices:
A. 123
B. 267
C. 277
D. 124
E. 120

Explanation: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 110 x = 124 answer : d"


Question: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each . the radius of the sphere is

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

<gadget id="calculator">14 * 7</gadget>
<output>98</output>

<gadget id="calculator">pi * 98</gadget>
<output>98*pi = around 307.87608</output>

<gadget id="calculator">(98*pi) * 2</gadget>
<output>196*pi = around 615.75216</output>

<gadget id="calculator">pi * 4</gadget>
<output>4*pi = around 12.566371</output>

<gadget id="calculator">(196*pi) / (4*pi)</gadget>
<output>49</output>

<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 3 cm
B. 4 cm
C. 6 cm
D. 7 cm
E. none

sqrt(divide(multiply(multiply(const_pi, multiply(14, divide(14, const_2))), const_2), multiply(const_pi, const_4)))

Explanation: "solution 4 î r 2 = 2 î 7 x 14 â ‡ ’ r 2 = ( 7 x 14 / 2 ) â ‡ ’ 49 â ‡ ’ r = 7 cm . answer d"


Question: if 8 men or 12 women can do a piece of work in 30 days , in how many days can the same work be done by 6 men and 11 women ?

<gadget id="calculator">8 * 30</gadget>
<output>240</output>

<gadget id="calculator">6 / 240</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">12 * 30</gadget>
<output>360</output>

<gadget id="calculator">11 / 360</gadget>
<output>11/360 = around 0.030556</output>

<gadget id="calculator">(1/40) + (11/360)</gadget>
<output>1/18 = around 0.055556</output>

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

Choices:
A. 10 days
B. 11 days
C. 13 days
D. 15 days
E. 18 days

inverse(add(divide(6, multiply(8, 30)), divide(11, multiply(12, 30))))

Explanation: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 30 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 30 = 1 / 360 so , 20 women work = 20 / 360 = 1 / 18 ans : 18 days answer : e"


Question: set s consists of integers { 8 , 11 , 12 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 25 % . what is the value of integer n ?

<gadget id="calculator">12 + 14</gadget>
<output>26</output>

<gadget id="calculator">26 + 14</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 28
B. 32
C. 36
D. 40
E. 44

Explanation: the average of the numbers in set s is 12 . if we increase the mean by 25 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d .


Question: the average marks obtained by 50 candidates in a certain examination is 40 . find the total marks .

<gadget id="calculator">50 * 40</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 1800
B. 2000
C. 1640
D. 2200
E. 2400

Explanation: following the above formula , we have the total marks = 50 * 40 = 2000 answer is b


Question: the speed of a car is 95 km in the first hour and 60 km in the second hour . what is the average speed of the car ?

<gadget id="calculator">95 + 60</gadget>
<output>155</output>

<gadget id="calculator">155 / 2</gadget>
<output>155/2 = around 77.5</output>
<result>155/2 = around 77.5</result>

Choices:
A. 76 kmph
B. 75 kmph
C. 77.5 kmph
D. 56 kmph
E. 86 kmph

Explanation: "s = ( 95 + 60 ) / 2 = 77.5 kmph answer : c"


Question: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 30 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?

<gadget id="calculator">5 / 60</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">30 * (1/12)</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">4 * (1/12)</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(5/2) - (1/3)</gadget>
<output>13/6 = around 2.166667</output>

<gadget id="calculator">(13/6) / 4</gadget>
<output>13/24 = around 0.541667</output>

<gadget id="calculator">(13/24) * 60</gadget>
<output>65/2 = around 32.5</output>
<result>65/2 = around 32.5</result>

Choices:
A. 7.5
B. 15
C. 17.5
D. 25
E. 32.5

multiply(divide(subtract(multiply(30, divide(5, const_60)), multiply(4, divide(5, const_60))), 4), const_60)

Explanation: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 30 = 2.5 km . the time it takes the hiker to complete this distance is 2.5 / 4 hours = 37.5 minutes the cyclist needs to wait 37.5 - 5 = 32.5 minutes the answer is e ."


Question: 3 ltr of water is added with 9 ltr of a solution containing 57 % of alcohol in the water . the % of alcohol in the new mixture is ?

<gadget id="calculator">57 / 100</gadget>
<output>57/100 = around 0.57</output>

<gadget id="calculator">(57/100) * 9</gadget>
<output>513/100 = around 5.13</output>

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

<gadget id="calculator">(513/100) / 12</gadget>
<output>171/400 = around 0.4275</output>

<gadget id="calculator">100 * (171/400)</gadget>
<output>171/4 = around 42.75</output>
<result>171/4 = around 42.75</result>

Choices:
A. 41.5 %
B. 42.75 %
C. 43 %
D. 45 %
E. 45.75 %

multiply(const_100, divide(multiply(divide(57, const_100), 9), add(3, 9)))

Explanation: "we have a 9 litre solution containing 57 % of alcohol in the water . = > quantity of alcohol in the solution = 9 ã — 57 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 9 + 3 = 12 percentage of alcohol in the new solution = 9 ã — 57 / 100 12 ã — 100 = 9 ã — 5710012 ã — 100 = 9 ã — 4.75 / 100 = 42.75 % b"


Question: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 11.00 ?

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

<gadget id="calculator">0.5 / 3</gadget>
<output>0.166667</output>

<gadget id="calculator">(1/4) - 0.166667</gadget>
<output>0.083333</output>

<gadget id="calculator">11 / 0.083333</gadget>
<output>132.000528</output>
<result>132.000528</result>

Choices:
A. 40
B. 60
C. 90
D. 132
E. 240

Explanation: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 11 ( 1 / 12 ) * x = 11 x = 132 answer : d"


Question: the length and breadth of a rectangle is increased by 5 % and 15 % respectively . what is the increase in the area ?

<gadget id="calculator">5 + 100</gadget>
<output>105</output>

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

<gadget id="calculator">105 * 115</gadget>
<output>12_075</output>

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

<gadget id="calculator">12_075 - 10_000</gadget>
<output>2_075</output>

<gadget id="calculator">2_075 * 100</gadget>
<output>207_500</output>

<gadget id="calculator">207_500 / 10_000</gadget>
<output>83/4 = around 20.75</output>
<result>83/4 = around 20.75</result>

Choices:
A. 21.25
B. 22.75
C. 19.25
D. 20.75
E. 22.25

divide(multiply(subtract(rectangle_area(add(5, const_100), add(15, const_100)), rectangle_area(const_100, const_100)), const_100), rectangle_area(const_100, const_100))

Explanation: "100 * 100 = 10000 105 * 115 = 12075 - - - - - - - - - - - 2075 10000 - - - - - - 2075 100 - - - - - ? = > 20.75 answer d"


Question: a train running at the speed of 40 km / hr crosses a pole in 9 seconds . what is the length of the train ?

<gadget id="calculator">40 * 1_000</gadget>
<output>40_000</output>

<gadget id="calculator">40_000 / 3_600</gadget>
<output>100/9 = around 11.111111</output>

<gadget id="calculator">(100/9) * 9</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 120 metres
B. 180 metres
C. 324 metres
D. 150 metres
E. 100 meters

multiply(divide(multiply(40, const_1000), const_3600), 9)

Explanation: "speed = 40 x 5 / 18 m / sec = 100 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 100 / 9 x 9 m = 100 m . answer : e"


Question: a chemical supply company has 60 liters of a 35 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?

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

<gadget id="calculator">60 * 35</gadget>
<output>2_100</output>

<gadget id="calculator">2_100 / 100</gadget>
<output>21</output>

<gadget id="calculator">30 - 21</gadget>
<output>9</output>

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

Choices:
A. 18
B. 15
C. 20
D. 24
E. 30

multiply(subtract(divide(60, const_2), divide(multiply(60, 35), const_100)), const_2)

Explanation: "60 liters of a 35 % hno 3 solution means hno 3 = 21 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 21 + x = 50 % of ( 60 + x ) or x = 18 hence , a"


Question: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 140 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">140 + 208</gadget>
<output>348</output>

<gadget id="calculator">348 / 2</gadget>
<output>174</output>
<result>174</result>

Choices:
A. 179
B. 367
C. 269
D. 177
E. 174

divide(add(140, 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 € “ 140 x + ( x - 140 ) = 208 2 x = 348 x = 174 runs answer : e"


Question: if m ^ 2 - 8 m + 1 = 0 , then m ^ 3 + m ^ ( - 3 ) = ?

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

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

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

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

<gadget id="calculator">60 ** (1/2)</gadget>
<output>2*sqrt(15) = around 7.745967</output>

<gadget id="calculator">8 + (2*sqrt(15))</gadget>
<output>2*sqrt(15) + 8 = around 15.745967</output>

<gadget id="calculator">(2*sqrt(15) + 8) / 2</gadget>
<output>sqrt(15) + 4 = around 7.872983</output>

<gadget id="calculator">(sqrt(15) + 4) ** 3</gadget>
<output>(sqrt(15) + 4)**3 = around 487.997951</output>
<result>(sqrt(15) + 4)**3 = around 487.997951</result>

Choices:
A. 487
B. 488
C. 489
D. 457
E. 495

power(divide(add(add(const_4, const_4), sqrt(add(add(const_10, const_10), multiply(const_10, const_4)))), 2), 3)

Explanation: here from equation 1 we will get m ^ 2 - 8 m + 1 = 0 m ^ 2 = 8 m - 1 m = ( 8 m - 1 ) / m . . . . . . . . . ( 1 ) m = 8 - 1 / m so m + 1 / m = 8 now in equation 2 m ^ 3 + 1 / m ^ 3 ( m + 1 / m ) ( m ^ 2 - m * 1 / m + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 - 1 + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 + 1 / m ^ 2 - 1 ) ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 m * 1 / m - 1 } { since a ^ 2 + b ^ 2 = ( a + b ) ^ 2 - 2 ab } ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 - 1 } now putting the value of m from equation 1 8 ( 8 ^ 2 - 2 - 1 ) 8 ( 64 - 3 ) = 488 answer : b


Question: if 3 a – 3 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?

<gadget id="calculator">32 - 4</gadget>
<output>28</output>

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

<gadget id="calculator">24 - 2</gadget>
<output>22</output>

<gadget id="calculator">22 - 2</gadget>
<output>20</output>

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

<gadget id="calculator">19 - 3</gadget>
<output>16</output>

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

<gadget id="calculator">15 + 2</gadget>
<output>17</output>

<gadget id="calculator">17 - 3</gadget>
<output>14</output>

<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 3
B. 9
C. 10
D. 12
E. 14

subtract(subtract(add(subtract(subtract(subtract(subtract(subtract(subtract(subtract(32, 4), 4), const_2), const_2), const_1), 3), const_1), 2), 3), const_4)

Explanation: when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c


Question: in a group of 100 cars , 47 cars do not have air conditioning . if at least 55 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?

<gadget id="calculator">100 - 55</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 45
B. 47
C. 49
D. 51
E. 53

Explanation: "lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 55 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 55 . . we have to assign atleast 8 tocars with ac and racing stripes . hence ac = 53 - 8 = 45 . the answer is a"


Question: at a certain conference , 78 % of the attendees registered at least two weeks in advance and paid their conference fee in full . if 10 % of the attendees who paid their conference fee in full did not register at least two weeks in advance , what percent of conference attendees registered at least two weeks in advance ?

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

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

<gadget id="calculator">7_800 / 90</gadget>
<output>260/3 = around 86.666667</output>
<result>260/3 = around 86.666667</result>

Choices:
A. 18.0 %
B. 62.0 %
C. 79.2 %
D. 86.67 %
E. 82.0 %

divide(multiply(78, const_100), subtract(const_100, 10))

Explanation: i do not think that venn will be helpful here . a table will make more sense . but here is my approach . 78 % regestered at least 2 weeks and paid full fee . 10 % paid full fee and did not registered at least 2 weeks in advance . then 90 % paid full fee and registered at least 2 weeks before . 90 % * x = 78 % where x is the number of people who registerd 2 weeks in advance and paid full fee . ( answer d )


Question: if the volume of two cubes are in the ratio 8 : 1 , the ratio of their edges is :

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

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

Explanation: explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 8 / 1 = > ( a / b ) 3 = ( 2 / 1 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option a


Question: what is the dividend . divisor 15 , the quotient is 8 and the remainder is 5

<gadget id="calculator">15 * 8</gadget>
<output>120</output>

<gadget id="calculator">120 + 5</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 145
B. 148
C. 150
D. 125
E. 158

Explanation: "d = d * q + r d = 15 * 8 + 5 d = 120 + 5 d = 125 answer : d"


Question: x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 20 days . how long will y take to complete the work ?

<gadget id="calculator">8 / 40</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

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

<gadget id="calculator">20 * (5/4)</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 10
B. 12
C. 25
D. 18
E. 20

multiply(20, inverse(subtract(const_1, divide(8, 40))))

Explanation: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 20 days whole work will be done by y in 20 * 5 / 4 = 25 days answer is c"


Question: by selling an article at rs . 500 , a profit of 25 % is made . find its cost price ?

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

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

<gadget id="calculator">50_000 / 125</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 400
B. 267
C. 287
D. 480
E. 811

divide(multiply(500, const_100), add(const_100, 25))

Explanation: "sp = 500 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 500 * [ 100 / ( 100 + 25 ) ] = 500 * [ 100 / 125 ] = rs . 400 answer : a"


Question: in a class of 32 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?

<gadget id="calculator">32 + 12</gadget>
<output>44</output>

<gadget id="calculator">44 - 22</gadget>
<output>22</output>

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

Choices:
A. 30
B. 10
C. 18
D. 28
E. 32

Explanation: "total = english + german - both + neither - - > 40 = english + 22 - 12 + 0 - - > english = 22 - - > only english = english - both = 22 - 12 = 10 . answer : b ."


Question: the ratio of radius of a circle and the side of a square is 2 : 5 . find the ratio of their areas :

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

<gadget id="calculator">(2/5) ** 2</gadget>
<output>4/25 = around 0.16</output>
<result>4/25 = around 0.16</result>

Choices:
A. 2 : 1
B. 4 : 25
C. 8 : 77
D. 4 : 121
E. none

Explanation: "radius / side = 2 / 5 â ‡ ’ area of circle / area of square = 4 / 25 answer : b"


Question: a lion chases a pony 7 hours after the pony runs . lion takes 8 hours to reach the pony . if the average speed of the lion is 49 kmph , what s the average speed of the pony ?

<gadget id="calculator">49 * 8</gadget>
<output>392</output>

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

<gadget id="calculator">392 / 14</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28.3 kmph
B. 29.8 kmph
C. 28.4 kmph
D. 29.5 kmph
E. 29.4 kmph

divide(multiply(49, 8), multiply(7, const_2))

Explanation: pony take 15 hours and lion take 8 hours . . . then distance chased by them is 49 * 8 . so speed of pony is ( 49 * 8 ) / 15 = 29.4 kmph . answer is e


Question: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 360 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?

<gadget id="calculator">360 * 2</gadget>
<output>720</output>
<result>720</result>

Choices:
A. 237
B. 287
C. 197
D. 287
E. 720

Explanation: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 360 ) = 2 + 2 ( extra ) = > 2 x - 720 = x = > x = 720 . answer : e"


Question: the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is ?

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

<gadget id="calculator">106.25 - (1/4)</gadget>
<output>106</output>
<result>106</result>

Choices:
A. 366
B. 106
C. 102
D. 192
E. 122

Explanation: "cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b"


Question: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 900 , what is the reduced price for kg ?

<gadget id="calculator">900 * 25</gadget>
<output>22_500</output>

<gadget id="calculator">22_500 / 100</gadget>
<output>225</output>

<gadget id="calculator">225 / 5</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 45
B. 60
C. 70
D. 80
E. 20

divide(divide(multiply(900, 25), const_100), 5)

Explanation: "a 900 * ( 25 / 100 ) = 225 - - - - 5 ? - - - - 1 = > rs . 45"


Question: rectangular tile each of size 80 cm by 55 cm must be laid horizontally on a rectangular floor of size 210 cm by 330 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :

<gadget id="calculator">210 * 330</gadget>
<output>69_300</output>

<gadget id="calculator">80 * 55</gadget>
<output>4_400</output>

<gadget id="calculator">69_300 / 4_400</gadget>
<output>63/4 = around 15.75</output>
<result>63/4 = around 15.75</result>

Choices:
A. 26
B. 16
C. 18
D. 19
E. 20

divide(multiply(210, 330), multiply(80, 55))

Explanation: "area of tile = 80 * 55 = 4400 area of floor = 210 * 330 = 72600 no of tiles = 72600 / 4400 = 16.5 so , the no of tile = 16 answer : b"


Question: sowdharya had 90 currency notes in all , some of which are of rs 95 denomination and the remaining of rs 45 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 45 ?

<gadget id="calculator">90 * 45</gadget>
<output>4_050</output>

<gadget id="calculator">5_000 - 4_050</gadget>
<output>950</output>

<gadget id="calculator">95 - 45</gadget>
<output>50</output>

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

<gadget id="calculator">90 - 19</gadget>
<output>71</output>
<result>71</result>

Choices:
A. 75
B. 72
C. 71
D. 76
E. 73

subtract(90, divide(subtract(5000, multiply(90, 45)), subtract(95, 45)))

Explanation: let the number of 45 - rupee notes = x then , the number of 95 - rupee notes = ( 90 – x ) 45 x + 95 ( 90 – x ) = 5000 : x = 71 answer : c