Question: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container h ?

<gadget id="calculator">9 + 16</gadget>
<output>25</output>

<gadget id="calculator">9 / 25</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) ** (1/2)</gadget>
<output>3/5 = around 0.6</output>

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

<gadget id="calculator">15 / (2/5)</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>

Choices:
A. a : 45
B. b : 25
C. c : 37.5
D. d : 36
E. e : 42

divide(15, subtract(const_1, sqrt(divide(9, add(9, 16)))))

Explanation: if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .


Question: after decreasing 90 % in the price of an article costs rs . 320 . find the actual cost of an article ?

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

<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">320 / (1/10)</gadget>
<output>3_200</output>
<result>3_200</result>

Choices:
A. 2777
B. 2987
C. 3200
D. 9977
E. 1671

divide(320, subtract(const_1, divide(90, const_100)))

Explanation: "cp * ( 10 / 100 ) = 320 cp = 32 * 100 = > cp = 3200 answer : c"


Question: the perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?

<gadget id="calculator">(2.5 * 44) / 2</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 76
B. 88
C. 66
D. 55
E. 35

Explanation: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 44 / 2 = 55 cm 2 answer : d"


Question: if 0.45 : x : : 4 : 2 , then x is equal to

<gadget id="calculator">0.45 * 2</gadget>
<output>0.9</output>

<gadget id="calculator">0.9 / 4</gadget>
<output>0.225</output>
<result>0.225</result>

Choices:
A. 0.225
B. 0.228
C. 0.254
D. 0.256
E. none

Explanation: "sol . ( x × 4 ) = ( 0.45 × 2 ) ⇒ x = 0.9 / 4 = 0.225 . answer a"


Question: a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability e that both selected dogs are not littermates ?

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

Choices:
A. 1 / 6
B. 2 / 9
C. 5 / 6
D. 7 / 9
E. 8 / 9

Explanation: "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability e of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c"


Question: if 0.75 : x : : 5 : 12 , then x is equal to :

<gadget id="calculator">0.75 * 12</gadget>
<output>9</output>

<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>

Choices:
A. 1.12
B. 1.16
C. 1.8
D. 1.3
E. none of these

Explanation: "explanation : ( x * 5 ) = ( 0.75 * 12 ) x = 9 / 5 = 1.80 answer : c"


Question: two employees x and y are paid a total of rs . 650 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

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

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

<gadget id="calculator">650 * 10</gadget>
<output>6_500</output>

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

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

<gadget id="calculator">6_500 / 22</gadget>
<output>3_250/11 = around 295.454545</output>
<result>3_250/11 = around 295.454545</result>

Choices:
A. s . 200.45
B. s . 250.45
C. s . 295.45
D. s . 300.45
E. s . 310.45

divide(multiply(650, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 650 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 650 ⇒ y [ 12 / 10 + 1 ] = 650 ⇒ 22 y / 10 = 650 ⇒ 22 y = 6500 ⇒ y = 6500 / 22 = rs . 295.45 c )"


Question: the average speed of a car is 1 3 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 4 hrs if the speed of the bike is twice speed of the tractor ?

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

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

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

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

<gadget id="calculator">(8/5) * 50</gadget>
<output>80</output>

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

Choices:
A. 400 km
B. 320 km
C. 360 km
D. 550 km
E. 600 km

multiply(multiply(add(1, divide(3, 5)), multiply(const_2, divide(575, 23))), 4)

Explanation: sol . average speed of a tractor = 25 km / h the speed of a bike in an hour = 25 × 2 = 50 km the speed of a car in an hour = 8 / 5 * 50 = 80 km so , the distance covered by car in 4 h is 80 × 4 = 320 km ans . ( b )


Question: in a factory , there are 40 % technicians and 60 % non - technicians . if the 60 % of the technicians and 40 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?

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

<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>

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

<gadget id="calculator">(2/5) * 60</gadget>
<output>24</output>

<gadget id="calculator">24 + 24</gadget>
<output>48</output>

<gadget id="calculator">100 - 48</gadget>
<output>52</output>
<result>52</result>

Choices:
A. 62 %
B. 57 %
C. 52 %
D. 22 %
E. 42 %

subtract(const_100, add(multiply(40, divide(60, const_100)), multiply(divide(40, const_100), 60)))

Explanation: total = 100 t = 40 nt = 60 40 * ( 60 / 100 ) = 24 60 * ( 40 / 100 ) = 24 24 + 24 = 48 = > 100 - 48 = 52 % answer : c


Question: harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ?

<gadget id="calculator">8 * 70</gadget>
<output>560</output>

<gadget id="calculator">9 * 75</gadget>
<output>675</output>

<gadget id="calculator">560 + 675</gadget>
<output>1_235</output>
<result>1_235</result>

Choices:
A. 1235
B. 1055
C. 1065
D. 1075
E. 1080

Explanation: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 75 × 9 = 675 . total cost he has to pay = 560 + 675 = 1235 . a )"


Question: if the area of a square with sides of length 11 centimeters is equal to the area of a rectangle with a width of 11 centimeters , what is the length of the rectangle , in centimeters ?

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

<gadget id="calculator">121 / 11</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 4
B. 8
C. 11
D. 16
E. 18

Explanation: "let length of rectangle = l 11 ^ 2 = l * 11 = > l = 121 / 11 = 11 answer c"


Question: tanks p and b are each in the shape of a right circular cylinder . the interior of tank p has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank p is what percent of the capacity of tank b ?

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

<gadget id="calculator">4 / pi</gadget>
<output>4/pi = around 1.27324</output>

<gadget id="calculator">pi * ((4/pi) ** 2) * 10</gadget>
<output>160/pi = around 50.929582</output>

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

<gadget id="calculator">5 / pi</gadget>
<output>5/pi = around 1.591549</output>

<gadget id="calculator">pi * ((5/pi) ** 2) * 8</gadget>
<output>200/pi = around 63.661977</output>

<gadget id="calculator">(160/pi) / (200/pi)</gadget>
<output>4/5 = around 0.8</output>

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

Choices:
A. 75 %
B. 80 %
C. 100 %
D. 120 %
E. 125 %

multiply(divide(volume_cylinder(divide(divide(8, const_2), const_pi), 10), volume_cylinder(divide(divide(10, const_2), const_pi), 8)), const_100)

Explanation: b . for p , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi p / b = 160 pi / 200 pi = 0.8


Question: x and y are both integers . if x / y = 59.40 , then what is the sum of all the possible two digit remainders of x / y ?

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

<gadget id="calculator">(3/2) * 100</gadget>
<output>150</output>

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

<gadget id="calculator">5 * 59.4</gadget>
<output>297</output>

<gadget id="calculator">297 + 3</gadget>
<output>300</output>

<gadget id="calculator">150 + 300</gadget>
<output>450</output>
<result>450</result>

Choices:
A. 450
B. 616
C. 672
D. 900
E. 1024

add(multiply(divide(const_3, const_2), const_100), add(multiply(add(const_2, const_3), 59.4), const_3))

Explanation: remainder = 0.40 - - > 40 / 100 - - > can be written as ( 40 / 4 ) / ( 100 / 4 ) = 10 / 25 so remainders can be 10 , 20 , 30 , 40 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = 450 answer : a


Question: what quantity of water should be added to reduce 20 liters of 80 % acidic liquid to 20 % acidic liquid ?

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

<gadget id="calculator">20 * (4/5)</gadget>
<output>16</output>

<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>

<gadget id="calculator">1_600 / 20</gadget>
<output>80</output>

<gadget id="calculator">80 - 20</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 30 liters
B. 50 liters
C. 60 liters
D. 70 liters
E. 80 liters

subtract(divide(multiply(multiply(20, divide(80, const_100)), const_100), 20), 20)

Explanation: "acid in 20 liters = 80 % of 20 = 16 liters suppose x liters of water be added . then 16 liters of acid in 20 + x liters of diluted solution 20 % of 20 + x = 16 20 + x = 80 x = 60 liters answer is c"


Question: if the compound interest on a certain sum of money for 5 years at 10 % per annum be rs . 993 , what would be the simple interest ?

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

<gadget id="calculator">300 * 10</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 * 10</gadget>
<output>30_000</output>

<gadget id="calculator">30_000 * 5</gadget>
<output>150_000</output>

<gadget id="calculator">150_000 / 100</gadget>
<output>1_500</output>
<result>1_500</result>

Choices:
A. rs . 1500
B. rs . 890
C. rs . 895
D. rs . 900
E. none

divide(multiply(multiply(multiply(multiply(const_3.0, const_100), 10), 10), 5), const_100)

Explanation: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 5 yrs = ( 3000 x 10 x 5 ) / 100 = 1500 / - answer : a ."


Question: the percentage profit earned by selling an article for rs . 1620 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?

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

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

<gadget id="calculator">1_620 + 1_280</gadget>
<output>2_900</output>

<gadget id="calculator">2_900 / 2</gadget>
<output>1_450</output>

<gadget id="calculator">(5/4) * 1_450</gadget>
<output>3_625/2 = around 1_812.5</output>
<result>3_625/2 = around 1_812.5</result>

Choices:
A. 3000
B. 1812.5
C. 2000
D. 5600
E. 3400

multiply(divide(add(const_100, 25), const_100), divide(add(1620, 1280), const_2))

Explanation: "c . p . be rs . x . then , ( 1620 - x ) / x * 100 = ( x - 1280 ) / x * 100 1620 - x = x - 1280 2 x = 2900 = > x = 1450 required s . p . = 125 % of rs . 1450 = 125 / 100 * 1450 = rs . 1812.5 . answer b"


Question: a 750 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?

<gadget id="calculator">750 / 18</gadget>
<output>125/3 = around 41.666667</output>

<gadget id="calculator">(125/3) * 39</gadget>
<output>1_625</output>

<gadget id="calculator">1_625 - 750</gadget>
<output>875</output>
<result>875</result>

Choices:
A. 300
B. 875
C. 360
D. 770
E. 380

subtract(multiply(speed(750, 18), 39), 750)

Explanation: "speed = 750 / 18 = 125 / 3 m / sec . let the length of the platform be x meters . then , ( x + 750 ) / 39 = 125 / 3 = > x = 1625 m . l = 1625 - 750 = 875 answer : option b"


Question: when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ?

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

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

Explanation: "let possible value of x is 76 least possible value of x / 18 is 76 / 18 = > 4 quotient with remainder 4 thus answer is ( d ) 4"


Question: marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 35 % . what percent of the projected revenue was the actual revenue ?

<gadget id="calculator">100 - 35</gadget>
<output>65</output>

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

<gadget id="calculator">65 / 120</gadget>
<output>13/24 = around 0.541667</output>

<gadget id="calculator">(13/24) * 100</gadget>
<output>325/6 = around 54.166667</output>
<result>325/6 = around 54.166667</result>

Choices:
A. 54.2 %
B. 58 %
C. 62.5 %
D. 64 %
E. 75 %

multiply(divide(subtract(const_100, 35), add(20, const_100)), const_100)

Explanation: "last year revenue = 100 ( assume ) ; this year revenue = 65 ; projected revenue = 120 . actual / projected * 100 = 65 / 120 * 100 = 54.2 % . answer : a ."


Question: mr . shah decided to walk down the escalator of a tube station . he found â that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stairs he would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins â to descend to the time he steps off the last step at the bottom , find out the height of the stair way in steps ?

<gadget id="calculator">34 - 26</gadget>
<output>8</output>

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

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

<gadget id="calculator">(2/3) * 30</gadget>
<output>20</output>

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

Choices:
A. 44
B. 45
C. 46
D. 47
E. 48

add(26, multiply(divide(subtract(34, 26), subtract(30, 18)), 30))

Explanation: ( s 1 * t 2 ~ s 2 * t 1 ) / ( t 2 ~ t 1 ) = ( 26 * 18 ~ 34 * 30 ) / ( 18 ~ 30 ) = 46 answer : c


Question: the average age of 18 students of a class is 18 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 18 th student is

<gadget id="calculator">18 * 18</gadget>
<output>324</output>

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

<gadget id="calculator">9 * 16</gadget>
<output>144</output>

<gadget id="calculator">70 + 144</gadget>
<output>214</output>

<gadget id="calculator">324 - 214</gadget>
<output>110</output>
<result>110</result>

Choices:
A. 101
B. 66
C. 110
D. 160
E. 12

subtract(multiply(18, 18), add(multiply(5, 14), multiply(9, 16)))

Explanation: "explanation : age of the 18 th student = [ 18 * 18 - ( 14 * 5 + 16 * 9 ) ] = ( 324 - 214 ) = 110 years . answer : c"


Question: on dividing 123 by a number , the quotient is 7 and the remainder is 4 . find the divisor .

<gadget id="calculator">123 / 7</gadget>
<output>123/7 = around 17.571429</output>

<gadget id="calculator">floor(123/7)</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 15
B. 16
C. 17
D. 18
E. 19

Explanation: "d = ( d - r ) / q = ( 123 - 4 ) / 7 = 119 / 7 = 17 c"


Question: a reduction of 10 % in the price of tea enables a dealer to purchase 25 kg more tea for rs . 22500 . what is the reduced price per kg of tea ?

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

<gadget id="calculator">100 / 90</gadget>
<output>10/9 = around 1.111111</output>

<gadget id="calculator">(10/9) - 1</gadget>
<output>1/9 = around 0.111111</output>

<gadget id="calculator">22_500 * (1/9)</gadget>
<output>2_500</output>

<gadget id="calculator">2_500 / 25</gadget>
<output>100</output>

<gadget id="calculator">100 / (10/9)</gadget>
<output>90</output>
<result>90</result>

Choices:
A. rs . 70
B. rs . 80
C. rs . 90
D. rs . 100
E. none

divide(divide(multiply(22500, subtract(divide(const_100, subtract(const_100, 10)), const_1)), 25), divide(const_100, subtract(const_100, 10)))

Explanation: solution : 1 st method : let the original price of tea be rs . x / kg . after reduction the price becomes = x - 10 % of x = 9 x / 10 per kg . now , ( 22500 / ( 9 x / 10 ) ) - 22500 / x = 25 or , 22500 [ 10 / 9 x - 1 / x ] = 25 or , 25 * 9 x = 22500 ; or , x = ( 22500 / 2589 ) = rs . 100 . hence , new price = 90 per kg . thought process method : let the original price be rs . 100 per kg , he get tea = 22500 / 100 = 225 kg . after reduction the price becomes = 90 per kg , he get tea = 22500 / 90 = 250 kg . so , reduction price is rs . 90 per kg as it enables him to buy 25 kg of more tea . answer : option c


Question: two pipes a and b can fill a tank in 36 hours and 45 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>

<gadget id="calculator">1 / 45</gadget>
<output>1/45 = around 0.022222</output>

<gadget id="calculator">(1/36) + (1/45)</gadget>
<output>1/20 = around 0.05</output>

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

Choices:
A. 20 hrs
B. 22 hrs
C. 23 hrs
D. 24 hrs
E. 21 hrs

divide(const_1, add(divide(const_1, 36), divide(const_1, 45)))

Explanation: "1 / ( 1 / 36 + 1 / 45 ) = 180 / 9 = 20 hrs answer : a"


Question: a certain country is divided into 6 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 18 the total number of progressives in the entire country , what fraction of the country is traditionalist ?

<gadget id="calculator">6 / 18</gadget>
<output>1/3 = around 0.333333</output>

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

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

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

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

subtract(1, divide(divide(6, 18), add(divide(6, 18), 1)))

Explanation: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 18 the total number of traditionalists is 6 p / 18 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."


Question: in order to obtain an income of rs . 1250 from 10 % stock at rs . 210 , one must make an investment of

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

<gadget id="calculator">21 * 1_250</gadget>
<output>26_250</output>
<result>26_250</result>

Choices:
A. 5363
B. 26250
C. 28678
D. 29002
E. 2732

Explanation: "to obtain rs . 10 , investment = rs . 210 . to obtain rs . 1250 , investment = = rs . 26250 . answer : b"


Question: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 400 per sq . metre .

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>

<gadget id="calculator">400 * 20.625</gadget>
<output>8_250</output>
<result>8_250</result>

Choices:
A. rs . 15,000
B. rs . 8,250
C. rs . 15,600
D. rs . 16,500
E. none

Explanation: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 400 x 20.625 ) = rs . 8,250 . answer b"


Question: given that 268 x 74 = 19632 , find the value of 2.68 x . 74 .

<gadget id="calculator">268 / 100</gadget>
<output>67/25 = around 2.68</output>

<gadget id="calculator">74 / 100</gadget>
<output>37/50 = around 0.74</output>

<gadget id="calculator">(67/25) * (37/50)</gadget>
<output>2_479/1_250 = around 1.9832</output>
<result>2_479/1_250 = around 1.9832</result>

Choices:
A. 1.9632
B. 1.0025
C. 1.5693
D. 1.0266
E. none

multiply(divide(268, const_100), divide(74, const_100))

Explanation: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9632 answer a"


Question: a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?

<gadget id="calculator">4 * 56</gadget>
<output>224</output>

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

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

<gadget id="calculator">224 + 1</gadget>
<output>225</output>

<gadget id="calculator">225 ** (1/2)</gadget>
<output>15</output>

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

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

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

divide(add(const_1, sqrt(add(multiply(const_4, 56), power(negate(const_1), const_2)))), const_2)

Explanation: xc 1 * ( x - 1 ) c 1 = 56 x ^ 2 - x - 56 = 0 ( x - 8 ) ( x + 7 ) = 0 x = 8 , - 7 - 7 ca n ' t possible . hence 8 should be the answer b


Question: a businessman earns $ 26800 in december , thus decreasing his average annual ( january to december ) earnings by $ 1200 . his average annual earnings would be source : cmat preparation

<gadget id="calculator">12 * 1_200</gadget>
<output>14_400</output>

<gadget id="calculator">26_800 + 14_400</gadget>
<output>41_200</output>
<result>41_200</result>

Choices:
A. $ 29000
B. $ 33500
C. $ 40000
D. $ 41000
E. $ 42300

Explanation: ( x - 26,800 ) / 11 - x / 12 = 1,200 x = 480,000 x / 12 = 40,000 answer : c .


Question: a can complete a certain job in 16 days . b is 60 % more efficient than a . in how many days can b complete the same job ?

<gadget id="calculator">16 * 60</gadget>
<output>960</output>

<gadget id="calculator">960 / 100</gadget>
<output>48/5 = around 9.6</output>
<result>48/5 = around 9.6</result>

Choices:
A. 6
B. 6.25
C. 7
D. 7.5
E. 10

Explanation: let , total work unit = 160 units a can finish in 16 days = 160 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 60 / 100 ) * 10 = 16 unit work days in which b will complete the work alone = 160 / 16 = 10 days answer : option e


Question: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 7 % of bananas were rotten . find the percentage of fruits in good condition ?

<gadget id="calculator">600 + 400</gadget>
<output>1_000</output>

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

<gadget id="calculator">600 * (3/20)</gadget>
<output>90</output>

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">400 * (7/100)</gadget>
<output>28</output>

<gadget id="calculator">90 + 28</gadget>
<output>118</output>

<gadget id="calculator">1_000 - 118</gadget>
<output>882</output>

<gadget id="calculator">882 / 1_000</gadget>
<output>441/500 = around 0.882</output>

<gadget id="calculator">(441/500) * 100</gadget>
<output>441/5 = around 88.2</output>
<result>441/5 = around 88.2</result>

Choices:
A. 92.5 %
B. 88.2 %
C. 85.2 %
D. 96.8 %
E. 78.9 %

multiply(divide(subtract(add(600, 400), add(multiply(600, divide(15, const_100)), multiply(400, divide(7, const_100)))), add(600, 400)), const_100)

Explanation: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 7 % of 400 = 28 therefore , total number of rotten fruits = 90 + 28 = 118 therefore number of fruits in good condition = 1000 - 118 = 882 therefore percentage of fruits in good condition = ( 882 / 1000 × 100 ) % = ( 88200 / 1000 ) % = 88.2 % answer : b"


Question: sandy had $ 231 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

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

<gadget id="calculator">231 / (7/10)</gadget>
<output>330</output>
<result>330</result>

Choices:
A. $ 270
B. $ 290
C. $ 310
D. $ 330
E. $ 350

divide(231, divide(subtract(const_100, 30), const_100))

Explanation: "let the money sandy took for shopping be x . 0.7 x = 231 x = 330 the answer is d ."


Question: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 12 pumps work to empty the tank in 1 day ?

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

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

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

Choices:
A. 4
B. 10
C. 11
D. 12
E. 13

Explanation: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 12 pumps then 48 / 12 = 4 hrs . answer : a"


Question: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 70 / kg . how much did a kg of coffee cost in june ?

<gadget id="calculator">20 / 100</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">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(4/5) * (6/5)</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">70 / (24/25)</gadget>
<output>875/12 = around 72.916667</output>
<result>875/12 = around 72.916667</result>

Choices:
A. 70
B. 60
C. 80
D. 100
E. 120

divide(70, multiply(subtract(const_1, divide(20, const_100)), add(divide(20, const_100), const_1)))

Explanation: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 700 gm ) of tea and 1 / 2 kg ( 700 gm ) of coffee ( equal quantities ) = 70 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 70 = > x = 70 thus proved . . . option a ."


Question: a sum of rs . 66000 is divided into 3 parts such that the simple interests accrued on them for 6 , two and 11 years respectively may be equal . find the amount deposited for 11 years .

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

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

Choices:
A. 6500
B. 2000
C. 4500
D. 3000
E. 6000

Explanation: let the amounts be x , y , z in ascending order of value . as the interest rate and interest accrued are same for 2 years 6 years and 11 years i . e . 2 x = 6 y = 11 z = k . l . c . m . of 2 , 611 = 66 so x : y : z : = 33000 : 11000 : 6000 the amount deposited for 11 years = 6000 answer : e


Question: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what percent z of all the people in smithtown are left - handed women ?

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

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

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

<gadget id="calculator">2 * (4/5)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">3 * (4/5)</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">3 - (12/5)</gadget>
<output>3/5 = around 0.6</output>

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

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

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

Choices:
A. 50 %
B. 40 %
C. 25 %
D. 20 %
E. 10 %

multiply(divide(subtract(multiply(2, divide(add(3, 1), add(3, 2))), subtract(3, multiply(3, divide(add(3, 1), add(3, 2))))), add(3, 1)), const_100)

Explanation: looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c


Question: the average age of 20 men in the class is 15.6 years . 5 new men join and the new average becomes 14.56 years . what was the average age of 5 new men ?

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

<gadget id="calculator">25 * 14.56</gadget>
<output>364</output>

<gadget id="calculator">20 * 15.6</gadget>
<output>312</output>

<gadget id="calculator">364 - 312</gadget>
<output>52</output>

<gadget id="calculator">52 / 5</gadget>
<output>52/5 = around 10.4</output>
<result>52/5 = around 10.4</result>

Choices:
A. 15.5
B. 15.4
C. 15.25
D. 10.4
E. 15.6

divide(subtract(multiply(add(20, 5), 14.56), multiply(20, 15.6)), 5)

Explanation: total age of 20 men = 15.6 x 20 = 312 now , total age of 25 men = 364 . total age of five men added later = 364 - 312 = 52 . hence , the total average of five men = 52 / 5 = 10.4 answer : d


Question: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?

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

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

<gadget id="calculator">9 * 16</gadget>
<output>144</output>

<gadget id="calculator">70 + 144</gadget>
<output>214</output>

<gadget id="calculator">225 - 214</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 11 years
B. 17 years
C. 67 years
D. 14 years
E. 12 years

subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16)))

Explanation: "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a"


Question: rob also compared the empire state building and the petronas towers . what is the height difference between the two if the empire state building is 435 m tall and the petronas towers is 458 m tall ?

<gadget id="calculator">458 - 435</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 9
B. 17
C. 23
D. 45
E. 12

Explanation: 458 - 435 = 23 . answer is c .


Question: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">109.9 / (7/100)</gadget>
<output>1_570</output>

<gadget id="calculator">1_000 + 1_570</gadget>
<output>2_570</output>
<result>2_570</result>

Choices:
A. $ 1940
B. $ 2150
C. $ 2360
D. $ 2570
E. $ 2780

Explanation: let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d .


Question: find the area , diameter = 11 m .

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

<gadget id="calculator">pi * ((11/2) ** 2)</gadget>
<output>121*pi/4 = around 95.033178</output>
<result>121*pi/4 = around 95.033178</result>

Choices:
A. 113.00 square meter
B. 95.07 square meter
C. 93.08 square meter
D. 93.24 square meter
E. 113.43 square meter

Explanation: diameter = 11 meter . radius = diameter / 2 . = 11 / 2 . = 5.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 5.5 . area of a circle = 3.14 ã — 5.5 ã — 5.5 . . = 3.14 ã — 30.25 . = 95.07 square meter answer : b


Question: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 4 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 ?

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

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

Choices:
A. 1
B. 2
C. 5
D. 7
E. 20

Explanation: when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 5 , the remainder is 5 . . i . e . , n = 5 y + 4 values of n can be one of { 4 , 9 , 14 , 19 , . . . } combining both the sets we get n = { 4,19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 or 11 x in case of n = 4 p = 7 so for min value of p , we take min value of n . d is the answer .


Question: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12400 after a year ?

<gadget id="calculator">6_300 + 4_200</gadget>
<output>10_500</output>

<gadget id="calculator">10_500 + 10_500</gadget>
<output>21_000</output>

<gadget id="calculator">6_300 / 21_000</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 12_400</gadget>
<output>3_720</output>
<result>3_720</result>

Choices:
A. 3630
B. 2881
C. 3720
D. 9977
E. 2212

Explanation: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12400 = 3720 . answer : c"


Question: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 100 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

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

<gadget id="calculator">100 / 15</gadget>
<output>20/3 = around 6.666667</output>

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

<gadget id="calculator">(20/3) + 10</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">200 / (50/3)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 11.9
C. 16
D. 20
E. 18

Explanation: sol . speed of the first train = [ 100 / 10 ] m / sec = 10 m / sec . speed of the second train = [ 100 / 15 ] m / sec = 6.7 m / sec . relative speed = ( 10 + 6.7 ) = m / sec = 16.7 m / sec . ∴ required time = ( 100 + 100 ) / 16.7 secc = 11.9 sec . answer b


Question: if 40 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?

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

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

<gadget id="calculator">20 / 60</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. 50.5 %
B. 44.4 %
C. 22.2 %
D. 33.3 %
E. 25 %

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

Explanation: "40 % of ( x - y ) = 20 % of ( x + y ) 40 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 3 y required percentage = y / x * 100 = y / 3 y * 100 = 33.3 % answer is d"


Question: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 170 m . then , a wins by :

<gadget id="calculator">500 - 170</gadget>
<output>330</output>

<gadget id="calculator">330 * 4</gadget>
<output>1_320</output>

<gadget id="calculator">1_320 / 3</gadget>
<output>440</output>

<gadget id="calculator">500 - 440</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 60 m
B. 20 m
C. 43 m
D. 20 m
E. 23 m

subtract(500, divide(multiply(subtract(500, 170), 4), 3))

Explanation: "to reach the winning post a will have to cover a distance of ( 500 - 170 ) m , i . e . , 330 m . while a covers 3 m , b covers 4 m . while a covers 330 m , b covers 4 x 330 / 3 m = 440 m . thus , when a reaches the winning post , b covers 440 m and therefore remains 60 m behind . a wins by 60 m . answer : a"


Question: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a red king ?

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

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

<gadget id="calculator">13 / 52</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">2 / 52</gadget>
<output>1/26 = around 0.038462</output>

<gadget id="calculator">(1/4) * (1/26)</gadget>
<output>1/104 = around 0.009615</output>
<result>1/104 = around 0.009615</result>

Choices:
A. 1 / 13
B. 1 / 15
C. 1 / 26
D. 1 / 52
E. 1 / 104

multiply(divide(add(multiply(const_3, const_4), const_1), const_52), divide(const_2, const_52))

Explanation: p ( club ) = 1 / 4 p ( red king ) = 1 / 26 p ( club then a red king ) = 1 / 4 * 1 / 26 = 1 / 104 the answer is e .


Question: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many cubes are painted on only 2 faces ?

<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">4 * 3</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 8
C. 6
D. 10
E. 16

multiply(const_4, power(27, divide(const_1, const_3)))

Explanation: the mini - cubes with 2 painted sides are all on the edge of the cube , in the ` ` middle ' ' of the edge . there are 4 in front , 4 in back and 4 more on the ` ` strip ' ' that runs around the left / top / right / bottom of the cube . 4 + 4 + 4 = 12 . answer a


Question: a man can do a piece of work in 6 days , but with the help of his son he can do it in 3 days . in what time can the son do it alone ?

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

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

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

Choices:
A. 7 days
B. 6 days
C. 5 days
D. 4 days
E. none of these

Explanation: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 3 − 1 / 6 ) = ( 6 − 3 ) / 18 = 1 / 6 so son will do whole work in 6 days answer : b"


Question: if 3 < x < 6 < y < 9 , then what is the greatest possible positive integer difference of x and y ?

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

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

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

Explanation: "3 < x < 6 < y < 9 ; 3 < x y < 9 3 + y < x + 9 y - x < 6 . positive integer difference is 5 ( for example y = 8.5 and x = 3.5 ) answer : c ."


Question: if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 150 % of j ?

<gadget id="calculator">125 * 150</gadget>
<output>18_750</output>

<gadget id="calculator">18_750 * 175</gadget>
<output>3_281_250</output>

<gadget id="calculator">25 * 50</gadget>
<output>1_250</output>

<gadget id="calculator">1_250 * 75</gadget>
<output>93_750</output>

<gadget id="calculator">3_281_250 / 93_750</gadget>
<output>35</output>

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

<gadget id="calculator">700 / 150</gadget>
<output>14/3 = around 4.666667</output>

<gadget id="calculator">(14/3) * 100</gadget>
<output>1_400/3 = around 466.666667</output>
<result>1_400/3 = around 466.666667</result>

Choices:
A. 0.35
B. 466
C. 35
D. 350
E. 3500

multiply(divide(multiply(divide(multiply(multiply(125, 150), 175), multiply(multiply(25, 50), 75)), 20), 150), const_100)

Explanation: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 150 % of 10 is 15 . . . . ( 70 * 100 ) / 15 = 466.66 . . . . ans : b"


Question: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 22 per kg , then his gain percent is

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

<gadget id="calculator">22 * 8</gadget>
<output>176</output>

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

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

<gadget id="calculator">90 + 60</gadget>
<output>150</output>

<gadget id="calculator">176 - 150</gadget>
<output>26</output>

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

<gadget id="calculator">2_600 / 150</gadget>
<output>52/3 = around 17.333333</output>
<result>52/3 = around 17.333333</result>

Choices:
A. 12 %
B. 13 %
C. 14 %
D. 15 %
E. 17 %

divide(multiply(subtract(multiply(22, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

Explanation: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 22 ) = rs . 176 . profit = 176 - 150 = 26 so , profit % = ( 26 / 150 ) * 100 = 17 % option e"


Question: the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , find out the value of x

<gadget id="calculator">20 * 4</gadget>
<output>80</output>

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

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

Choices:
A. 13
B. 14
C. 15
D. 16
E. 17

divide(multiply(20, const_4), add(const_4, const_1))

Explanation: "explanation : let the cost price of one article = rs . 1 cp of x articles = rs . x cp of 20 articles = 20 selling price of x articles = 20 profit = 25 % [ given ] ⇒ ( sp − cp / cp ) = 25 / 100 = 1 / 4 ⇒ ( 20 − x ) / x = 1 / 4 ⇒ 80 − 4 x = x ⇒ 5 x = 80 option d ⇒ x = 805 = 16"


Question: an error 5 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?

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

<gadget id="calculator">105 ** 2</gadget>
<output>11_025</output>

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

<gadget id="calculator">11_025 - 10_000</gadget>
<output>1_025</output>

<gadget id="calculator">1_025 * 100</gadget>
<output>102_500</output>

<gadget id="calculator">102_500 / 10_000</gadget>
<output>41/4 = around 10.25</output>
<result>41/4 = around 10.25</result>

Choices:
A. 4.05 %
B. 4.02 %
C. 4 %
D. 10.28 %
E. 2 %

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

Explanation: "percentage error in calculated area = ( 5 + 5 + ( 5 ã — 5 ) / 100 ) % = 10.25 % answer : d"


Question: a can give b 100 meters start and c 170 meters start in a kilometer race . how much start can b give c in a kilometer race ?

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

<gadget id="calculator">1_000 - 170</gadget>
<output>830</output>

<gadget id="calculator">1_000 * 830</gadget>
<output>830_000</output>

<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>

<gadget id="calculator">830_000 / 900</gadget>
<output>8_300/9 = around 922.222222</output>

<gadget id="calculator">1_000 - (8_300/9)</gadget>
<output>700/9 = around 77.777778</output>
<result>700/9 = around 77.777778</result>

Choices:
A. 11.77 meters
B. 55.77 meters
C. 77.77 meters
D. 113.77 meters
E. none of these

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 170)), subtract(multiply(const_100, const_10), 100)))

Explanation: "explanation : a runs 1000 meters while b runs 900 meters and c runs 830 meters . therefore , b runs 900 meters while c runs 830 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 830 ) / 900 = 922.22 meters thus , b can give c ( 1000 - 922.22 ) = 77.77 meters start answer : c"


Question: company t produces two kinds of stereos : basic and deluxe . of the stereos produced by company t last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?

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

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

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

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

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

<gadget id="calculator">7 / 17</gadget>
<output>7/17 = around 0.411765</output>
<result>7/17 = around 0.411765</result>

Choices:
A. 5 / 17
B. 7 / 17
C. 4 / 17
D. 3 / 17
E. 5

divide(multiply(5, divide(7, 5)), add(multiply(multiply(2, 5), const_1), multiply(5, divide(7, 5))))

Explanation: # of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 7 / 5 = 7 - - > total time for both of them would be 10 + 7 = 17 - - > deluxe / total = 7 / 17 . b


Question: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 45 % ?

<gadget id="calculator">800 * 100</gadget>
<output>80_000</output>

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

<gadget id="calculator">80_000 / 125</gadget>
<output>640</output>

<gadget id="calculator">640 * 45</gadget>
<output>28_800</output>

<gadget id="calculator">28_800 / 100</gadget>
<output>288</output>

<gadget id="calculator">640 - 288</gadget>
<output>352</output>
<result>352</result>

Choices:
A. s . 429
B. s . 352
C. s . 429
D. s . 128
E. s . 419

subtract(divide(multiply(800, const_100), add(25, const_100)), divide(multiply(divide(multiply(800, const_100), add(25, const_100)), 45), const_100))

Explanation: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 45 % = 45 % of 640 = rs . 288 sp = cp - loss = 640 - 288 = rs . 352 answer : b"


Question: at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 5 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?

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

<gadget id="calculator">15 * 30</gadget>
<output>450</output>

<gadget id="calculator">100 - 30</gadget>
<output>70</output>

<gadget id="calculator">70 * 10</gadget>
<output>700</output>

<gadget id="calculator">450 + 700</gadget>
<output>1_150</output>
<result>1_150</result>

Choices:
A. $ 1220
B. $ 1200
C. $ 1300
D. $ 1340
E. $ 1880

add(multiply(add(10, 5), 30), multiply(subtract(100, 30), 10))

Explanation: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 5 ) = $ 200 total revenue : 1000 + 200 = $ 1200 the answer is b ."


Question: pat , kate , and mark charged a total of 126 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?

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

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

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

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

<gadget id="calculator">(4/3) + (1/6)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">126 / (3/2)</gadget>
<output>84</output>

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

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

Choices:
A. 18
B. 36
C. 72
D. 70
E. 108

subtract(divide(126, add(add(1, divide(1, 3)), divide(1, multiply(3, const_2)))), divide(divide(126, add(add(1, divide(1, 3)), divide(1, multiply(3, const_2)))), multiply(3, const_2)))

Explanation: "70 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 126 = > x = 14 28 : 14 : 84 84 - 14 = 70 answer d"


Question: calculate the area of a triangle , if the sides of are 52 cm , 48 cm and 20 cm , what is its area ?

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

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

Choices:
A. 480 cm 2
B. 580 cm 2
C. 380 cm 2
D. 180 cm 2
E. 280 cm 2

Explanation: "the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"


Question: the amount of time that three people worked on a special project was in the ratio of 2 to 4 to 6 . if the project took 144 hours , how many more hours did the hardest working person work than the person who worked the least ?

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

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

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

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

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

<gadget id="calculator">72 - 24</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 47 hours
B. 45 hours
C. 48 hours
D. 49 hours
E. 50 hours

subtract(multiply(divide(144, add(add(2, 4), 6)), 6), multiply(divide(144, add(add(2, 4), 6)), 2))

Explanation: let the persons be a , b , c . hours worked : a = 2 * 144 / 12 = 24 hours b = 4 * 144 / 12 = 48 hours c = 6 * 144 / 12 = 72 hours c is the hardest worker and a worked for the least number of hours . so the difference is 72 - 24 = 48 hours . answer : c


Question: a car is purchased on hire - purchase . the cash price is $ 24 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?

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

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

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

<gadget id="calculator">24_000 * (9/10)</gadget>
<output>21_600</output>

<gadget id="calculator">21_600 / 60</gadget>
<output>360</output>

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

<gadget id="calculator">(3/25) / 12</gadget>
<output>1/100 = around 0.01</output>

<gadget id="calculator">(1/100) * 21_600</gadget>
<output>216</output>

<gadget id="calculator">360 + 216</gadget>
<output>576</output>
<result>576</result>

Choices:
A. $ 503
B. $ 504
C. $ 555
D. $ 576
E. $ 587

add(divide(multiply(multiply(24, const_1000), subtract(const_1, divide(10, const_100))), 60), multiply(divide(divide(12, const_100), 12), multiply(multiply(24, const_1000), subtract(const_1, divide(10, const_100)))))

Explanation: "explanation : cash price = $ 24 000 deposit = 10 % ã — $ 24 000 = $ 2400 loan amount = $ 24000 â ˆ ’ $ 2400 number of payments = 60 = $ 21600 i = p * r * t / 100 i = 12960 total amount = 21600 + 12960 = $ 34560 regular payment = total amount / number of payments = 576 answer : d"


Question: a truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of 33 kms in 45 minutes . what is the ratio of their speed ?

<gadget id="calculator">33 / 45</gadget>
<output>11/15 = around 0.733333</output>

<gadget id="calculator">(11/15) * 1_000</gadget>
<output>2_200/3 = around 733.333333</output>

<gadget id="calculator">550 / (2_200/3)</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>

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

divide(550, multiply(divide(33, 45), const_1000))

Explanation: "explanation : speed of the truck = distance / time = 550 / 1 = 550 meters / minute speed of the train = distance / time = 33 / 45 km / minute = 33000 / 45 meters / minut speed of the truck / speed of the train = 550 / ( 33000 / 45 ) = ( 550 × 45 ) / 33000 = ( 55 × 45 ) / 3300 = ( 11 × 45 ) / 660 = ( 11 × 9 ) / 132 = 9 / 12 = 34 hence , speed of the truck : speed of the train = 3 : 4 answer : option d"


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 380 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">380 * 2</gadget>
<output>760</output>
<result>760</result>

Choices:
A. 237
B. 287
C. 760
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 - 380 ) = 2 + 2 ( extra ) = > 2 x - 760 = x = > x = 760 . answer : c"


Question: in town p , 70 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town p are females ?

<gadget id="calculator">70 - 42</gadget>
<output>28</output>

<gadget id="calculator">28 / 70</gadget>
<output>2/5 = around 0.4</output>

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

Choices:
A. 25 %
B. 30 %
C. 35 %
D. 40 %
E. 45 %

multiply(divide(subtract(70, 42), 70), const_100)

Explanation: "the percent of the population who are employed females is 70 - 42 = 28 % the percent of employed people who are female is 28 % / 70 % = 40 % . the answer is d ."


Question: andy solves problems 74 to 135 inclusive in a math exercise . how many problems does he solve ?

<gadget id="calculator">135 - 74</gadget>
<output>61</output>

<gadget id="calculator">61 + 1</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 53
B. 62
C. 51
D. 50
E. 49

Explanation: "135 - 74 + 1 = 62 ' b ' is the answer"


Question: a number increased by 25 % gives 520 . the number is ?

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

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

<gadget id="calculator">520 / (5/4)</gadget>
<output>416</output>
<result>416</result>

Choices:
A. 216
B. 316
C. 616
D. 516
E. 416

divide(520, add(const_1, divide(25, const_100)))

Explanation: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 25 % = 125 % 125 % - - - - - - - > 520 ( 120 ã — 4.16 = 520 ) 100 % - - - - - - - > 416 ( 100 ã — 4.16 = 416 ) option ' e '"


Question: joe drives 240 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?

<gadget id="calculator">240 + 120</gadget>
<output>360</output>

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

<gadget id="calculator">120 / 40</gadget>
<output>3</output>

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

<gadget id="calculator">360 / 7</gadget>
<output>360/7 = around 51.428571</output>
<result>360/7 = around 51.428571</result>

Choices:
A. 42
B. 51
C. 50
D. 54
E. 56

Explanation: "t 1 = 240 / 60 = 4 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 7 hours avg speed = total distance / t = 360 / 7 = 51 mph = b"


Question: what is the sum of the multiples of 4 between 38 and 127 inclusive ?

<gadget id="calculator">127 - 3</gadget>
<output>124</output>

<gadget id="calculator">38 + 2</gadget>
<output>40</output>

<gadget id="calculator">124 + 40</gadget>
<output>164</output>

<gadget id="calculator">164 / 2</gadget>
<output>82</output>

<gadget id="calculator">124 - 40</gadget>
<output>84</output>

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

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

<gadget id="calculator">82 * 22</gadget>
<output>1_804</output>
<result>1_804</result>

Choices:
A. 1804
B. 1816
C. 1824
D. 1828
E. 1832

multiply(divide(add(subtract(127, const_3), add(38, const_2)), const_2), add(divide(subtract(subtract(127, const_3), add(38, const_2)), 4), const_1))

Explanation: "the fastest way in an ap is to find the average and multiply with total integers . . between 38 and 127 , the smallest multiple of 4 is 40 and largest = 124 . . average = ( 40 + 124 ) / 2 = 164 / 2 = 82 . . total numbers = ( 124 - 40 ) / 4 + 1 = = 84 / 4 + 1 = 27 + 1 = 22 . . sum = 82 * 22 = 1804 ans a"


Question: a train 110 m long is running with a speed of 30 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?

<gadget id="calculator">30 + 6</gadget>
<output>36</output>

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

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

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

Choices:
A. 7 sec
B. 6 sec
C. 8 sec
D. 11 sec
E. 2 sec

divide(110, multiply(add(30, 6), const_0_2778))

Explanation: "speed of train relative to man = 30 + 6 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . time taken to pass the men = 110 / 10 = 11 sec . answer : d"


Question: there are 50 boys in a class . their average weight is 45 kg . when one boy leaves the class , the average reduces by 100 g . find the weight of the boy who left the class .

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

<gadget id="calculator">49 * 100</gadget>
<output>4_900</output>

<gadget id="calculator">4_900 / 1_000</gadget>
<output>49/10 = around 4.9</output>

<gadget id="calculator">45 + (49/10)</gadget>
<output>499/10 = around 49.9</output>
<result>499/10 = around 49.9</result>

Choices:
A. 40.9 kg
B. 42.9 kg
C. 49.9 kg
D. 39.9 kg
E. none of these

add(45, divide(multiply(subtract(50, const_1), 100), const_1000))

Explanation: here one boy is excluded and final average of the group decreases . ∴ change in average is ( – ) ve = – 0.1 kg . using the formula sum of the quantities excluded = ( changein no . ofquantities × origina laverage ) + ( changeinaverage × final no . ofquantities ) ⇒ weight of the boy who left = ( 1 × 45 ) – ( – 0.1 × 49 ) = 49.9 kg answer c


Question: if w / x = 1 / 3 and w / y = 4 / 15 , then ( x + y ) / y =

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

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

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

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

Choices:
A. 4 / 5
B. 6 / 5
C. 7 / 5
D. 8 / 5
E. 9 / 5

add(divide(divide(4, 1), divide(15, 3)), const_1)

Explanation: "w / x = 1 / 3 = > x = 3 w and w / y = 4 / 15 = > y = 15 / 4 w ( x + y ) / y = ( 3 w + 15 / 4 w ) / ( 15 / 4 w ) = ( 27 / 4 w ) / ( 15 / 4 w ) = 9 / 5 correct option : e"


Question: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 52 people bought tickets to the concert , what was the total revenue from ticket sales ?

<gadget id="calculator">52 - 20</gadget>
<output>32</output>

<gadget id="calculator">32 - 10</gadget>
<output>22</output>

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

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

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

<gadget id="calculator">22 + 6</gadget>
<output>28</output>

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

<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">(17/20) * 20</gadget>
<output>17</output>

<gadget id="calculator">28 + 17</gadget>
<output>45</output>

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

Choices:
A. $ 600
B. $ 740
C. $ 850
D. $ 900
E. $ 1,140

multiply(add(add(subtract(subtract(52, 20), 10), multiply(subtract(const_1, divide(40, const_100)), 10)), multiply(subtract(const_1, divide(15, const_100)), 20)), 20)

Explanation: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 22 tickets = 20 * 22 = 440 revenue generated from sales of 52 tickets = 120 + 340 + 440 = 900 $ answer d"


Question: a university cafeteria offers 6 flavors of pizza - pork , gobi - manjurian , pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?

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

Choices:
A. 4
B. 8
C. 12
D. 36
E. 32

Explanation: 6 flavours * 6 choices = 6 c 1 * 6 c 1 = 6 * 6 = 36 = d


Question: in a zoo , the ratio of the number of cheetahs to the number 4 then what is the increase in the number of pandas ?

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

<gadget id="calculator">16 - 4</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 2
B. 12
C. 5
D. 10
E. 15

Explanation: one short cut to solve the problem is c : p = 1 : 3 c increased to 5 = > 1 : 3 = 5 : x = > x = 15 = > p increased by 12 b is the answer


Question: a train 250 m long running at 72 kmph crosses a platform in 50 sec . what is the length of the platform ?

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

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

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

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

Choices:
A. 150 m
B. 200 m
C. 250 m
D. 750 m
E. 300 m

subtract(multiply(50, multiply(72, const_0_2778)), 250)

Explanation: "d = 72 * 5 / 18 = 50 = 1000 â € “ 250 = 750 m answer : d"


Question: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 12 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .

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

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

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

<gadget id="calculator">9 + 12</gadget>
<output>21</output>

<gadget id="calculator">36 / 21</gadget>
<output>12/7 = around 1.714286</output>
<result>12/7 = around 1.714286</result>

Choices:
A. 12 / 7
B. 4 / 1
C. 2 / 3
D. 3 / 4
E. 3 / 2

divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 12))

Explanation: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 12 ) = 36 / 21 = 12 / 7 . answer : a ."


Question: in 1979 approximately 1 / 3 of the 32.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?

<gadget id="calculator">32.3 / 3</gadget>
<output>10.766667</output>

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

<gadget id="calculator">10.766667 / 8</gadget>
<output>1.345833</output>
<result>1.345833</result>

Choices:
A. 18.6
B. 9.3
C. 6.2
D. 1.33
E. 1.6

Explanation: "number of passengers using kennedy airport = 32 / 3 = ~ 10.67 passengers using miami airport = 10.67 / 2 = ~ 5.34 passengers using logan airport = 5.34 / 4 = ~ 1.33 so d"


Question: what is the greater of the two numbers whose product is 2496 , given that the sum of the two numbers exceeds their difference by 64 ?

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

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

<gadget id="calculator">2_496 / 32</gadget>
<output>78</output>
<result>78</result>

Choices:
A. 96
B. 108
C. 110
D. 78
E. of these

divide(2496, multiply(power(const_2, const_4), const_2))

Explanation: "let the greater and the smaller number be g and s respectively . gs = 2496 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2496 / s = 78 . answer : d"


Question: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 125 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?

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

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

<gadget id="calculator">125 / (2/5)</gadget>
<output>625/2 = around 312.5</output>

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

<gadget id="calculator">(625/2) / (3/4)</gadget>
<output>1_250/3 = around 416.666667</output>

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

<gadget id="calculator">(1_250/3) / (2/3)</gadget>
<output>625</output>
<result>625</result>

Choices:
A. 280
B. 400
C. 540
D. 625
E. 840

divide(divide(divide(125, subtract(const_1, divide(3, 5))), divide(3, 4)), divide(const_2, const_3))

Explanation: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 120 geese survived the first year : 1 / 5 * ( total ) = 125 - - > ( total ) = 625 . answer : d .


Question: the average salary per month of 55 employees in a company is rs 8500 . if the managers salary is added , the average salary increases to rs 8800 , what is the salary of the manager ?

<gadget id="calculator">55 + 1</gadget>
<output>56</output>

<gadget id="calculator">56 * 8_800</gadget>
<output>492_800</output>

<gadget id="calculator">55 * 8_500</gadget>
<output>467_500</output>

<gadget id="calculator">492_800 - 467_500</gadget>
<output>25_300</output>
<result>25_300</result>

Choices:
A. 10000
B. 12000
C. 23000
D. 25300
E. 45000

subtract(multiply(add(55, const_1), 8800), multiply(55, 8500))

Explanation: explanation : salary of the manager = ( 56 * 8800 - 55 * 8500 ) = 25300 answer : d


Question: there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches were planted ?

<gadget id="calculator">3 * 24</gadget>
<output>72</output>

<gadget id="calculator">72 - 24</gadget>
<output>48</output>

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

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

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

Choices:
A. 2
B. 5
C. 8
D. 6
E. 4

divide(subtract(multiply(3, 24), 24), subtract(multiply(3, 3), 1))

Explanation: "let x be the number of roses . then the number of birches is 24 − x , and the number of boys is 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 216 − 72 = 8 x 1448 = x 1 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . correct answer is d ) 6"


Question: in a simultaneous throw of pair of dice . find the probability of getting the total more than 7

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

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

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

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

<gadget id="calculator">15 / 36</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>

Choices:
A. 5 / 7
B. 4 / 7
C. 5 / 12
D. 4 / 7
E. 1 / 6

divide(add(add(7, const_4), const_4), multiply(add(const_4, const_2), add(const_4, const_2)))

Explanation: here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option c


Question: a green grocer received a boxful of tomatoes and on opening the box found that several had gone bad . he then counted them up so that he could make a formal complaint and found that 68 were mouldy , which was 16 per cent of the total contents of the box . how many tomatoes were in the box ?

<gadget id="calculator">68 * 4</gadget>
<output>272</output>

<gadget id="calculator">272 * 2</gadget>
<output>544</output>

<gadget id="calculator">544 - 100</gadget>
<output>444</output>
<result>444</result>

Choices:
A. 336
B. 425
C. 275
D. 235
E. 689

subtract(multiply(multiply(68, const_4), const_2), const_100)

Explanation: b 425 ( 68 ã · 16 ) ã — 100


Question: how many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples ?

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

Choices:
A. 9
B. 5
C. 7
D. 10
E. none of the above

Explanation: sol . apples 250 each carries 25 = 250 / 25 = 10 answer : d


Question: how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 15 km / hr ?

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

<gadget id="calculator">15 * (5/18)</gadget>
<output>25/6 = around 4.166667</output>

<gadget id="calculator">600 / (25/6)</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 128
B. 136
C. 144
D. 152
E. 160

Explanation: "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 600 / ( 25 / 6 ) = 144 seconds the answer is c ."


Question: if shares of two persons in profits are rs . 600 and rs . 300 then ratio of their capitals is

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

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

Explanation: "total profit = 1000 ratio = 600 / 300 = 2 : 1 answer : e"


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

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

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

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

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

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

Choices:
A. 36.5
B. 35
C. 34
D. 33
E. 32.5

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

Explanation: "correct sum = ( 36 * 50 + 48 - 23 ) = 1825 . correct mean = 1825 / 50 = 36.5 answer a"


Question: a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 500 each from people already solicited . people already solicited represent 50 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?

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

<gadget id="calculator">(1/2) * 500</gadget>
<output>250</output>

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

<gadget id="calculator">250 / (3/5)</gadget>
<output>1_250/3 = around 416.666667</output>

<gadget id="calculator">(1_250/3) * (1/2)</gadget>
<output>625/3 = around 208.333333</output>

<gadget id="calculator">(625/3) / (3/5)</gadget>
<output>3_125/9 = around 347.222222</output>
<result>3_125/9 = around 347.222222</result>

Choices:
A. $ 200
B. $ 333.33
C. $ 100.25
D. $ 277.78
E. $ 377.00

divide(multiply(divide(multiply(divide(50, const_100), 500), divide(60, const_100)), divide(50, const_100)), divide(60, const_100))

Explanation: "let us suppose there are 100 people . 50 % of them donated $ 25000 ( 500 * 50 ) $ 25000 is 60 % of total amount . so total amount = 25000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 25000 * ( 100 / 60 ) * ( 40 / 100 ) = 50000 / 3 this amount has to be divided by 50 ( remaining people are 50 ) so per head amount is 50000 / 3 / 50 = 32000 / 180 = 333.33 ; answer : b"


Question: a certain bacteria colony doubles in size every day for 19 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?

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

<gadget id="calculator">19 - 1</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 6.33
B. 7.5
C. 10
D. 18
E. 19

Explanation: "if there is one bacteria colony , then it will reach the limit of its habitat in 20 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 18 times . answer : d . similar questions to practice : hope it helps ."


Question: the diameter of a circle is 4 / π . find the circumference of the circle .

<gadget id="calculator">4 / pi</gadget>
<output>4/pi = around 1.27324</output>

<gadget id="calculator">2 * pi * (4/pi)</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 8
B. 4 π
C. 4
D. 6
E. 5

Explanation: circumference = 2 * pi * r = 2 * pi * 4 / pi = > 8 a


Question: simplify : 0.3 * 0.3 + 0.3 * 0.3

<gadget id="calculator">0.3 * 0.3</gadget>
<output>0.09</output>

<gadget id="calculator">0.09 + 0.09</gadget>
<output>0.18</output>
<result>0.18</result>

Choices:
A. 0.52
B. 0.42
C. 0.18
D. 0.64
E. 0.46

Explanation: "given exp . = 0.3 * 0.3 + ( 0.3 * 0.3 ) = 0.09 + 0.09 = 0.18 answer is c ."


Question: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x - 4 ) ( x + 9 ) ( 2 x + 5 ) = 0 ?

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

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

Choices:
A. 1 / 12
B. 1 / 6
C. 1 / 4
D. 1 / 3
E. 1 / 2

Explanation: x = - 2.5 prob = 1 / 12 answer - a


Question: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 300 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?

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

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

<gadget id="calculator">9_000 / 1_000</gadget>
<output>9</output>

<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">9 / (3/2)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 1
B. 2
C. 4
D. 6
E. 8

divide(divide(multiply(300, multiply(15, const_2)), const_1000), divide(15, const_10))

Explanation: "the distance between the nest and the ditch is 300 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 300 = 9000 . d = st 9000 / 1.5 = t , i think we can take 9000 meters as 9 km , then only we get t = 6 . ( 1000 meters = 1 km ) d )"


Question: if 30 % of a class averages 95 % on a test , 50 % of the class averages 79 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .

<gadget id="calculator">30 * 95</gadget>
<output>2_850</output>

<gadget id="calculator">50 * 79</gadget>
<output>3_950</output>

<gadget id="calculator">2_850 + 3_950</gadget>
<output>6_800</output>

<gadget id="calculator">30 + 50</gadget>
<output>80</output>

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

<gadget id="calculator">20 * 60</gadget>
<output>1_200</output>

<gadget id="calculator">6_800 + 1_200</gadget>
<output>8_000</output>

<gadget id="calculator">8_000 / 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 76 %
B. 77 %
C. 78 %
D. 79 %
E. 80 %

divide(add(add(multiply(30, 95), multiply(50, 79)), multiply(subtract(const_100, add(30, 50)), 60)), const_100)

Explanation: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 30 % - 50 % = 20 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.30 x 95 + 0.50 x 79 + 0.20 x 60 = 80 the class average ( rounded ) is 80 % final answer e ) 80 %"


Question: if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ?

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

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

Explanation: if the tens digit of positive integers m , y are 6 , how many values of the tens digit of 2 ( m + y ) can be there ? a . 2 b . 3 c . 4 d . 5 e . 6 - > if m = y = 60 , 2 ( m + y ) = 240 is derived . if m = y = 69 , 2 ( m + y ) = 276 is derived , which makes 4,5 , 6,7 possible for the tens digit . therefore , the answer is c .


Question: the maximum number of students among them 848 pens and 630 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?

<gadget id="calculator">gcd(848, 630)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 10
B. 4
C. 2
D. 14
E. 16

Explanation: "number of pens = 848 number of pencils = 630 required number of students = h . c . f . of 848 and 630 = 2 answer is c"


Question: find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1 : 2 ?

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

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

Explanation: 1 : 2 answer : a


Question: the captain of a cricket team of 11 members is 29 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?

<gadget id="calculator">29 + 3</gadget>
<output>32</output>

<gadget id="calculator">29 + 32</gadget>
<output>61</output>

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

<gadget id="calculator">61 - 9</gadget>
<output>52</output>

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

Choices:
A. 20 years
B. 21 years
C. 22 years
D. 23 years
E. 26 years

divide(subtract(add(29, add(29, 3)), multiply(3, 3)), const_2)

Explanation: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 29 + 32 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer e"


Question: if the sides of a triangle are 31 cm , 29 cm and 15 cm , what is its area ?

<gadget id="calculator">29 * 15</gadget>
<output>435</output>

<gadget id="calculator">435 / 2</gadget>
<output>435/2 = around 217.5</output>
<result>435/2 = around 217.5</result>

Choices:
A. 220.75 cm 2
B. 258 cm 2
C. 225.50 cm 2
D. 222.25 cm 2
E. 217.5 cm 2

Explanation: "the triangle with sides 31 cm , 29 cm and 15 cm is right angled , where the hypotenuse is 31 cm . area of the triangle = 1 / 2 * 29 * 15 = 217.5 cm 2 answer : e"


Question: in what ratio should a variety of rice costing rs . 6.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?

<gadget id="calculator">8.75 - 7.5</gadget>
<output>1.25</output>

<gadget id="calculator">8.75 - 6.5</gadget>
<output>2.25</output>

<gadget id="calculator">1.25 / 2.25</gadget>
<output>0.555556</output>

<gadget id="calculator">1 - 0.555556</gadget>
<output>0.444444</output>

<gadget id="calculator">0.555556 / 0.444444</gadget>
<output>1.250002</output>
<result>1.250002</result>

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

divide(divide(subtract(8.75, 7.50), subtract(8.75, 6.5)), subtract(const_1, divide(subtract(8.75, 7.50), subtract(8.75, 6.5))))

Explanation: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 6.5 ) = 5 / 4 answer : c"


Question: a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is

<gadget id="calculator">7 + 8</gadget>
<output>15</output>

<gadget id="calculator">8 / 15</gadget>
<output>8/15 = around 0.533333</output>

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

<gadget id="calculator">15 - 1</gadget>
<output>14</output>

<gadget id="calculator">7 / 14</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(8/15) * (1/2)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>

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

<gadget id="calculator">6 / 14</gadget>
<output>3/7 = around 0.428571</output>

<gadget id="calculator">(7/15) * (3/7)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(4/15) + (1/5)</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>

Choices:
A. 7 / 16
B. 7 / 12
C. 7 / 19
D. 7 / 12
E. 7 / 15

add(multiply(divide(8, add(7, 8)), divide(subtract(8, const_1), subtract(add(7, 8), const_1))), multiply(divide(7, add(7, 8)), divide(subtract(7, const_1), subtract(add(7, 8), const_1))))

Explanation: "drawing two balls of same color from seven green balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = ⁷ c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 7 / 15 answer : e"


Question: the average monthly salary of 20 employees in an organisation is rs . 1400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?

<gadget id="calculator">1_400 + 100</gadget>
<output>1_500</output>

<gadget id="calculator">20 + 1</gadget>
<output>21</output>

<gadget id="calculator">1_500 * 21</gadget>
<output>31_500</output>

<gadget id="calculator">1_400 * 20</gadget>
<output>28_000</output>

<gadget id="calculator">31_500 - 28_000</gadget>
<output>3_500</output>
<result>3_500</result>

Choices:
A. 3600
B. 3890
C. 88798
D. 2789
E. 3500

subtract(multiply(add(1400, 100), add(20, const_1)), multiply(1400, 20))

Explanation: "explanation : manager ' s monthly salary rs . ( 1500 * 21 - 1400 * 20 ) = rs . 3500 . answer : e"


Question: a train 400 m long can cross an electric pole in 10 sec and then find the speed of the train ?

<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">10 / 3_600</gadget>
<output>1/360 = around 0.002778</output>

<gadget id="calculator">(2/5) / (1/360)</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 165 kmph
B. 144 kmph
C. 172 kmph
D. 175 kmph
E. 178 kmph

divide(divide(400, const_1000), divide(10, const_3600))

Explanation: "length = speed * time speed = l / t s = 400 / 10 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : b"


Question: a man can row his boat with the stream at 30 km / h and against the stream in 14 km / h . the man ' s rate is ?

<gadget id="calculator">30 - 14</gadget>
<output>16</output>

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

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

Explanation: "ds = 30 us = 14 s = ? s = ( 30 - 14 ) / 2 = 8 kmph answer : e"


Question: 3 men and 7 women can complete a work in 10 days . but 4 men and 6 women need 8 days to complete the same work . in how many days will 10 women complete the same work ?

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

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

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

<gadget id="calculator">(7/6) * (1/8)</gadget>
<output>7/48 = around 0.145833</output>

<gadget id="calculator">(1/10) - (7/48)</gadget>
<output>-11/240 = around -0.045833</output>

<gadget id="calculator">4 * (7/6)</gadget>
<output>14/3 = around 4.666667</output>

<gadget id="calculator">3 - (14/3)</gadget>
<output>-5/3 = around -1.666667</output>

<gadget id="calculator">(-11/240) / (-5/3)</gadget>
<output>11/400 = around 0.0275</output>

<gadget id="calculator">4 * (11/400)</gadget>
<output>11/100 = around 0.11</output>

<gadget id="calculator">(1/8) - (11/100)</gadget>
<output>3/200 = around 0.015</output>

<gadget id="calculator">(3/200) / 6</gadget>
<output>1/400 = around 0.0025</output>

<gadget id="calculator">(1/400) * 10</gadget>
<output>1/40 = around 0.025</output>

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

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

inverse(multiply(divide(subtract(divide(const_1, 8), multiply(4, divide(subtract(divide(const_1, 10), multiply(divide(7, 6), divide(const_1, 8))), subtract(3, multiply(4, divide(7, 6)))))), 6), 10))

Explanation: explanation : work done by 4 men and 6 women in 1 day = 1 / 8 work done by 3 men and 7 women in 1 day = 1 / 10 let 1 man does m work in 1 day and 1 woman does w work in 1 day . the above equations can be written as 4 m + 6 w = 1 / 8 - - - ( 1 ) 3 m + 7 w = 1 / 10 - - - ( 2 ) solving equation ( 1 ) and ( 2 ) , we get m = 11 / 400 and w = 1 / 400 amount of work 10 women can do in a day = 10 × ( 1 / 400 ) = 1 / 40 ie , 10 women can complete the work in 40 days answer : option b


Question: what is the characteristic of the logarithm of 0.0000134 ?

<gadget id="calculator">log(0.000013)</gadget>
<output>-11.250561</output>

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

<gadget id="calculator">(-11.250561) / log(10)</gadget>
<output>-11.250561/log(10) = around -4.886057</output>

<gadget id="calculator">floor(-11.250561/log(10))</gadget>
<output>-5</output>
<result>-5</result>

Choices:
A. 5
B. - 5
C. 6
D. - 6
E. 7

Explanation: log ( 0.0000134 ) . since there are four zeros between the decimal point and the first significant digit , the characteristic is – 5 . answer : b


Question: in the game of dubblefud , red chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection doubles the number of green chips , how many red chips are in the selection ?

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

<gadget id="calculator">2 ** 3</gadget>
<output>8</output>

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

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

<gadget id="calculator">128 * 125</gadget>
<output>16_000</output>

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

<gadget id="calculator">2 ** 6</gadget>
<output>64</output>

<gadget id="calculator">64 * 125</gadget>
<output>8_000</output>

<gadget id="calculator">16_000 / 8_000</gadget>
<output>2</output>
<result>2</result>

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

divide(multiply(multiply(power(2, 4), power(2, const_3)), power(5, const_3)), multiply(power(const_2, multiply(2, const_3)), power(5, const_3)))

Explanation: this is equivalent to : - 2 x * 4 y * 5 z = 16000 y / 2 = z ( given ) 2 x * 4 y * 5 y / 2 = 16000 2 x * y ^ 2 = 16000 / 10 2 x * y ^ 2 = 1600 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 2 as 2 * 2 * y ^ 2 = 1600 y ^ 2 = 400 y = 20 number of red chips = 2 hence b


Question: compound interest of rs . 2000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .

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

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

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

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

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

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

<gadget id="calculator">(21/20) ** 3</gadget>
<output>9_261/8_000 = around 1.157625</output>

<gadget id="calculator">2_000 * (9_261/8_000)</gadget>
<output>9_261/4 = around 2_315.25</output>

<gadget id="calculator">(9_261/4) - 2_000</gadget>
<output>1_261/4 = around 315.25</output>
<result>1_261/4 = around 315.25</result>

Choices:
A. rs . 473
B. rs . 374
C. rs . 495
D. rs . 315
E. none of the above

subtract(multiply(2000, power(add(1, divide(divide(10, 2), const_100)), multiply(add(1, divide(1, 2)), 2))), 2000)

Explanation: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 2000 [ 1 + ( 5 / 100 ) ] ^ 3 - 2000 = 2000 [ ( 21 / 20 ) ^ 3 - 1 ] = 2000 ( 9261 - 8000 ) / 8000 = 2 * 1261 / 8 = 315 answer : d"


Question: on average , the boys in the class have 20 pencils and the girls have 38 pencils . if the overall class average is 30 pencils , what is the ratio of boys to girls in the class ?

<gadget id="calculator">30 / 38</gadget>
<output>15/19 = around 0.789474</output>
<result>15/19 = around 0.789474</result>

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

Explanation: ( 38 g + 20 b ) / ( g + b ) = 30 38 g + 20 b = 30 ( g + b ) 8 g = 10 b b / g = 4 / 5 the answer is d .


Question: in a certain village , 200 litres of water are required per household per month . at this rate , if there are 5 households in the village , how long ( in months ) will 2000 litres of water last ?

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

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

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

Explanation: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 200 litres of water are required per household per month . at this rate , if there aren 5 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 200 * 5 = 1000 ( m * n ) water available is 2000 ( p ) it will last 2 months ( p / m * n ) ans : d"


Question: rs . 925 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 925 become in 3 years ?

<gadget id="calculator">956 - 925</gadget>
<output>31</output>

<gadget id="calculator">31 * 100</gadget>
<output>3_100</output>

<gadget id="calculator">925 * 3</gadget>
<output>2_775</output>

<gadget id="calculator">3_100 / 2_775</gadget>
<output>124/111 = around 1.117117</output>

<gadget id="calculator">(124/111) + 4</gadget>
<output>568/111 = around 5.117117</output>

<gadget id="calculator">925 * (568/111)</gadget>
<output>14_200/3 = around 4_733.333333</output>

<gadget id="calculator">(14_200/3) * 3</gadget>
<output>14_200</output>

<gadget id="calculator">14_200 / 100</gadget>
<output>142</output>

<gadget id="calculator">925 + 142</gadget>
<output>1_067</output>
<result>1_067</result>

Choices:
A. rs . 1020.80
B. rs . 1025
C. rs . 1067
D. data inadequate
E. none of these

add(925, divide(multiply(multiply(925, add(divide(multiply(subtract(956, 925), const_100), multiply(925, 3)), 4)), 3), const_100))

Explanation: "solution s . i . = rs . ( 956 - 925 ) = rs . 31 rate = ( 100 x 31 / 925 x 3 ) = 124 / 111 % new rate = ( 124 / 111 + 4 ) % = 568 / 111 % new s . i . = rs . ( 925 x 568 / 111 x 3 / 100 ) rs . 142 ∴ new amount = rs . ( 925 + 142 ) = rs . 1067 . answer c"


Question: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?

<gadget id="calculator">7 * 12</gadget>
<output>84</output>

<gadget id="calculator">84 * 3</gadget>
<output>252</output>

<gadget id="calculator">252 / 7</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 21
B. 35
C. 36
D. 60
E. 65

Explanation: "the total number of the people in the room must be a multiple of both 7 and 12 ( in order 3 / 7 and 5 / 12 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 12 , which is 84 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 84 people in the room . therefore there are 3 / 7 * 84 = 36 people in the room under the age of 21 . answer : c ."


Question: if the average of r , b , c , 14 and 15 is 12 . what is the average value of r , b , c and 29

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

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

<gadget id="calculator">14 + 15</gadget>
<output>29</output>

<gadget id="calculator">60 - 29</gadget>
<output>31</output>

<gadget id="calculator">31 + 29</gadget>
<output>60</output>

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

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

divide(add(subtract(multiply(add(const_4, const_1), 12), add(14, 15)), 29), const_4)

Explanation: r + b + c + 14 + 15 = 12 * 5 = 60 = > r + b + c = 60 - 29 = 31 r + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d


Question: if 15 % of a is the same as 30 % of b , then a : b is :

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

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

<gadget id="calculator">(3/10) / (3/20)</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 1 : 4
B. 4 : 3
C. 6 : 7
D. 3 : 5
E. 2 : 1

divide(divide(30, const_100), divide(15, const_100))

Explanation: expl : 15 % of a i = 30 % of b = 15 a / 100 = 30 b / 100 = 2 / 1 = 2 : 1 answer : e