Cheukting/mathqa huggingface dataset:
Question (physics): john and steve are speed walkers in a race . john is 10 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 24 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 10 + 2 - - - > 0.5 t = 12 - - - > t = 24 seconds . c is the correct answer ."
Answer: c
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 171 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1425 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 171 . ∴ x 16 x 9 / 12 x 1 / 100 } = 171 or x = 1425 . ∴ p . w . = rs . 1425 . answer c"
Answer: c
Question (general): suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 540 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 720 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 15 , e ) 16
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 540 . . . eq 1 8 x + 32 y = 720 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1080 8 x = 720 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 720 . . . then we get 32 y = 640 then y = 20 differenece between x and y is 10 answer : c"
Answer: c
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45
b ) 50
c ) 55
d ) 60
e ) 63
Rationale: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a
Answer: a
Question (physics): sum of two numbers prime to each other is 12 and their l . c . m . is 35 . what are the numbers ?
Options: a ) 8 and 4 , b ) 7 and 5 , c ) 6 and 5 , d ) 8 and 5 , e ) 6 and 5
Rationale: "as two numbers are prime , only options satisfy ie option b and c and d , e but option a will not make the product of numbers i . e 35 answer : b"
Answer: b
Question (general): two employees x and y are paid a total of rs . 440 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 440 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 440 â ‡ ’ y [ 12 / 10 + 1 ] = 440 â ‡ ’ 22 y / 10 = 440 â ‡ ’ 22 y = 4400 â ‡ ’ y = 4400 / 22 = 400 / 2 = rs . 200 b )"
Answer: b
Question (general): how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 4 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.25 * 8 = 0.2 ( x + 8 ) - - > x = 4 . answer : a ."
Answer: a
Question (general): a envelop weight 8.5 gm , if 820 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.97 kg , e ) 7.8 kg
Rationale: "820 * 8.5 6970.0 gm 6.97 kg answer : d"
Answer: d
Question (geometry): the area of a rectangular field is equal to 500 square meters . its perimeter is equal to 90 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 500 : area , l is the length and w is the width . 2 l + 2 w = 90 : perimeter l = 45 - w : solve for l ( 45 - w ) * w = 500 : substitute in the area equation w = 20 and l = 25 correct answer d"
Answer: d
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 11.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 165 ° , e ) 95 °
Rationale: angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 11 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 11 − 30 / 5 ) + 30 / 2 = 30 ( 11 − 6 ) + 15 = 30 × 5 + 15 = 165 ° answer is d .
Answer: d
Question (general): there are 16 bees in the hive , then 6 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 22 , d ) 17 , e ) 25
Rationale: 16 + 6 = 22 . answer is c .
Answer: c
Question (physics): a train moves with a speed of 108 kmph . its speed in metres per second is :
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 38.8 , e ) none of these
Rationale: "explanation : 108 kmph = ( 108 x 5 / 18 ) m / sec = 30 m / s . answer : c"
Answer: c
Question (gain): 20 is subtracted from 60 % of a number , the result is 88 . find the number ?
Options: a ) 120 , b ) 300 , c ) 180 , d ) 170 , e ) 148
Rationale: "( 60 / 100 ) * x â € “ 20 = 88 6 x = 1080 x = 180 answer : c"
Answer: c
Question (gain): by how much is 50 % of 250 greater than 25 % of 400 .
Options: a ) 25 , b ) 26 , c ) 29 , d ) 39 , e ) 26
Rationale: "( 50 / 100 ) * 250 â € “ ( 25 / 100 ) * 400 125 - 100 = 25 answer : b"
Answer: b
Question (other): find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these
Rationale: solution required ratio = 60 : 90 = 2 : 3 answer b
Answer: b
Question (general): in a rectangular coordinate system , if a line passes through the points ( - 15 , - 18 ) , ( 1522 ) and ( x , 2 ) then what is the value of x ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: the slope of the line m is rise / run = 22 - ( - 18 ) / 15 - ( - 15 ) = 4 / 3 4 / 3 = 22 - 2 / 15 - x 60 - 4 x = 66 - 6 x = 0 the answer is c .
Answer: c
Question (physics): the sector of a circle has radius of 21 cm and central angle 108 o . find its perimeter ?
Options: a ) 81.6 cm , b ) 85.9 cm , c ) 90 cm , d ) 92 cm , e ) 95 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 108 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 39.6 + 42 = 81.6 cm answer : a"
Answer: a
Question (gain): a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 35 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water 70 l syrup . to make 35 % syrup solution , the result solution must have 97.5 l syrup and 52.5 l syrup . therefore we are taking 17.5 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 17.5 l syrup in 37.5 l solution we started by multiplying 10 now to get to the result we need to divide by 17.5 = > amount of solution to be replaced with water ( 37.5 / 17.5 ) = 2.14 . correct option : c"
Answer: c
Question (gain): running at the same constant rate , 100 identical machines can produce a total of 500 coffee bar per minute . at this rate , how many bottles could 20 such machines produce in 2 minutes ?
Options: a ) 110 , b ) 220 , c ) 330 , d ) 200 , e ) 789
Rationale: let ' s take the approach that uses the answer choices to eliminate wasted time . 500 / 100 = 5 coffee bar per minute per machine . 20 machines = 100 per minute . 2 minutes worth = 200 coffe bar . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d .
Answer: d
Question (other): a certain fraction has the same ratio to 1 / 36 , as 4 / 5 does to 2 / 9 . what is this certain fraction ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25
Rationale: "x / ( 1 / 36 ) = ( 4 / 5 ) / ( 2 / 9 ) x = 4 * 9 * 1 / 36 * 5 * 2 = 1 / 10 the answer is b ."
Answer: b
Question (general): what is the units digit of ( 5 ! * 5 ! + 6 ! * 5 ! ) / 3 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "( 5 ! * 5 ! + 6 ! * 5 ! ) / 3 = 5 ! ( 5 ! + 6 ! ) / 3 = 120 ( 120 + 720 ) / 3 = ( 120 * 840 ) / 3 = 120 * 280 units digit of the above product will be equal to 0 answer e"
Answer: e
Question (general): find the constant k so that : - x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 14 , d ) 19 , e ) 15
Rationale: "- x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 8 ) x - 8 = - x 2 + 6 x - 8 - ( k + 8 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 14 : solve the above for k correct answer c"
Answer: c
Question (gain): a , b and c invested rs . 6000 , rs . 4000 and rs . 10000 respectively , in a partnership business . find the share of a in profit of rs . 11000 after a year ?
Options: a ) 3300 , b ) 1100 , c ) 2667 , d ) 600 , e ) 4000
Rationale: "explanation : 6000 : 4000 : 10000 3 : 2 : 5 3 / 10 * 11000 = 3300 answer : a"
Answer: a
Question (other): a group of people participate in some curriculum , 30 of them practice yoga , 20 study cooking , 15 study weaving , 5 of them study cooking only , 8 of them study both the cooking and yoga , 5 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 20 - ( 5 + 8 + 5 ) = 2 so , the correct answer is b ."
Answer: b
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 825 in 5 years ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "75 = ( 750 * 5 * r ) / 100 r = 2 % . answer : a"
Answer: a
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 690 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 23
Rationale: "690 = 2 * 3 * 5 * 23 so the least value forncan be 23 . e"
Answer: e
Question (general): two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of b crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of b ?
Options: a ) b / 2 , b ) b , c ) 3 b / 2 , d ) 2 b , e ) 3 b
Rationale: lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( b ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e
Answer: e
Question (general): a certain number of badges were distributed among a class of students . the student who got 1 / 6 th of the total number of badges actually got 5 times the average number of badges the others got ! how many students were there in the class ?
Options: a ) 30 , b ) 26 , c ) 11 , d ) 31 , e ) 32
Rationale: detailed solution let the total students be ( n + 1 ) let total badges be x let the average of ‘ n ’ students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore ‘ n ’ students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b
Answer: b
Question (general): 23 , 27 , 36 , 52 , . . .
Options: a ) 40 , b ) 24 , c ) 77 , d ) 36 , e ) 12
Rationale: "explanation : 23 23 + 2 ^ 2 = 27 23 + 3 ^ 2 = 36 23 + 4 ^ 2 = 52 23 + 5 ^ 2 = 77 answer : c"
Answer: c
Question (general): tough and tricky questions : work / rate problems . a group of 4 junior lawyers require 7 hours to complete a legal research assignment . how many hours would it take a group of 3 legal assistants to complete the same research assignment assuming that a legal assistant works at two - thirds the rate of a junior lawyer ? source : chili hot gmat
Options: a ) 14 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: # of people times the # of hours : 4 * 7 = 28 - - > 4 lawyers do 28 worksin 7 hours . 3 * 14 / 3 = 14 - - > 3 assistants do 14 worksin 4 hours so , since the amount of work the assistants do is half the work the lawyers do , the time will be double , soans a
Answer: a
Question (physics): mahesh can do a piece of work in 30 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 90 , b ) 25 , c ) 37 , d ) 41 , e ) 30
Rationale: "work done by mahesh in 30 days = 20 * 1 / 30 = 2 / 3 remaining work = 1 - 2 / 3 = 1 / 3 1 / 3 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 3 = 90 days answer is a"
Answer: a
Question (general): if x and y are numbers such that ( x + 6 ) ( y - 6 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 16 , c ) 25 , d ) 36 , e ) 49
Rationale: from ( x + 6 ) ( y - 6 ) = 0 it follows that either x = - 6 or y = 6 . thus either x ^ 2 = 36 or y ^ 2 = 36 . now , if x ^ 2 = 36 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 36 + 0 = 36 . similarly if y ^ 2 = 36 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 36 = 36 . answer : d .
Answer: d
Question (general): the difference of a larger number and a smaller number is 6 . the sum of the larger number and twice the smaller is 15 . what is the larger number ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: let x be the larger number and y be the smaller number . x - y = 6 x + 2 ( y ) = 15 solve by substitution : y = x - 6 x + 2 ( x - 6 ) = 15 x + 2 x - 12 = 15 3 x = 27 x = 9 the larger number is 9 , so answer c is correct .
Answer: c
Question (physics): a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "explanation : length of the platform = speed of train * extra time taken to cross the platform . length of platform = 72 kmph * 12 seconds convert 72 kmph into m / sec 1 kmph = 518518 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 72 kmph = 518 ∗ 72518 ∗ 72 = 20 m / sec therefore , length of the platform = 20 m / s * 12 sec = 240 meters . correct answer : a"
Answer: a
Question (general): a vessel of capacity 2 litre has 16 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 27.2 % . , e ) 51 % .
Rationale: "16 % of 2 litres = 0.32 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.72 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.2 % answer : d"
Answer: d
Question (geometry): the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their surface area ?
Options: a ) 1 : 0
b ) 1 : 4
c ) 1 : 6
d ) 1 : 2
e ) 1 : 1
Rationale: 1 : 4 answer : b
Answer: b
Question (general): there are 3 prizes to be distributed among 10 students . if no students gets more than one prize , then this can be done in ?
Options: a ) 10 , b ) 45 , c ) 95 , d ) 120 , e ) none of these
Rationale: explanation : 3 prize among 10 students can be distributed in 10 c 3 ways = 120 ways . answer : d
Answer: d
Question (general): a student got 72 % in math and 82 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 69 % , b ) 71 % , c ) 73 % , d ) 75 % , e ) 77 %
Rationale: "72 + 82 + x = 3 * 75 x = 71 the answer is b ."
Answer: b
Question (other): a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital ?
Options: a ) rs . 9228 , b ) rs . 9129 , c ) rs . 9120 , d ) rs . 9000 , e ) rs . 1922
Rationale: let b ' s capital be rs . x . { 3500 \ 12 } / { 7 x } = { 2 } / { 3 } = > x = 9000 . answer : d
Answer: d
Question (general): how much water must be added to 60 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 60 litres of milk = ( 1 ⁄ 4 × 60 ) litres = 15 litres . answer c"
Answer: c
Question (gain): a car dealership has 40 cars on the lot , 15 % of which are silver . if the dealership receives a new shipment of 80 cars , 45 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of silver cars is 0.15 * 40 + 0.45 * 80 = 42 the percentage of cars which are silver is 42 / 120 = 35 % the answer is b ."
Answer: b
Question (other): how many of the positive factors of 24 are not factors of 27
Options: a ) 2 , b ) 6 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 27 - 1 , 3 , 9,27 comparing both , we have 6 factors of 24 which are not factors of 27 - 2,4 , 6,8 , 12,24 answer : b"
Answer: b
Question (general): a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 20 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 77 , c ) 48 , d ) 66 , e ) 21
Rationale: "speed on return trip = 120 % of 60 = 72 km / hr . average speed of trip = 60 + 72 / 2 = 132 / 2 = 66 km / hr answer : d"
Answer: d
Question (physics): a and b can together finish a work in 10 days . they worked together for 5 days and then b left . after another 5 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 5 , e ) 30
Rationale: "a + b 5 days work = 5 * 1 / 10 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by a in 5 days whole work will be done by a in 5 * 2 = 10 days answer is a"
Answer: a
Question (geometry): a rectangular field has a length 10 meters more than it is width . if the area of the field is 200 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 200 trial and error : 19 * 9 = 171 ( too low ) 20 * 10 = 200 the length is 20 meters . the answer is a ."
Answer: a
Question (other): 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 - .
Options: a ) 7 / 18 , b ) 7 / 19 , c ) 7 / 11 , d ) 7 / 12 , e ) 7 / 15
Rationale: "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 ways . 7 / 15 answer : e"
Answer: e
Question (physics): if 4 men working 10 hours a day earn rs . 1600 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 2160 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1600 : x hence 4 * 10 * x = 9 * 6 * 1600 or x = 9 * 6 * 1600 / 4 * 10 = 2160 answer : d"
Answer: d
Question (general): a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 9 more than the correct answer . find the number .
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 9 25 x = 16 x + 180 9 x = 180 x = 20 the answer is c ."
Answer: c
Question (gain): raman mixed 24 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) rs . 135 , b ) rs . 162 , c ) rs . 189 , d ) rs . 198 , e ) none of these
Rationale: cp per kg of mixture = [ 24 ( 150 ) + 36 ( 125 ) ] / ( 24 + 36 ) = rs . 135 sp = cp [ ( 100 + profit % ) / 100 ] = 135 * [ ( 100 + 40 ) / 100 ] = rs . 189 . answer : c
Answer: c
Question (general): if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 284 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 176 , b ) 180 , c ) 184 , d ) 188 , e ) 192
Rationale: "j + k = 284 and so k = 284 - j j - 8 = 2 k j - 8 = 2 ( 284 - j ) 3 j = 576 j = 192 the answer is e ."
Answer: e
Question (physics): arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 40 days .
Options: a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 24 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 40 * 6 / 10 = 24 days . answer : e"
Answer: e
Question (general): what least number must be added to 1145 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 8
Rationale: "50 * 23 = 1150 1150 - 1145 = 5 answer : d"
Answer: d
Question (gain): a towel , when bleached , lost 30 % of its length and 20 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 30 % , c ) 44 % , d ) 54 % , e ) 64 %
Rationale: percentage change in area = ( − 30 − 20 + ( 30 × 20 ) / 100 ) % = − 44 % i . e . , area is decreased by 44 % answer : c
Answer: c
Question (general): a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 28 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . then â € ¹ = â € º ( x + 30 ) + 2 = 2 ( x + 2 ) â € ¹ = â € º x + 32 = 2 x + 4 x = 28 . answer b"
Answer: b
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.73 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 13 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.73 9.9 - 45 x + 36 x = 8.73 9 x = 1.17 x = 0.13 the answer is e ."
Answer: e
Question (gain): a trader bought a car at 20 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 18 % , b ) 13 % , c ) 12 % , d ) 32 % , e ) 44 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 180 / 100 ) = 112 100 - 144 = 44 % answer : e"
Answer: e
Question (physics): 800 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 11.5 , b ) 12.5 , c ) 10.5 , d ) 11 , e ) 12
Rationale: "800 * 15 = 1000 * x x = 12 answer : e"
Answer: e