Cheukting/mathqa huggingface dataset:
Question (general): in the formula a = ( 2 r ) ^ 3 , if r is halved , then a is multiplied by ?
Options: a ) 64 , b ) 1 / 8 , c ) 1 , d ) 8 , e ) 1 / 64
Rationale: say r = 2 = > a 1 = 64 when r = 1 ; v 2 = 8 v 2 = 1 / 8 * v 1 . answer : b
Answer: b
Question (gain): the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 22,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 118000 , d ) 277768 , e ) 188871
Rationale: the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 22,000 is made = 96,000 + 24,000 = rs . 1 , 18,000 answer : c
Answer: c
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1180 , find the gain percent ?
Options: a ) 11 , b ) 31 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 280 100 - - - - ? = > 31 % answer : b"
Answer: b
Question (general): all the students of class are told to sit in circle shape . here the boy at the 8 th position is exactly opposite to 33 th boy . total number of boys in the class ?
Options: a ) 40 , b ) 50 , c ) 28 , d ) 38 , e ) 48
Rationale: "as half the circle shape consist of 33 - 8 = 25 boys , so total number of boys in full circle = 2 * 25 = 50 answer : b"
Answer: b
Question (probability): 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be not a couple ?
Options: a ) 17 / 2900 , b ) 2683 / 2700 , c ) 2496 / 2700 , d ) 2369 / 2700 , e ) 198 / 270
Rationale: in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . probability of there will not be a couple = 1 - ( 17 / 2700 ) = 2683 / 2700 ans - b
Answer: b
Question (general): if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 11 / 15 find p ( a | b )
Options: a ) 11 / 4 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a â ˆ ª b ) / p ( b ) p ( a | b ) = ( 11 / 15 ) / ( 4 / 15 ) = 11 / 4 . a"
Answer: a
Question (physics): how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 134 m length ?
Options: a ) 82.1 sec . , b ) 12.2 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 134 = 244 m . required time = 244 / 20 = 12.2 sec . answer : b"
Answer: b
Question (gain): what percent is 70 of 280 ?
Options: a ) 12 % , b ) 25 % , c ) 26 % , d ) 27 % , e ) 28 %
Rationale: "70 / 280 = 1 / 4 1 / 4 × 100 = 25 % b"
Answer: b
Question (general): ifaequals the sum of the even integers from 2 to 40 , inclusive , andbequals the sum of the odd integers from 1 to 39 , inclusive , what is the value of a - b ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 20 , e ) 21
Rationale: this is a solution from beatthegmat : even numbers : ( 40 - 2 ) / 2 + 1 = 20 even integers . ( 40 + 2 ) / 2 = 21 is the average of the even set . sum = avg * ( # of elements ) = 21 * 20 = 420 = a odd numbers : ( 39 - 1 ) / 2 + 1 = 20 odd integers . ( 39 + 1 ) / 2 = 20 is the average of the odd set . sum = avg * ( # of elements ) = 20 * 20 = 400 = b a - b = 420 - 400 = 20 . answer : d
Answer: d
Question (physics): a train running at the speed of 90 km / hr crosses a pole in 12 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 300
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 75 / 3 m / sec length of train ( distance ) = speed * time ( 75 / 3 ) * 12 = 300 meter answer : e"
Answer: e
Question (physics): two cars , car 1 and car 2 move towards each other from e and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach e starting from y ?
Options: a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec
Rationale: e - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance ey = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d
Answer: d
Question (geometry): the radius of a semicircular plot is 25 . what is the approximate perimeter of the plot ?
Options: a ) 114
b ) 150
c ) 129
d ) 25
e ) 57
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 25 + 2 * 25 = 128.50 approximately 129 answer c
Answer: c
Question (general): how many two - digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4 ? options :
Options: a ) one , b ) two , c ) three , d ) four , e ) five
Rationale: numbers giving remainder 3 when divided by 10 = 13,23 , 33,43 , 53,63 , 73,83 , 93 numbers giving remainder 3 when divided by 4 = alternate numbers ( coloured in red ) = 4 correct option : d
Answer: d
Question (general): on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number t of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "t = 7 is the correct answer . good solution buneul . b"
Answer: b
Question (gain): from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 30 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 117 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 30 % = 90 * 1.3 = 117 thus ratio = 117 / 100 = 1.17 ( in % terms = 117 % ) . thus b is the correct answer ."
Answer: b
Question (geometry): a rectangular tiled patio is composed of 40 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 40 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "r * c = 70 and ( 6 + 4 ) ( c - 2 ) = 70 - - > r = 6 and c = 6 . answer : b ."
Answer: b
Question (general): set s consists of integers { 6 , 7 , 10 , 12 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 40 % . what is the value of integer n ?
Options: a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 40 % , the new mean is 14 . thus , on average , 5 numbers increase by 4 . therefore n = 14 + 20 = 34 the answer is c ."
Answer: c
Question (general): a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1224 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1224 or 9 x = 1224 or x = 136 . required number = 136 . answer : d"
Answer: d
Question (gain): what will be the difference between simple and compound interest @ 20 % per annum on a sum of $ 500 after 2 years ?
Options: a ) $ 10 , b ) $ 20 , c ) $ 25 , d ) $ 30 , e ) $ 40
Rationale: "s . i . = 500 * 20 * 2 / 100 = $ 200 c . i . = 500 * ( 1 + 20 / 100 ) ^ 2 - 500 = $ 220 difference = 220 - 200 = $ 20 answer is b"
Answer: b
Question (general): martins made a part payment of $ 650 toward buying a brand new washing machine , which represents 15 % of the total cost of the washing machine , how much remains to be paid ?
Options: a ) $ 1116.3 , b ) $ 3583.3 , c ) $ 3283.3 , d ) $ 3683.3 , e ) $ 2683.3
Rationale: explanation : let ' s start with what the total price of the washing machine would be . if 15 % is equal to $ 650 then 100 % equals $ x . we just have to multiply $ 650 by 6.67 to get total amount = $ 4333.3 . out of this amount we then need to deduct the amount already paid which was $ 650 so we have $ 4333.3 - $ 650 = $ 3683.3 answer : option d
Answer: d
Question (geometry): a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet . what is its area , in square feet ?
Options: a ) 43,200 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 300 , you can deduce the following a = 180 b = 240 180 x 240 = 43,200 a is the answer ."
Answer: a
Question (general): in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 6 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2000
Rationale: "sugar : flour = 5 : 6 = 25 : 30 ; flour : soda = 10 : 1 = 30 : 3 ; thus we have that sugar : flour : soda = 25 x : 30 x : 3 x . also given that 30 x / ( 3 x + 60 ) = 8 / 1 - - > x = 80 - - > sugar = 25 x = 2,000 . answer : e ."
Answer: e
Question (physics): the h . c . f of two numbers is 19 and their l . c . m is 4263 . if one of the numbers is 399 , then the other is ?
Options: a ) 202 , b ) 203 , c ) 204 , d ) 205 , e ) 206
Rationale: "other number = ( 19 * 4263 ) / 399 = 203 . answer : b"
Answer: b
Question (gain): in a restaurant , the profit is 110 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 47 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: explanation : let c . p . = rs . 100 . then , profit = rs . 110 , s . p . = rs . 210 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 210 . profit = rs . ( 210 - 112 ) = rs . 98 . required percentage = ( 98 / 210 * 100 ) % = 47 % appox answer : b
Answer: b
Question (physics): at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 3 / 4 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 11 / 15 , d ) 16 / 25 , e ) 19 / 25
Rationale: "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 3 x / 4 ) ( 3 y / 4 ) = 9 xy / 16 the total number of boxes is xy + 9 xy / 16 = 25 xy / 16 the fraction loaded by the day crew is xy / ( 25 xy / 16 ) = 16 / 25 the answer is d ."
Answer: d
Question (gain): walking 6 / 5 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 24 , e ) 20
Rationale: "speed ratio = 1 : 6 / 5 = 5 : 6 time ratio = 6 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? 24 m . answer : d"
Answer: d
Question (physics): how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 66 km / hr ?
Options: a ) 11 , b ) 30 , c ) 29 , d ) 88 , e ) 61
Rationale: "speed of train relative to man = 66 - 3 = 63 km / hr . = 63 * 5 / 18 = 35 / 2 m / sec . time taken to pass the man = 500 * 2 / 35 = 28.57 sec . approx . 29 sec answer : c"
Answer: c
Question (general): what number times ( 1 ⁄ 4 ) ^ 2 will give the value of 4 ^ 3 ?
Options: a ) 4 , b ) 16 , c ) 64 , d ) 256 , e ) 1024
Rationale: "x * ( 1 / 4 ) ^ 2 = 4 ^ 3 x = 4 ^ 2 * 4 ^ 3 = 4 ^ 5 = 1024 the answer is e ."
Answer: e
Question (gain): a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 25 % ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 3 , e ) 5
Rationale: "c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 150 % of re . 1 = rs . 3 / 2 for rs . 3 / 2 , toffees sold = 6 . for re . 1 , toffees sold = 6 x 3 / 2 = 9 . answer b"
Answer: b
Question (gain): one night 19 percent of the female officers on a police force were on duty . if 152 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 76 . 0.19 x = 76 x = 400 the answer is c ."
Answer: c
Question (general): a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 6 tons ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "the weight of one car and one truck is 6.75 tons . 70 / 6.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is a ."
Answer: a
Question (physics): a train passes a platform in 35 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 225 meter , d ) 200 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 35 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 35 = > 300 + l = 15 × 35 = 525 = > l = 525 - 300 = 225 meter answer : option c"
Answer: c
Question (gain): a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 26 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 %
Rationale: "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 50 % of 100 = 50 pounds of decaffeinated coffee 3 . wt have 130 pounds of decaffeinated out of 500 pounds , that means 130 / 500 * 100 % = 26 % . the correct answer is a ."
Answer: a
Question (other): praveen starts business with rs . 3220 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8000 , c ) s . 8280 , d ) s . 9000 , e ) s . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3220 * 12 / 7 x = 2 / 3 = > 14 x = 115920 = > x = 8280 . answer : c"
Answer: c
Question (general): how many integers from 22 to 160 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 22 to 160 , inclusive is ( 147 - 42 ) / 21 + 1 = 6 ; 46 - 6 = 40 . answer : c ."
Answer: c
Question (physics): 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 4 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 16 hours
Rationale: let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 4 machines 4 units of work ( 4 machines ) - - - > 1 hour for 48 units of work 4 * 12 - - - > 1 * 12 hours c 12 hours
Answer: c
Question (gain): a candidate got 35 % of the votes and lost to the rival by 2100 votes . how many votes were cast ?
Options: a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 2100 10 % = 700 100 % of the votes = 7000 answer : a"
Answer: a
Question (general): if you write down all the numbers from 1 to 25 , then how many times do you write 3 ?
Options: a ) a ) 11 , b ) b ) 3 , c ) c ) 2 , d ) d ) 1 , e ) e ) 6
Rationale: "explanation : explanation : clearly , from 1 to 25 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 so , required number = 3 answer : b"
Answer: b
Question (other): what is the square root of 81 , divided by 3 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 3 , e ) 1
Rationale: "square root is a number times itself square root of 81 = 6 , 9 / 3 = 3 ( d ) 3"
Answer: d
Question (general): the mean of 30 values was 250 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 251 , e ) none of the above
Rationale: "corrected mean = 250 × 30 − 135 + 165 / 30 = 7500 − 135 + 165 / 30 = 7530 / 30 = 251 answer d"
Answer: d
Question (general): a cyclist rides a bicycle 9 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.3 , b ) 9.6 , c ) 9.8 , d ) 10.1 , e ) 10.3
Rationale: "distance = 20 km time = 9 / 11 + 11 / 9 = ( 81 + 121 ) / 99 = 202 / 99 hours average speed = ( 20 * 99 ) / 202 = 9.8 km / h the answer is c ."
Answer: c
Question (physics): a man can row upstream at 26 kmph and downstream at 30 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 28 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 26 ds = 30 m = ( 30 + 26 ) / 2 = 28 answer : b"
Answer: b
Question (other): in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d
Answer: d
Question (gain): a reduction of 5 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 5000 , what is the reduced price for kg ?
Options: a ) 23 , b ) 27 , c ) 25 , d ) 35 , e ) 15
Rationale: "5000 * ( 5 / 100 ) = 250 - - - - 10 ? - - - - 1 = > rs . 25 answer : c"
Answer: c
Question (general): if a 2 - b 2 = 10 and a * b = 8 , find a 4 + b 4 .
Options: a ) 200 , b ) 228 , c ) 182 , d ) 102 , e ) 128
Rationale: "a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 8 : given a 2 b 2 = 82 : square both sides . a 4 + b 4 - 2 ( 64 ) = 100 : substitute a 4 + b 4 = 228 correct answer b"
Answer: b
Question (general): find the sum of first 80 odd numbers
Options: a ) 6400 , b ) 8000 , c ) 5000 , d ) 4980 , e ) 4960
Rationale: "explanation : n 2 = 802 = 6400 answer : option a"
Answer: a
Question (general): of 58 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 51 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: total = 58 thrower = 37 rest = 58 - 37 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 37 + 14 = 51 so a . 51 is the right answer
Answer: a
Question (gain): the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 6 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 10721 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 6 = rs 10721 answer : c"
Answer: c
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: let the weekly sales of both = x 590 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c
Answer: c
Question (geometry): the product of the squares of two positive integers is 1600 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : e - 4 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 1600 [ square root both sides ] xy = 40 40 = 1 x 40 , 4 x 10 , 40 x 1 , 10 x 4 , 5 x 8 , 8 x 5 , 20 x 2 , 2 x 20 cancel the repeats this leaves us with exactly 4 options . hence , e"
Answer: e
Question (gain): what percent is 20 % of 25 % ?
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: required percentage = 20 % / 25 % * 100 = 20 / 25 * 100 = 80 % answer is e
Answer: e
Question (physics): walking at 40 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 16 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: speed is inversly proprtional to time walking at 40 % of speed meand 2 / 5 s takes 5 / 2 t . it takes 24 minutes extra to cover the distance . then 5 / 2 t = t + 24 5 t = 2 t + 48 3 t = 48 t = 16 . option a is correct
Answer: a
Question (geometry): the area of the largest circle that can be drawn inside a square of side 70 cm in length is :
Options: a ) 3600
b ) 2646
c ) 3850
d ) 4215
e ) 5205
Rationale: radius of required circle = 35 cm its area = 22 / 7 × 35 × 35 110 × 35 = 3850 cm ( power ) 2 answer is c .
Answer: c
Question (general): there are 660 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 110 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 660 - x x / 2 + 660 - x / 4 = 1 / 3 * ( 660 ) = 220 x = 220 x / 2 = 110 is supposed to be the answer m is missing something correct option b"
Answer: b
Question (physics): the speed of a train is 70 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 10.66 kmph , b ) 11.66 kmph , c ) 21.66 kmph , d ) 12.66 kmph , e ) 11.96 kmph
Rationale: "70 * 10 / 60 = 11.66 kmph answer : b"
Answer: b