Cheukting/mathqa huggingface dataset:
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 7 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 153601 , b ) 153600 , c ) 153602 , d ) 117600 , e ) 153604
Rationale: "perimeter = distance covered in 7 min . = ( 12000 / 60 ) x 7 m = 1400 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1400 or x = 140 . length = 420 m and breadth = 280 m . area = ( 420 x 280 ) m 2 = 117600 m 2 . answer : d"
Answer: d
Question (physics): james took a 3 - hour bike ride . in the second hour he traveled 6 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 18.5 , d ) 57.0 , e ) 63.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 6 , x = 5 . now , the distance travelled in the 3 rd hour = 6 + 1 / 4 â ˆ — 6 = 7.5 the only option ending with a 0.5 in the decimal place is c . answer : c"
Answer: c
Question (general): what least number must be added to 9599 , so that the sum is completely divisible by 100 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "if we divide 9599 by 100 remainder is 99 100 - 99 = 1 answer : a"
Answer: a
Question (general): in august , a cricket team that played 120 matches won 28 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 60 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 33.6 + x by solving we get x = 60 answer : c"
Answer: c
Question (physics): a fish can go upstream at 35 kmph and downstream at 55 kmph , and then find the speed of the fish in still water ?
Options: a ) 45 , b ) 55 , c ) 35 , d ) 65 , e ) 70
Rationale: us = 35 ds = 55 m = ( 35 + 55 ) / 2 = 45 answer : a
Answer: a
Question (gain): two numbers are respectively 20 % and 25 % more than a third number . so find the percentage that is first of the second is ?
Options: a ) 96 , b ) 20 , c ) 35 , d ) 78 , e ) 89
Rationale: "first - 120 second - 125 third - 100 125 - - - - 120 100 - - - - - 96 answer a"
Answer: a
Question (gain): a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 450 . find the total worth of the stock ?
Options: a ) 20029 , b ) 22500 , c ) 20289 , d ) 20027 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 450 = > x = 22500 answer : b"
Answer: b
Question (gain): the number which exceeds 16 % of it by 126 is :
Options: a ) 150 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 126 x - 16 / 100 x = 126 x - 4 / 25 x = 126 21 / 25 x = 126 x = ( 126 x 25 / 21 ) = 150 answer a"
Answer: a
Question (general): a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old id the mother at present ?
Options: a ) 46 , b ) 49 , c ) 40 , d ) 21 , e ) 19
Rationale: "let the mother ' s present age be x years . then , the person ' s present age = 2 / 5 x years . ( 2 / 5 x + 8 ) = 1 / 2 ( x + 8 ) 2 ( 2 x + 40 ) = 5 ( x + 8 ) = > x = 40 answer : c"
Answer: c
Question (general): 4.509 / 10.02 =
Options: a ) 0.45 , b ) 0.3505 , c ) 0.3509 , d ) 0.351 , e ) 0.3527
Rationale: "4.509 / 10.02 4509 / 1002 = 4.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.45 . answer : a"
Answer: a
Question (general): the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 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 ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 31 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d ."
Answer: d
Question (other): the ratio of type of pen and type of notebook is 5 : 4 . and in 80 ways one can start writing . tell me the no . of pen and no . of notebook .
Options: a ) 6,12 , b ) 10,6 , c ) 10,8 , d ) 8,4 , e ) 6,8
Rationale: let the ratio constant be x . no . of pen = 5 x , no . of notebook = 4 x . total no . of ways of start writing = 5 x * 4 x = 20 ( square of x ) = 80 x = â ˆ š 4 = 2 pen = 10 , notebook = 8 answer c
Answer: c
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 50 . he was allowed to drop his lowest score . after doing so , his average test score improved to 55 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 35 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 50 . so what we can assume is that we have 4 test scores , each 50 . he dropped his lowest score and the avg went to 55 . this means that the lowest score was not 50 and other three scores had given the lowest score 5 each to make it up to 50 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 50 . so the lowest score = 50 - 15 = 35 answer ( b )"
Answer: b
Question (general): jamshid and irwin decided to make up their own version of basketball . in addition to being able to score 2 - point baskets , they created ways to score 5 - , 11 - , and 13 - point baskets . if at halftime the product of the point values of irwin ’ s baskets was 2420 , how many 11 - point baskets e did irwin score ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: first thing i noticed was that all these numbers are prime . . . prime factorization gives the following step 1 : 2 * 1210 step 2 : 2 * 11 * 110 step 4 : 2 * 11 * 11 * 10 step 5 : 2 * 11 * 11 * 2 * 5 so he scored e = 2 11 - point baskets in my opinion . answer c
Answer: c
Question (physics): a train is running at a speed of 40 km / hr and it crosses a post in 18 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 18 s distance covered , d = vt = ( 400 / 36 ) × 18 = 200 m distance covered is equal to the length of the train = 200 m correct answer is 200 metres
Answer: c
Question (general): 70 % of 300 + 25 % of 400 - ? = 256
Options: a ) 48 , b ) 68 , c ) 54 , d ) 60 , e ) none of these
Rationale: "explanation : solution : let 70 % of 300 + 25 % of 400 - x = 256 . then , x = ( 70 / 100 * 300 ) + ( 25 / 100 * 400 ) - 256 = 210 + 100 - 256 = 54 . answer : c"
Answer: c
Question (physics): riya and priya set on a journey . riya moves eastward at a speed of 30 kmph and priya moves westward at a speed of 50 kmph . how far will be priya from riya after 45 minutes
Options: a ) 25 kms , b ) 60 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 30 kmph * 3 / 4 hr = 22.50 km total westward distance = 50 kmph * 3 / 4 hr = 37.5 km total distn betn them = 22.5 + 37.5 = 60 km ans 60 km answer : b"
Answer: b
Question (general): let c be defined as the sum of all prime numbers between 0 and 23 . what is c / 3
Options: a ) 155 , b ) 129 , c ) 61 , d ) 25.3 , e ) 43
Rationale: "prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 sum , c = 77 c / 3 = 25.3 answer d"
Answer: d
Question (physics): a cistern which could be filled in 10 hours takes 2 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ?
Options: a ) 50 hours , b ) 80 hours , c ) 100 hours , d ) 150 hours , e ) 110 hours
Rationale: "let the leak empty the full cistern in x hours 10 x / x - 10 = 10 + 1 x = 110 hours answer is e"
Answer: e
Question (general): when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 5 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 7
Rationale: "i tried plugging in numbers x = 9 q + 5 x = 14 5 x = 70 5 x / 9 = 63 + 7 remainder is 7 . answer is e ."
Answer: e
Question (general): when positive integer x is divided by positive integer y , the remainder is 7 . if x / y = 86.1 , what is the value of y ?
Options: a ) 72 , b ) 71 , c ) 70 , d ) 30 , e ) 45
Rationale: "when positive integer x is divided by positive integer y , the remainder is 7 - - > x = qy + 7 ; x / y = 86.1 - - > x = 86 y + 0.1 y ( so q above equals to 86 ) ; 0.1 y = 7 - - > y = 70 . answer : c ."
Answer: c
Question (gain): find the simple interest on $ 10000 at 8 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 800 , e ) $ 1000
Rationale: "p = $ 10000 r = 8 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 8 * 1 / 100 = $ 800 answer is d"
Answer: d
Question (general): a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 6 : 5 : 2 , respectively , by weight . if 78 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 24 , b ) 12 , c ) 9 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 6 x + 5 x + 2 x = 78 13 x = 78 x = 6 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 2 ) ( 6 ) = 12 pounds of apples = ( 6 ) ( 6 ) = 36 thus we know that there are 36 - 12 = 24 more pounds of apples than grapes . answer is a ."
Answer: a
Question (general): if ( a + b ) = 11 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 5 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 11 = > a = 11 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 11 - b + 3 - c = > 14 - ( b + c ) = > 14 - 9 = 5 . option c . . ."
Answer: c
Question (physics): from a vessel on the first day , 1 / 3 rd of the liquid evaporates . on the second day 3 / 4 th of the remaining liquid evaporates . what fraction of the volume is present at the end of the 2 day
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: let x be the volume . . . after 1 st day volume remaining = ( x - x / 3 ) = 2 x / 3 after 2 st day volume remaining = ( 2 x / 3 ) - ( ( 2 x / 3 ) * ( 3 / 4 ) ) = ( 2 x / 3 ) ( 1 - 3 / 4 ) = ( 2 x / 3 ) * ( 1 / 4 ) = x / 6 answer : d
Answer: d
Question (other): the ratio of the incomes of uma and bala is 8 : 7 and the ratio of their expenditure is 7 : 6 . if at the end of the year , each saves $ 2000 then the income of uma is ?
Options: a ) $ 16800 , b ) $ 16500 , c ) $ 16000 , d ) $ 16300 , e ) $ 16200
Rationale: let the income of uma and bala be $ 8 x and $ 7 x let their expenditures be $ 7 y and $ 6 y 8 x - 7 y = 2000 - - - - - - - 1 ) 7 x - 6 y = 2000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 uma ' s income = 8 x = 8 * 2000 = $ 16000 answer is c
Answer: c
Question (general): the average of 6 numbers is 30 . if the average of first 4 is 25 and that of last 3 is 35 , the fourth number is :
Options: a ) 25 , b ) 26 , c ) 18 , d ) 19 , e ) 10
Rationale: let the six numbers be , a , b , c , d , e , f . a + b + c + d + e + f = 30 × 6 = 180 - - - - ( 1 ) a + b + c + d = 25 × 4 = 100 - - - - ( 2 ) d + e + f = 35 × 3 = 105 - - - - ( 3 ) add 2 nd and 3 rd equations and subtract 1 st equation from this . d = 25 answer : a
Answer: a
Question (other): how many of the positive factors of 15 , 45 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: factors of 15 - 1 , 3 , 5 , and 15 factors of 45 - 1 , 3 , 9 , 15 and 45 comparing both , we have three common factors of 45,16 - 3 answer c
Answer: c
Question (other): divide rs . 32000 in the ratio 1 : 9 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 3200 , 28800 , e ) 12000 , 20001
Rationale: "1 / 10 * 32000 = 3200 9 / 10 * 32000 = 28800 answer : d"
Answer: d
Question (physics): if a car had traveled 25 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 75 km , at what speed did it travel ?
Options: a ) 30 kmh , b ) 40 kmh , c ) 45 kmh , d ) 50 kmh , e ) 55 kmh
Rationale: time = distance / speed difference in time = 1 / 2 hrs 75 / x - 75 / ( x + 25 ) = 1 / 2 substitute the value of x from the options . - - > x = 50 - - > 75 / 50 - 75 / 75 = 3 / 2 - 1 = 1 / 2 answer : d
Answer: d
Question (general): in the faculty of reverse - engineering , 240 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 661 . , d ) 644 . , e ) 666 .
Rationale: "answer is c : 661 solution : total number of students studying both are 423 + 240 - 134 = 529 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 529 , so 100 % is approx . 661 ."
Answer: c
Question (gain): machine a and machine b are each used to manufacture 770 sprockets . it takes machine a 10 hours longer to produce 770 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 7.7
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 770 qt = 700 for a : ( t + 10 ) ( q ) = 770 qt + 10 q = 770 700 + 10 q = 770 q = 7 so a can produce 7 / hour . then b can produce = 7 ( 1.1 ) = 7.7 / hour . e"
Answer: e
Question (general): for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 5 + 3 and * 5 + 5 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 5 would be divisible by all numbers from 1 to 5 . = > * 5 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 5 is divisible by 3 ) in fact adding anyprimenumber between 1 to 5 to * 5 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 5 + 3 and * 5 + 11 then the answer would be 1 . for * 5 + 3 and * 5 + 13 , it is 2 and so on . . . a
Answer: a
Question (general): the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a"
Answer: a
Question (general): two numbers are respectively 40 % and 30 % more than a third number . the second number expressed in terms of percentage of the first is ?
Options: a ) 95 % , b ) 93 % , c ) 90 % , d ) 80 % , e ) none of these
Rationale: "here , x = 40 and y = 30 ; therefore second number = [ [ ( 100 + y ) / ( 100 + x ) ] x 100 ] % of first number = [ [ ( 100 + 30 ) / ( 100 + 40 ) ] x 100 ] % of first number = 92.8 % of the first answer : b"
Answer: b
Question (physics): a man can row downstream at 22 kmph and upstream at 14 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 13 , 3 , b ) 18 , 4 , c ) 15 , 3 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 22 - - - ( 1 ) and x - y = 14 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 36 = > x = 18 , y = 4 . answer : option b"
Answer: b
Question (general): 8.5 × 6.4 + 4.5 × 11.6 = ? ÷ 4
Options: a ) 426.2 , b ) 426.4 , c ) 106.6 , d ) 422.4 , e ) 522.5
Rationale: "explanation : ( 54.4 + 52.2 ) × 4 = 426.4 answer : option b"
Answer: b
Question (physics): a cubical tank is filled with water to a level of 2 feet . if the water in the tank occupies 50 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 3
b ) 2 / 3
c ) 3 / 4
d ) 2 / 5
e ) 5 / 6
Rationale: the volume of water in the tank is h * l * b = 50 cubic feet . since h = 2 , then l * b = 25 and l = b = 5 . since the tank is cubical , the capacity of the tank is 5 * 5 * 5 = 125 . the ratio of the water in the tank to the capacity is 50 / 125 = 2 / 5 the answer is d .
Answer: d
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 210 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 88 , b ) 45 , c ) 36 , d ) 80 , e ) 12
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 210 = 450 m . time taken = 450 / 10 = 45 sec . answer : b"
Answer: b
Question (physics): a cistern is normally filled in 12 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 84 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 12 - 1 / x = 1 / 14 , solving 1 / x = 1 / 84 so in 84 hours full cistern will be empty . answer : b"
Answer: b
Question (general): what is the units digit of the product of the first 100 odd numbers ?
Options: a ) 1 , b ) 3 , c ) 0 , d ) 5 , e ) 7
Rationale: 1 * 3 * 5 * 7 . . . . . . . . . . . . . . . . . . . will end up in 5 in the units place answer : d
Answer: d
Question (other): how many positive integers between 20 and 2000 ( both are inclusive ) are there such that they are multiples of 10 ?
Options: a ) 201 , b ) 193 , c ) 200 , d ) 199 , e ) 195
Rationale: "multiples of 10 = 20 , 30,40 - - - - - , 1990,2000 number of multiples of 10 = > 2000 - 20 / 10 + 1 = 199 answer is d"
Answer: d
Question (physics): what is the cost of leveling the field in the form of parallelogram at the rate of rs . 50 / 10 sq . metre , whose base & perpendicular distance from the other side being 54 m & 24 m respectively ?
Options: a ) rs . 5280 , b ) rs . 5500 , c ) rs . 6000 , d ) rs . 6480 , e ) rs . 7680
Rationale: area of the parallelogram = length of the base * perpendicular height = 54 * 24 = 1296 m . total cost of levelling = rs . 6480 d
Answer: d
Question (physics): a and b together can complete a piece of work in 4 days . if a alone can complete the same work in 12 days , in how many days , in how many days can b alone complete that work ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 5
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 4 a ' s 1 day ' s work = 1 / 12 b ' s 1 days ' s work = ( 1 / 4 ) - ( 1 / 12 ) = 1 / 6 hence , b alone can complete the work in 6 days . answer is a"
Answer: a
Question (geometry): the area of a square is added to one of its sides , and the perimeter is then subtracted from this total , the result is 4 . what is the length of one side ?
Options: a ) 5
b ) 4
c ) 3
d ) 2
e ) 1
Rationale: the equation is ; side + area - perimeter = s + a - p = s + s ^ 2 - 4 s = s ( 1 + s - 4 ) . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : b
Answer: b
Question (general): a , b and c rents a pasture for rs . 870 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should a pay ?
Options: a ) 240 , b ) 270 , c ) 276 , d ) 271 , e ) 272
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 8 / 29 * 870 = 240 answer : a"
Answer: a
Question (general): caleb spends $ 68.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 10 , c ) 37 , d ) 40 , e ) 45
Rationale: solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 68.50 . by solving the equations y = 37 . ans c .
Answer: c
Question (other): in a graduating class of 234 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 115 , c ) 113 , d ) 88 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 234 = 29 greatest - smallest is 144 - 29 = 115 so answer must be b . 115"
Answer: b
Question (physics): two trains are moving at 60 kmph and 70 kmph in opposite directions . their lengths are 150 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 5 sec , b ) 6 sec , c ) 7 sec , d ) 8 sec , e ) 9 sec
Rationale: "70 + 60 = 130 * 5 / 18 = 325 / 9 mps d = 150 + 100 = 250 m t = 250 * 9 / 325 = 7 sec answer : c"
Answer: c
Question (gain): one fourth of a solution that was 11 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 24 % , b ) 34 % , c ) 22 % , d ) 31 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.11 + 25 * x = 100 * 0.16 - - > x = 0.31 . answer : d ."
Answer: d
Question (general): 1297 x 1297 = ?
Options: a ) a ) 1682209 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1297 x 1297 = ( 1297 ) 2 = ( 1300 - 3 ) 2 = ( 1300 ) 2 + ( 3 ) 2 - ( 2 x 1300 x 3 ) = 1690000 + 9 - 7800 = 1690009 - 7800 = 1682209 . answer : a"
Answer: a
Question (gain): 80 percent of the members of a study group are women , and 40 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.45 , b ) 0.55 , c ) 0.65 , d ) 0.32 , e ) 0.35
Rationale: say there are 100 people in that group , then there would be 0.8 * 0.40 * 100 = 32 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 32 / 100 . answer : d
Answer: d
Question (general): if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 5 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 8 , b ) 64 , c ) 16 , d ) 32 , e ) 4
Rationale: "2 ^ ab = 2 ^ 5 therefore ab = 5 either a = 1 or 5 or b = 5 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 6 = 64 b"
Answer: b