Cheukting/mathqa huggingface dataset:
Question (general): a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many r ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total r of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."
Answer: c
Question (general): a 3 - digit positive integer is chosen at random . what is the probability that the product of its digits is even ?
Options: a ) 1 / 2 , b ) 31 / 36 , c ) 49 / 54 , d ) 7 / 8 , e ) 11 / 12
Rationale: p ( three odd digits ) = 5 / 9 * 5 / 10 * 5 / 10 = 5 / 36 ( first digit can not be 0 , so we have a total of 9 digits , 4 even and 5 odd ) . therefore , p ( at least one even digit ) = 1 - 5 / 36 = 31 / 36 . answer b .
Answer: b
Question (general): if x and y are positive integers and 7 + x + y + xy = 21 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 7 + 3 + xy = 21 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 7 + 5 + xy = 21 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 7 + 6 + xy = 21 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 7 + 8 + xy = 21 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 7 + 9 + xy = 21 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Question (general): the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 72 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 2 / 35 , e ) none
Rationale: answer we have , m x n = 6 x 210 = 1260 ∴ 1 / m + 1 / n = ( m + n ) / mn = 72 / 1260 = 4 / 70 = 2 / 35 correct option : d
Answer: d
Question (physics): in a kilometer race , a beats b by 48 meters or 12 seconds . what time does a take to complete the race ?
Options: a ) 238 sec , b ) 190 sec , c ) 667 sec , d ) 167 sec , e ) 176 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 12 ) / 48 = 250 sec . time taken by a = 250 - 12 = 238 sec . answer : a"
Answer: a
Question (gain): in a school of 650 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 163 , c ) 153 , d ) 143 , e ) 117
Rationale: 44 + 28 + 10 = 82 % 100 – 82 = 18 % 650 * 18 / 100 = 117 answer : e
Answer: e
Question (physics): a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it 2 hours . how long will b alone take to do it ?
Options: a ) 8 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) none of these
Rationale: "solution a ’ s 1 hour ’ s work = 1 / 4 ; ( b + c ) ' s 1 hour ’ s work = 1 / 3 ; ( a + c ) ' s 1 hour ’ s work = 1 / 2 ( a + b + c ) ’ s 1 hour ’ s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ’ s 1 hour ’ s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 ∴ b alone will take 12 hours to do the work . answer c"
Answer: c
Question (general): in a group of 160 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.44 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: "number of people whose age is less than 20 is given by 160 - 90 = 70 probability p that a person selected at random from the group is less than 20 is gieven by 70 / 160 = 0.4375 ~ 0.44 correct answer a"
Answer: a
Question (general): an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 800 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 1800 , c ) 540 , d ) 640 , e ) 720
Rationale: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 800 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 800 - - > { not on display } = 1200 . according to ( i ) 2 / 3 * { total } = 1200 - - > { total } = 1800 . answer : b ."
Answer: b
Question (general): if x and y are integers and | x - y | = 10 , what is the minimum possible value of xy ?
Options: a ) - 9 , b ) - 18 , c ) - 24 , d ) - 25 , e ) - 48
Rationale: "sometimes the answer choices to a given question provide a big ' hint ' as to how you can go about solving it . this prompt can also be solved without any complex math ideas - you just need to do a bit of ' brute force ' math and you ' ll have the answer relatively quickly . we ' re told that x and y are integers and | x - y | = 10 . we ' re asked for the minimum possible value of ( x ) ( y ) . since all of the answer choices are negative , this tells us that one of the two variables must be negative ( and the other must be positive ) , so we should restrict our work to those options . if . . . x = 9 , y = - 1 , then xy = - 9 x = 8 , y = - 2 , then xy = - 16 x = 7 , y = - 3 , then xy = - 21 x = 6 , y = - 4 , then xy = - 24 x = 5 , y = - 5 , then xy = - 25 x = 4 , y = - 6 , then xy = - 24 x = 3 , y = - 7 , then xy = - 21 from this , we can conclude the xy will start to get bigger as x continues to decrease down to 1 , so there ' s no need to do any additional work . final answer : d"
Answer: d
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 25 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 6 , b ) 4 : 3 , c ) 4 : 9 , d ) 4 : 5 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 16 : â ˆ š 25 = 4 : 5 . answer : d"
Answer: d
Question (physics): one copy machine can make 20 copies a minute , and a second copy machine makes 10 copies a minute . if the two copiers work together , how long would it take them to make 900 copies ?
Options: a ) 10 minutes , b ) 20 minutes , c ) 25 minutes , d ) 30 minutes , e ) 35 minutes
Rationale: "total work done by both machines in a minute = 20 + 10 = 30 copies total number of copies required = 900 time = 900 / 30 = 30 mins answer d"
Answer: d
Question (gain): at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years ?
Options: a ) 6 % , b ) 6.5 % , c ) 7 % , d ) 7.5 % , e ) 8 %
Rationale: explanation : let the rate be r % p . a . then , 1200 x ( 1 + r / 100 ) 2 = 1348.32 = ( 1 + r / 100 ) 2 = 134832 / 120000 = 11236 / 10000 ( 1 + r / 100 ) 2 = ( 106 / 100 ) 2 = > 1 + r / 100 = 106 / 100 r = 6 % answer is a
Answer: a
Question (gain): in the first 10 overs of a cricket game , the run rate was only 6.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 6.75 , d ) 7 , e ) 8
Rationale: "10 overs - run rate = 6.2 runs scored in first 10 overs = 62 remaining overs 40 total runs to be scored = 282 62 runs already scored 282 - 62 = 220 220 runs to be scored in 40 overs let required runrate be x 40 * x = 220 x = 220 / 40 x = 5.5 the required runrate is 5.5 answer : b"
Answer: b
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] + 2 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 5 , d ) 7 , e ) 13
Rationale: "answer = c = 5 f ( x ) = 3 x – 5 2 * [ f ( x ) ] + 2 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) + 2 = 3 ( 3 x - 6 ) - 5 6 x - 8 = 9 x - 23 x = 5"
Answer: c
Question (physics): during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 135 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 480
Rationale: easy 360 is the answer . 3 / 4 ( x / 2 ) = 135 x = 135 * 8 / 3 = 360 . answer c
Answer: c
Question (general): 5 , 11 , 23 , 41 , 64 , _
Options: a ) 95 , b ) 96 , c ) 97 , d ) 98 , e ) 99
Rationale: "5 + 6 = 11 11 + 6 * 2 ; 11 + 12 = 23 23 + 6 * 3 ; 23 + 18 = 41 41 + 6 * 4 ; 41 + 24 = 65 65 + 6 * 5 ; 65 + 30 = 95 answer : a"
Answer: a
Question (general): the smallest number which when diminished by 6 , is divisible 12 , 14 , 16 , 18 and 22 is :
Options: a ) 11099 , b ) 11094 , c ) 11091 , d ) 10323 , e ) 10483
Rationale: "required number = ( l . c . m . of 12 , 14 , 16 , 18 , 22 ) + 6 = 11088 + 6 = 11094 answer : option b"
Answer: b
Question (physics): 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 15 pumps work to empty the tank in 1 day ?
Options: a ) 3.5 , b ) 4.8 , c ) 5.1 , d ) 5.2 , e ) 6.3
Rationale: "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 15 pumps then 48 / 15 = 3.5 hrs . answer : a"
Answer: a
Question (physics): a and b go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 , b ) 775 , c ) 555 , d ) 288 , e ) 278
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 36 * 5 / 18 ) , 600 / ( 54 * 5 / 18 ) } = lcm ( 60 , 40 ) = 120 sec . answer : a"
Answer: a
Question (general): if x and y are integers and 2 x – y = 11 , then 4 x + y can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 55
Rationale: "2 x - y = 11 2 x = 11 + y 4 x = 22 + 2 y now we need to check the value of 4 x + 4 = > 22 + 2 y + y = 22 + 3 y hence 22 + 3 y = value ( in the options ) so y = value - 22 / 3 so checking the options only d is unfit answer : d"
Answer: d
Question (general): the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 132 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 134 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 132 . so , total number of ducks and frogs in the pond , = 2 * 132 = 262 . therefore , number of frogs , = ( 262 * 39 ) / 76 = 134 . answer : option b"
Answer: b
Question (physics): calculate the circumference of a circular field whose radius is 7 centimeters .
Options: a ) 11 π cm , b ) 15 π cm , c ) 1 π cm , d ) 4 π cm , e ) 14 π cm
Rationale: "circumference c is given by c = 2 π r = 2 π * 7 = 14 π cm answer : e"
Answer: e
Question (physics): a certain car can travel 32 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 32 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 32 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : a ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 32 x 3.9 x 3.8 / 5.7 x 1.6 = 52 a"
Answer: a
Question (general): a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did c get in a profit of rs . 2430 ?
Options: a ) s . 432 , b ) s . 486 , c ) s . 822 , d ) s . 812 , e ) s . 810
Rationale: "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 a ' s share in the profit of rs . 2430 = 12 ( 2430 / 60 ) = rs . 486 answer : b"
Answer: b
Question (other): the ratio of the number of females to males at a party was 1 : 2 but when 7 females and 7 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 42 , e ) 50
Rationale: the total number of people are x females + 2 x males . 3 * ( x - 7 ) = 2 x - 7 x = 14 there were 3 x = 42 people at the party originally . the answer is d .
Answer: d
Question (other): the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 is ?
Options: a ) 3 : 5 , b ) 2 : 7 , c ) 1 : 1 , d ) 1 : 4 , e ) none
Rationale: "answer : option c 5 / 6 : 3 / 2 : 4 / 5 = 1 : 1"
Answer: c
Question (physics): a woman complete a journey in 20 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 448 km . , e ) 544 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 20 - - > x / 21 + x / 24 = 40 - - > x = 448 km . d"
Answer: d
Question (gain): find the compound interest on $ 1200 for 6 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 2383 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 6 = $ 3583 ci = $ 2383 answer is c"
Answer: c
Question (physics): you need to unlock a secret code using following clues , can you ? here you have the clues : clue - 1 : 0 7 9 ( one of the numbers is correct and is placed in its correct position ) clue - 2 : 0 3 2 ( nothing is correct ) clue - 3 : 1 0 8 ( two numbers are correct but not placed at its correct position . ) clue - 4 : 9 2 6 ( one number is correct but not placed at its correct position . ) clue - 5 : 6 7 8 ( one number is correct but not placed at its correct position . )
Options: a ) 819 , b ) 918 , c ) 198 , d ) 189 , e ) 891
Rationale: 0 7 9 : 9 is placed correctly * 0 3 2 : none of the numbers is in the code * 1 0 8 : 1 and 8 are correct number of code but placed at wrong position * 9 2 6 : number 9 is there but placed at wrong position * 6 7 8 : number 8 is there but placed at wrong position correct answer is a ) 819
Answer: a
Question (general): two positive integers differ by 4 , and sum of their reciprocals is 2 . then one of the numbers is
Options: a ) a ) 3 , b ) 2 , c ) c ) 5 , d ) d ) 21 , e ) e ) 28
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 2 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 2 or ( n ^ 2 + 4 n ) * 2 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , b"
Answer: b
Question (general): set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 7 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9
Rationale: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 7 then total increased to 62 + 7 = 69 new avg - 69 / 10 = 6.9 . hence answer is e ."
Answer: e
Question (general): if p ( a ) = 1 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 25 , e ) 3 / 17
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 1 / 5 . 2 / 5 p ( a n b ) = 2 / 25 . d"
Answer: d
Question (physics): a train is 320 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 11 seconds , b ) 38 seconds , c ) 40 seconds , d ) 88 seconds , e ) 36.8 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 320 + 140 = 460 meter time = distance / speed = 460 * ( 2 / 25 ) = 36.8 seconds answer : e"
Answer: e
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units x digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : x . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Question (general): by the how much is two - fifth of 300 greater than 3 - fifths of 125 ?
Options: a ) 15 , b ) 3 , c ) 5 , d ) 45 , e ) none of these
Rationale: reqd no . = 2 â  „ 5 ã — 300 - 3 â  „ 5 ã — 125 = 120 - 75 = 45 answer d
Answer: d
Question (general): a collection of books went on sale , and 2 / 3 of them were sold for $ 3.50 each . if none of the 40 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 180 , b ) $ 250 , c ) $ 260 , d ) $ 280 , e ) $ 300
Rationale: "if 40 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 80 books amount received for sold books = 80 * 3.5 = $ 280 answer : d"
Answer: d
Question (physics): excluding stoppages , the speed of a train is 60 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "explanation : t = 20 / 60 * 60 = 20 answer : option e"
Answer: e
Question (gain): an error 10 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 16.64 % , c ) 15.64 % , d ) 21 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 10 + 10 + ( 10 ã — 10 ) / 100 ) % = 21 % answer : d"
Answer: d
Question (geometry): the perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm . find its area ?
Options: a ) 290 , b ) 240 , c ) 2870 , d ) 289 , e ) 292
Rationale: "4 a = 68 = > a = 17 172 – 82 = 152 1 / 2 * 16 * 30 = 240 answer : b"
Answer: b
Question (geometry): if b is the center of the circle in the figure above and the area of the shaded region is 16 π , what is the length of arc adc ?
Options: a ) 4
b ) 4 π
c ) 16
d ) 8 π
e ) 16
Rationale: area of 1 / 4 th of the circle is 16 pi so area of the circle = 64 pi radius of circle = 8 units circumference = 2 pi * radius = 16 pi 1 / 4 th the circumference = required length of adc = 4 pi ans : b
Answer: b
Question (general): in my , xiang sold 15 used cars . for these 15 used cars the range of selling prices was 15000 and the lowest selling price was 4500 . in june , xiang sold 10 cars . for these 10 cars the range of selling was 16000 and the lowest selling price was 5000 . what was the range of selling prices for the 25 used car sold by xiang in may and june ?
Options: a ) 15,600 , b ) 15,750 , c ) 16,820 , d ) 18,100 , e ) 19,200
Rationale: for 10 cars - 16000 + 5000 = 21,000 for 15 cars - 15000 + 4500 = 19,500 max = 21,000 min 4500 answer is approx 16,500 . option c is closest .
Answer: c
Question (general): if 2 a = 3 b and ab ≠ 0 , what is the ratio of a / 3 to b / 2 ?
Options: a ) 27 / 8 , b ) 8 / 27 , c ) 1 , d ) 9 / 4 , e ) 81 / 64
Rationale: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 2 a = 3 b here ' s one pair : a = 3 and b = 2 what is the ratio of a / 3 to b / 3 ? in other words , what is the value of ( a / 3 ) / ( b / 2 ) ? plug in values to get : ( a / 3 ) / ( b / 2 ) = ( 3 / 3 ) / ( 2 / 2 ) = 1 / 1 = 1 c"
Answer: c
Question (general): each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) 72 , d ) 78 , e ) 90
Rationale: total number of 5 digit numbers that can be formed = 5 ! = 120 . total number of 5 digit numbers in which 3 and 4 are adjacent = 48 . this can be calculated by taking 3 and 4 as a pair and considering positions where they can appear . number of 5 digit numbers in which 3 and 4 are not adjacent = total number of 5 digit numbers - total number of 5 digit numbers in which 3 and 4 are adjacent . ans = 120 - 48 = 72 c
Answer: c
Question (physics): in a 200 m race , a beats b by 20 m and c by 38 m . in a race of 600 m b will beat c by
Options: a ) 20 m , b ) 30 m , c ) 25 m , d ) 15 m , e ) 60 m
Rationale: "it means , when a covers 200 m , b covers only ( 200 - 20 ) = 180 m and c covers only ( 200 - 38 ) = 162 m = > when c covers 162 m , b covers 180 m = > when b covers 600 m , c covers 162 / 180 × 600 = 540 m hence , b beats c by 600 - 540 = 60 metre answer : e"
Answer: e
Question (physics): in what time will a train 120 m long cross an electric pole , it its speed be 121 km / hr ?
Options: a ) 2.5 , b ) 2.7 , c ) 2.9 , d ) 3.6 , e ) 2.1
Rationale: "speed = 121 * 5 / 18 = 33.6 m / sec time taken = 120 / 33.6 = 3.6 sec . answer : d"
Answer: d
Question (general): at a recent small town election for mayor a total of 963 votes were cast for the 4 candidates , the winner exceding his opponents by 53 , 79 and 105 votes , respectively . how many votes were cast for each candidate ?
Options: a ) 134 , b ) 178 , c ) 195 , d ) 166 , e ) 194
Rationale: c 195 the number of votes the winning candidate received was 963 + 53 + 79 + 105 / 4 = 300 . the second received 300 – 53 = 247 , the third received 300 – 105 = 195 .
Answer: c
Question (gain): a customer went to a shop and paid a total of $ 30 , out of which 90 cents was for sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) $ 12.70 , b ) $ 13.20 , c ) $ 14.10 , d ) $ 15.60 , e ) $ 16.80
Rationale: "the total cost was $ 30 . the tax was $ 0.90 let the original price of the taxable items = x given that tax rate = 6 % 0.06 x = 0.90 x = $ 15 the cost of the tax free items was $ 30 - $ 15 - $ 0.90 = $ 14.10 the answer is c ."
Answer: c
Question (gain): in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 5 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 500 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 5 / 50 ) * 100 = 10 % so , x * 10 % = 50 x = 500 ans b ."
Answer: b
Question (general): tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability taht the ticket drawn has a number which is a multiple of 3 or 5 ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 8 / 15 , d ) 9 / 20 , e ) none
Rationale: "solution here s = ( 1 , 2,3 , 4,5 , . . . , 19,20 ) . let e = event of getting a multiple of 3 or 5 = ( 3 , 6,9 , 12,15 , 18,5 , 10,20 ) p ( e ) = n ( e ) / n ( s ) = 9 / 20 . answer d"
Answer: d
Question (physics): together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many q hours would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job q in 44 hours . answer : c ."
Answer: c