regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: rectangular floors x and y have equal area . if floor x is 10 feet by 18 feet and floor y is 9 feet wide , what is the length of floor y , in feet ?
Options: a ) 13 1 / 2
b ) 20
c ) 18 3 / 4
d ) 21
e ) 24
Rationale: the area of a rectangle is : area = length x width we are given that floor x is 10 feet by 18 feet and that floor y is 9 feet wide . so we can say : length of x = 10 width of x = 18 width of y = 9 length of y = n we also can say : area of floor x = area of floor y ( length of x ) ( width of x ) = ( length of y ) ( width of y ) ( 10 ) ( 18 ) = 9 n ( 10 ) ( 2 ) = n 20 = n answer b .
Answer: b
Problem: find the product of the localvalue and absolutevalue of 6 in 20618 ?
Options: a ) 6300 , b ) 1100 , c ) 1200 , d ) 1300 , e ) 3600
Rationale: "local value of 6 = 6 x 100 = 600 place value of 6 = 6 there fore = 6 x 600 = 3600 e"
Answer: e
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 18 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 25 , b ) $ 26 , c ) $ 27 , d ) $ 28 , e ) $ 29
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 18 ) = 0.8 x x = 1.2 ( 18 ) / 0.8 = 1.5 ( 18 ) = $ 27 the answer is c ."
Answer: c
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 47 kg , then the weight of b is :
Options: a ) 39 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 47 x 2 ) = 94 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 174 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 39 . b ’ s weight = 39 kg . answer : a"
Answer: a
Problem: 6 women can do 75 units of work in 8 days by working 5 hrs / day . in how many days can 4 women do 30 units of work by working 8 hrs / day ?
Options: a ) 3 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 7 days
Rationale: 6 x 8 x 5 / 75 = 4 x 8 xa / 30 solve this for a then we get a = 3 days answer : a
Answer: a
Problem: the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 18 minutes is :
Options: a ) 9.5 , b ) 5.5 , c ) 7.5 , d ) 6.5 , e ) 5.1
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 18 / 60 ) ) km = 7.5 km . answer : c"
Answer: c
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 14 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 138 % , e ) 145 %
Rationale: "since michelle earns 14 % interest compounded semiannually , then she earns 7 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 7 % * 5 = 35 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 35 % , only answer choice d fits . answer : d"
Answer: d
Problem: the average of the marks of 30 students in a class is 45 . if the marks of each student are doubled , find the new average ?
Options: a ) 85 , b ) 77 , c ) 33 , d ) 90 , e ) 75
Rationale: "sum of the marks for the 30 students = 30 * 45 = 1350 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1350 * 2 = 2700 . so , the new average = 2700 / 30 = 90 . answer : d"
Answer: d
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 25 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 33 %
Rationale: "lets assume that candidate got 25 % votes and total votes is 100 . candidate won = 25 remaining = 75 to get 50 % , candidate requires 25 votes from 100 which is 25 % and 25 votes from 75 . 25 / 75 = 33.33 % which is approx 33 % . hence the answer is e"
Answer: e
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 100 shares of the company ' s stock ?
Options: a ) $ 92 , b ) $ 96 , c ) $ 52 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 100 - - > $ 52 answer is c"
Answer: c
Problem: the price of precious stone is directly proportional to square of its weight . what will be the loss incurred if a stone weighing 28 gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15 : 13 ?
Options: a ) no loss , b ) 10,000 , c ) 28,000 , d ) 9,500 , e ) 14,000
Rationale: x = 28000 / 28 ^ 2 = 35.71 cost of 15 g = 35.71 * 15 ^ 2 = 8035.714 cost of 13 g = 35.71 * 13 ^ 2 = 6035.714 total cost = 14071.428 loss = 28000 - 14071.428 = 13928.5 = 14000 answer : e
Answer: e
Problem: roy is now 6 years older than julia and half of that amount older than kelly . if in 4 years , roy will be twice as old as julia , then in 4 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 90 , d ) 96 , e ) 108
Rationale: r = j + 6 = k + 3 r + 4 = 2 ( j + 4 ) ( j + 6 ) + 4 = 2 j + 8 j = 2 r = 8 k = 5 in 4 years ( r + 4 ) ( k + 4 ) = 12 * 9 = 108 the answer is e .
Answer: e
Problem: what is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad
Options: a ) 814 , b ) 256 , c ) 3258 , d ) 896 , e ) 745
Rationale: "explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = ( 41 x 41 ) cm ^ 2 . required number of tiles = ( 1517 x 902 / 41 * 41 ) = 814 . answer : a"
Answer: a
Problem: x starts a business with rs . 45000 . y joins in the business after 4 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 3 , d ) 3 : 1 , e ) 9 : 4
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 8 = 45 ã — 12 : 30 ã — 8 = 3 ã — 12 : 2 ã — 8 = 9 : 4 answer : option e"
Answer: e
Problem: a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 38,000 commission , how many machines did she sell ?
Options: a ) 90 , b ) 103 , c ) 105 , d ) 115 , e ) 120
Rationale: "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 38000 - 30000 = 8000 so 20 more machines . . total = 120 machines imo e . . ."
Answer: e
Problem: a certain city with a population of 192,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 16,000 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 192 k x = 16,000 answer : b"
Answer: b
Problem: the mean of 50 observations was 36 . it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 39.1 , e ) none of these
Rationale: "solution correct sum = ( 36 × 50 + 48 - 23 ) = 1525 . ∴ correct mean = 1825 / 50 = 36.5 answer c"
Answer: c
Problem: there are 750 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 750 . hence , we have m + f = 750 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 750 / 3 = 250 solving the three equations yields the solution f = 250 , m = 500 , and d = 250 . the number of female democratic participants equals half the female participants equals 250 / 2 = 125 . answer : c"
Answer: c
Problem: in 2 triangle , the ratio of the areas is 4 : 3 and that of their heights is 3 : 4 . find the ratio of their bases ?
Options: a ) 10 : 8 , b ) 11 : 8 , c ) 16 : 9 , d ) 17 : 19 , e ) 17 : 10
Rationale: "given a 1 / a 2 = 4 / 3 , h 1 / h 2 = 3 / 4 also , we know that a 1 / a 2 = ( 1 / 2 × b 1 × h 1 ) / ( 1 / 2 × b 2 × h 2 ) on substituting in above equation , we get b 1 / b 2 = 16 / 9 therefore b 1 : b 2 = 16 : 9 c"
Answer: c
Problem: in what ratio must water be mixed with milk to gain 16 2 / 3 % on selling the mixture at cost price ?
Options: a ) 1 : 9 , b ) 1 : 1 , c ) 1 : 2 , d ) 1 : 6 , e ) 1 : 5
Rationale: required ratio is cheaper quantity : dearer quantity = ( d - m ) : ( m - c ) answer with explanation : step i ) let c . p of 1 litre of mild be rs . 1 and s . p of 1 litre of mild be rs . 1 gain = 50 / 3 per cent  c . p of 1 litre of mixture =              1 3 50 100 100 x = re . 100 x 3 / 350 x 1 = 6 / 7 ( mean price ) step ( ii ) by the rule of allegation i . c . p of 1 liter of water = 0 ii . c . p of 1 liter of milk = 1 iii . mean price ( p ) = 6 / 7 iv . d – m = 1 – 6 / 7 = 1 / 7 v . m – c = 6 / 7 - 0 = 6 / 7  ratio of water and milk = 1 / 7 : 6 / 7 = 1 : 6 answer : d
Answer: d
Problem: 9 friends decided to divide the hotel bill evenly . if the bill was $ 124.15 dollars , how much money did they pay if 1 cent is the smallest unit ?
Options: a ) $ 124.11 , b ) $ 124.12 , c ) $ 124.13 , d ) $ 124.14 , e ) $ 124.15
Rationale: this is equivalent to finding the first number that is divisible by 9 that occurs after 12415 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 12415 = 13 and 9 is divisible by 9 . hence , we need to remove 4 to this number for it to be divisible by 9 correct option : a
Answer: a
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 36 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 36 . . 4 x + 12 = 36 . . x = 6 . . ans = x + 4 = 6 + 4 = 10 answer e"
Answer: e
Problem: in a room with 8 people , 5 people have exactly 1 friend in the room and 4 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 25 / 28
Rationale: "( 5 / 8 ) ( 6 / 7 ) + ( 4 / 8 ) ( 5 / 7 ) if you choose one of the 5 with one other friend , then you have a 6 / 7 chance of not picking their friend 2 nd . if you choose one of the 4 with 2 friends , you have a 5 / 7 chance of not picking one of their friends second . add them up . 30 / 56 + 20 / 56 50 / 56 = 25 / 28 e . 25 / 28"
Answer: e
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 2000 resolutions ?
Options: a ) 1187 m , b ) 1704 m , c ) 2816 m , d ) 2827 m , e ) 2897 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2000 resolutions . = 2000 * 2 * 22 / 7 * 22.4 = 281600 cm = 2816 m answer : c"
Answer: c
Problem: find the smallest number which should be multiplied with 560 to make it a perfect square .
Options: a ) 60 , b ) 55 , c ) 45 , d ) 25 , e ) 35
Rationale: "560 = 2 * 2 * 2 * 2 * 7 * 5 required smallest number = 7 * 5 = 35 35 is the smallest number which should be multiplied with 560 to make it a perfect square . answer : e"
Answer: e
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 300 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 300 envelopes they will take 300 / 60 mins . i . e . , 5 mins . answer : b"
Answer: b
Problem: the sum of first 45 natural numbers is ?
Options: a ) 1030 , b ) 1034 , c ) 1035 , d ) 1037 , e ) 1040
Rationale: "let sn = ( 1 + 2 + 3 + . . . + 45 ) . this is an a . p . in which a = 1 , d = 1 , n = 45 . sn = n [ 2 a + ( n - 1 ) d ] = 45 x [ 2 x 1 + ( 45 - 1 ) x 1 ] = 45 x 46 = ( 45 x 23 ) 2 2 2 = 45 x ( 20 + 3 ) = 45 x 20 + 45 x 3 = 900 + 135 = 1035 . c )"
Answer: c
Problem: vehicle x is 22 miles ahead of vehicle y , which is traveling the same direction along the same route as vehicle x . if vehicle x is traveling at an average speed of 36 miles per hour and vehicle y is traveling at an average speed of 45 miles per hour , how long will it take vehicle y to overtake and drive 23 miles ahead of vehicle x ?
Options: a ) 5 hours , b ) 7 hours 20 minutes , c ) 4 hours , d ) 3 hours 45 minutes , e ) 2 hours 30 minutes
Rationale: relative speed = 45 - 36 = 9 miles per hour dist required = 22 + 23 = 45 miles time taken to overtake = 45 / 9 = 5 hours . a is the answer .
Answer: a
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 5 , 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 ) 2400
Rationale: "sugar : flour = 5 : 5 = 10 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 10 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 10 x = 2400 answer : e ."
Answer: e
Problem: the average weight of 8 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?
Options: a ) 94 kg , b ) 85 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 3 ) kg = 24 kg . weight of new person = ( 70 + 24 ) kg = 94 kg . answer : a"
Answer: a
Problem: a worker is paid a regular rate of rs . 10 for completing a survey . the worker completes 50 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 30 % higher than her regular rate . if she completed 35 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 605 , b ) 505 , c ) 105 , d ) 100 , e ) 200
Rationale: "earning 35 surveys using her cell phone = 13 * 35 = 455 balance 15 surveys = 10 x 15 = 150 total = 455 + 150 = 605 answer : a"
Answer: a
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 10 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 9060 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 10 = rs . 9060 answer : a"
Answer: a
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 7 days . b can do the work alone in ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 42 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 7 6 / x = 1 / 7 = > x = 42 so , b takes 21 hours to finish the work . answer : d"
Answer: d
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 3 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 3 ( 9 horizontal dots and 3 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 3 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 2 c 1 , ( 3 - 1 = 2 as 1 vertical dot is already occupied by a ) . 9 c 1 * 3 c 1 * 8 c 1 * 2 c 1 = 432 . answer : b ."
Answer: b
Problem: 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 ) 153200 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 117600
Rationale: "perimeter = distance covered in 7 min . = 12000 x 7 m = 1400 m . 60 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 . e"
Answer: e
Problem: a man can swim in still water at 4.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.0 , b ) 1.9 , c ) 1.6 , d ) 1.5 , e ) 1.1
Rationale: "m = 4.5 s = x ds = 4.5 + x us = 4.5 + x 4.5 + x = ( 4.5 - x ) 2 4.5 + x = 9 - 2 x 3 x = 4.5 x = 1.5 answer : d"
Answer: d
Problem: 0.99998 + 0.11112 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.1111 , e ) 1.111
Rationale: "0.99998 + 0.11112 = 0.99998 + 0.1111 + 0.00002 = ( 0.99998 + 0.00002 ) + 0.1111 = 1 + 0.1111 = 1.1111 d"
Answer: d
Problem: there are 2 red chips and 3 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ b _ b so . . 5 ! / number of repeated letters ( 2 ! ) ( 3 ! ) = 10 ans : e"
Answer: e
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 700 m ?
Options: a ) 148.75 m , b ) 127.5 m . , c ) 122.2 m , d ) 222.9 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 700 m , the number of meters by which a beats c = ( 700 * 212.5 ) / 1000 = 148.75 m . answer : a"
Answer: a
Problem: ifaequals the sum of the even integers from 2 to 120 , inclusive , andbequals the sum of the odd integers from 1 to 119 , inclusive , what is the value of a - b ?
Options: a ) 60 , b ) 10 , c ) 19 , d ) 20 , e ) 21
Rationale: "this is a solution from beatthegmat : even numbers : ( 120 - 2 ) / 2 + 1 = 60 even integers . ( 120 + 2 ) / 2 = 61 is the average of the even set . sum = avg * ( # of elements ) = 61 * 60 = 3660 = a odd numbers : ( 119 - 1 ) / 2 + 1 = 60 odd integers . ( 119 + 1 ) / 2 = 60 is the average of the odd set . sum = avg * ( # of elements ) = 60 * 60 = 3600 = b a - b = 3660 - 3600 = 60 . answer : a"
Answer: a
Problem: the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 10 more than the number who did not , and if receipts for registration and lunch totaled $ 61720 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 1,300 , d ) 500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 10 more than the number who did not . that means , total number of people who registered and paid for lunch = 10 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 10 + x ) = 720 + 72 x now , total amount received was 61,720 . thus , from the above data , 50 x + 720 + 72 x = 61720 122 x = 61720 - 720 122 x = 61000 x = 500 . hence the correct ans is d"
Answer: d
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 7 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 63.84 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 93 / 100 ) = 59.375 mp = 63.84 answer : a"
Answer: a
Problem: in may mrs lee ' s earnings were 50 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 55 , b ) 56 , c ) 34 , d ) 78 , e ) 23
Rationale: lets say the family income is 100 in may , lee earned 50 family income is 50 in june , lee earned 20 % more than may , so it is ( 50 + 20 * 50 / 100 = 60 ) family income is same 50 in june lee ' s income percent is 60 * 100 / 110 ~ 55 ans is a
Answer: a
Problem: what is 30 % of 80 ?
Options: a ) 24 , b ) 66 , c ) 367 , d ) 28 , e ) 267
Rationale: "30 % of 80 = 30 / 100 × 80 = ( 30 × 80 ) / 100 = 2400 / 100 = 24 answer : a"
Answer: a
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 69 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "there are 6 books less ( 75 - 69 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 30 answer b"
Answer: b