regisss/math_qa huggingface dataset:
Problem: julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if julie ' s savings by the end of the year from these monthly savings were 4 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 5 / 3 , b ) 3 / 9 , c ) 3 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: let julie ' s monthly savings = s julie ' s monthly pay = p julie ' s monthly expenditure = p - s julie ' s savings by the end of the year from these monthly savings were four times the amount she spent per month 12 s = 4 * ( p - s ) = > 3 s = p - s = > p = 4 s julie ' s monthly expenditure = p - s = 4 s - s = 3 s fraction of her salary that julie spent each month = 3 s / 4 s = p - s / p = 3 / 4 . answer is e
Answer: e
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 2 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 3 answer : c"
Answer: c
Problem: calculate the amount that an investor needs to be invest to earn $ 441 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 7 % compounded semi - annually ?
Options: a ) 6209 , b ) 6200 , c ) 6799 , d ) 6199 , e ) 6685
Rationale: the approach is substitution , our interest requirement is $ 441 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields $ 441 in 12 months 6200 yielded $ 441 using the formula a = p ( 1 + r / n ) nt hence answer is b
Answer: b
Problem: how many positive integers less than 6,000 are there in which the sum of the digits equals 5 ?
Options: a ) 65 , b ) 62 , c ) 61 , d ) 56 , e ) 58
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . d"
Answer: d
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 1 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 124545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 120000 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 1 x metres . then , 2 ( 3 x + 1 x ) = 1600 or x = 200 . length = 600 m and breadth = 200 m . area = ( 600 x 200 ) m 2 = 120000 m e"
Answer: e
Problem: the average ( arithmetic mean ) of 8 numbers is 8 . if 4 is added from each of 5 of the numbers , what is the new average ?
Options: a ) 4.5 , b ) 8.9 , c ) 10.5 , d ) 4.5 , e ) 5.6
Rationale: sum of 8 numbers = 8 * 8 = 64 if 4 is added from each of five of the numbers , we added 4 * 5 = 20 from the total sum sum of 8 number after adding 4 from each of five of the numbers = 64 + 20 = 84 new average = 84 / 8 = 10.5 answer c
Answer: c
Problem: list k consists of 10 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = a = 5 if least = - 3 , then largest = 6 range = 6 - 1 = 5"
Answer: a
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "total number of apples = 280 let the cost price be x selling price at 20 % profit = 1.2 x selling price at 30 % profit = 1.3 x profit % = ( ( sp - cp ) / cp ) * 100 profit % = ( ( 2 / 5 ) * 280 * 1.2 x + ( 3 / 5 ) * 280 * 1.3 x - 280 x ) / 280 x * 100 = ( 1 / 5 * ( 2.4 + 3.9 ) - 1 ) * 100 = ( 6.3 - 5 ) * 20 = 26 % answer : c"
Answer: c
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 14 per day , and a kayak rental costs $ 15 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 288 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be the number of canoes . then 2 x / 3 is the number of kayaks . 14 x + ( 2 x / 3 ) * 15 = 288 14 x + 10 x = 288 24 x = 288 x = 12 ( canoes ) 2 x / 3 = 8 ( kayaks ) there were 12 - 8 = 4 more canoes rented out . the answer is b .
Answer: b
Problem: positive integers from 1 to 45 , inclusive are placed in 5 groups of 9 each . what is the highest possible average of the medians of these 5 groups ?
Options: a ) 25 , b ) 31 , c ) 15 , d ) 26 , e ) 23
Rationale: answer we need to maximize the median in each group in order to maximize the average of all the medians . the highest possible median is 41 as there should be 4 numbers higher than the median in a group of 9 . so , if we have a group that has a , b , c , d , 41 , 42 , 43 , 44 , 45 , the median will be 41 . in this set , it is essential not to expend any more high values on a , b , c , or d as these do not affect the median . the median of a group that comprises 1 , 2 , 3 , 4 , 41 , 42 , 43 , 44 , 45 will be 41 . the next group can be 5 , 6 , 7 , 8 , 36 , 37 , 38 , 39 , 40 . the median will be 36 . extrapolating the findings in the two sets listed above , to maximize medians in all the 5 groups , the medians of the 5 groups will have to be 21 , 26 , 31 , 36 and 41 . the average of the highest possible medians will be the average of these 5 numbers = 31 . answer b
Answer: b
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 40 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 40 / 100 ) * 300 = 100 + 120 = 220 % comission = ( 220 / 800 ) * 100 = 27.5 ~ 28 % answer is e"
Answer: e
Problem: a salt manufacturing company produced a total of 5000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 180 , b ) 185 , c ) 190 , d ) 195 , e ) 200
Rationale: "total production of salt by the company in that year = 5000 + 5100 + 5200 + . . . . + 6100 = 66600 . average monthly production of salt for that year = 66600 / 365 = 185 answer : b"
Answer: b
Problem: the average weight of 9 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 88.5 , e ) 89.5
Rationale: "total increase in weight = 9 × 2.5 = 22.5 if x is the weight of the new person , total increase in weight = x − 65 = > 22.5 = x - 65 = > x = 22.5 + 65 = 87.5 answer : c"
Answer: c
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 5 miles per hour for 3 hours . how many miles in total did she walk ?
Options: a ) 53 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 3 hours - 15 miles total 18 + 20 + 15 = 53 answer : option a ."
Answer: a
Problem: a can do a job in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 5 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 5 days work = 7 / 60 * 5 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is d"
Answer: d
Problem: how many zeros are the end of 380 ! ?
Options: a ) 90 , b ) 91 , c ) 94 , d ) none , e ) 95
Rationale: 380 ! has 380 / 5 + 380 / 5 ^ 2 + 380 / 5 ^ 3 = 76 + 15 + 3 = 94 trailing zeros ( take only the quotient into account ) . answer : c .
Answer: c
Problem: find the least number which when divided by 38 and 3 leaves a remainder of 1 in each case .
Options: a ) 107 , b ) 109 , c ) 111 , d ) 113 , e ) 115
Rationale: "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 38 , 3 ) + 1 = 115 . answer : e"
Answer: e
Problem: in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the seventh row ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d .
Answer: d
Problem: q ' = 3 q - 3 , what is the value of ( 5 ' ) ' ?
Options: a ) 96 , b ) 108 , c ) 120 , d ) 132 , e ) 144
Rationale: "( 5 ' ) ' = ( 3 * 5 - 3 ) ' = 12 ' = 12 * 12 - 12 = 132 answer d"
Answer: d
Problem: a person can row at 9 kmph and still water . he takes 3 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 54 , e ) 16
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 3.5 = > x / 10 + x / 8 = 7 / 2 = > ( 4 x + 5 x ) / 40 = 7 / 2 = > x = 16 km . answer : e"
Answer: e
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 210 the other is
Options: a ) 330 , b ) 300 , c ) 270 , d ) 250 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 210 = 330 answer is a ."
Answer: a
Problem: the smallest number when increased by ` ` 1 ` ` is exactly divisible by 12 , 18 , 24 , 32 and 40 is :
Options: a ) 1439 , b ) 1440 , c ) 1459 , d ) 1449 , e ) 1500
Rationale: lcm = 1440 1440 - 1 = 1439 answer : a
Answer: a
Problem: if ( 2 ^ 17 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 17
Rationale: "given 2 ^ 17 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 17 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans e on comparing the power of 2 = > m = 17"
Answer: e
Problem: of the 720 students at a certain university , 25 percent are seniors . if x seniors were to graduate early and leave the university and no additional students entered or left the university , what value of x would reduce the number of seniors at the university to 20 percent ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 48
Rationale: sol : 180 - x = 20 % of ( 720 - x ) 4 x = 180 x = 45 answer : d
Answer: d
Problem: from given equation find the value of x : 2 x ² + 9 x − 5
Options: a ) 1 / 2 , b ) 1 , c ) 3 , d ) 4 , e ) 5
Rationale: that quadratic is factored as follows : 2 x ² + 9 x − 5 = ( 2 x − 1 ) ( x + 5 ) . lesson 17 . now , it is easy to see that the second factor will be 0 when x = − 5 . as for the value of x that will make 2 x − 1 = 0 , we must solve that little equation . ( lesson 9 . ) we have : 2 x = 1 x = 1 2 the solutions are : x = 1 / 2 or − 5 a
Answer: a
Problem: a can do a job in 15 days and b in 20 days . if they work on it together for 3 days , then the fraction of the work that is left is ?
Options: a ) 2 / 15 , b ) 8 / 15 , c ) 13 / 20 , d ) 1 / 12 , e ) 6 / 13
Rationale: a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 3 days work = 7 / 60 * 3 = 7 / 20 remaining work = 1 - 7 / 20 = 13 / 20 answer is c
Answer: c
Problem: how many positive integers between 100 and 500 are there such that they are multiples of 19 ?
Options: a ) 10 , b ) 15 , c ) 21 , d ) 18 , e ) 19
Rationale: multiples of 19 = 114 , 133,152 , - - - - - , 494 number of multiples of 19 = > 494 - 114 / 19 + 1 = 21 answer is c
Answer: c
Problem: p says to q ` ` i am thrice as old as you were when i was as old as you are ' ' . if the sum of their present age is 100 years , then the present age of q ?
Options: a ) 35.5 , b ) 36.5 , c ) 37.5 , d ) 38.5 , e ) 39.5
Rationale: let the present age of q be x the age of q years back ( to be defined ) is x / 3 as the age of p will be x by then . years passed = x - x / 3 = 2 x / 3 ( subtracting age of q ) so p acurrent age is x + 2 x / 3 and q current age is x adding them to 100 we get x = 37.5 answer : c
Answer: c
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 15 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . in the next 15 minutes , sam rides 3 km so sam will be 1 km ahead . it will take annie 20 minutes to catch sam . the answer is a ."
Answer: a
Problem: what percent of 75 is 45 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 60 %
Rationale: "75 * x / 100 = 45 x = 4 * 45 / 3 x = 60 ans : e"
Answer: e
Problem: a car was driving at 50 km / h for 30 minutes , and then at 90 km / h for another 40 minutes . what was its average speed ?
Options: a ) 102 , b ) 80 , c ) 75 , d ) 70 , e ) 65
Rationale: "driving at 50 km / h for 30 minutes , distance covered = 50 * 1 / 2 = 25 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 85 / 5 / 6 = 102 km / h answer : a"
Answer: a
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent w of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march w = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction r of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose r = 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Problem: 1234 + 123 + 12 + x = 1221 . find the value of x .
Options: a ) 10 , b ) 148 , c ) 12 , d ) 13 , e ) 189
Rationale: "x = 1234 + 123 + 12 - 1221 x = 148 correct answer : b"
Answer: b
Problem: in 110 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22 m , d ) 9 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 110 / 45 x 9 m = 22 m . a beats b by 20 metres . answer : option c"
Answer: c
Problem: at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 16.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 13.0 , b ) 13.3 , c ) 13.6 , d ) 13.9 , e ) 14.2
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 16.9 x ^ 2 = 1.69 x = 1.3 at 4 : 00 pm , the amount of bacteria was 10 ( 1.3 ) = 13 grams . the answer is a ."
Answer: a
Problem: a certain tax rate is $ 65 per $ 100.00 . what is the rate , expressed as a percent ?
Options: a ) 82 % , b ) 6.5 % , c ) 0.82 % , d ) 65 % , e ) 0.0065 %
Rationale: here in question it is asking $ 65 is what percent of $ 100 . suppose $ 65 is x % of 100 means 100 * ( x / 100 ) = 65 hence x = 65 so answer is d
Answer: d
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 27 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 457 km , b ) 444 km , c ) 547 km , d ) 645 km , e ) 576 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 27 + 21 = 48 t = 12 d = 48 * 12 = 576 answer : e"
Answer: e
Problem: what is the sum of the multiples of 4 between 53 and 145 inclusive ?
Options: a ) 2000 , b ) 2200 , c ) 2300 , d ) 2450 , e ) 2500
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 53 and 145 , the smallest multiple of 4 is 56 and largest = 144 . . average = ( 56 + 144 ) / 2 = 100 . . total numbers = ( 144 - 56 ) / 4 + 1 = 22 + 1 = 23 . . sum = 23 * 100 = 2300 ans c"
Answer: c
Problem: the simple interest on a certain sum of money at the rate of 4 % p . a . for 5 years is rs . 1680 . at what rate of interest the same amount of interest can be received on the same sum after 4 years ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: s . i . = 1680 , r = 4 % t = 5 years principal = ( 100 * 1680 ) / ( 5 * 4 ) = 8400 so p = 8400 rate = ( 100 * 1680 ) / ( 8400 * 4 ) = 5 % answer : a
Answer: a
Problem: the edge of a cube is 6 a cm . find its surface ?
Options: a ) 216 a 2 , b ) 24 a 4 , c ) 24 a 1 , d ) 24 a 2 , e ) 24 a 7
Rationale: "6 a 2 = 6 * 6 a * 6 a = 216 a 2 answer : a"
Answer: a
Problem: if ( 1 / 2 ) ^ 25 ( 1 / 81 ) ^ k = 1 / 18 ^ 25 , then k =
Options: a ) 8 , b ) 12.5 , c ) 16 , d ) 24 , e ) 36
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 25 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 25 ( 2 ^ 25 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 25 ( 2 ^ 25 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 25 ) . ( 3 ^ 2 ) ^ 25 hence 4 k = 50 k = 12,5 answer b i hope it ' s quite clear"
Answer: b
Problem: a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 4 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 100 , b ) 150 , c ) 140 , d ) 120 , e ) 110
Rationale: "a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 100 ) . 750 = 400 + x + 200 x = 150 b"
Answer: b
Problem: 180 metres long yard , 11 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 18 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "11 trees have 10 gaps between them , required distance ( 180 / 10 ) = 18 a"
Answer: a
Problem: a can do a work in 4 days . b can do the same work in 6 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 550,450
Rationale: "ratio of their works a : b = 4 : 6 ratio of their wages a : b = 3 : 2 a ' s share = ( 3 / 5 ) 1000 = 600 b ' s share = ( 2 / 5 ) 1000 = 400 correct option is a"
Answer: a
Problem: if it is assumed that 70 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 428.5 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 70 % = 300 / 0.7 = 428.5 option b"
Answer: b
Problem: the difference between a positive proper fraction and its reciprocal is 9 / 20 . the fraction is ?
Options: a ) 4 / 5 , b ) 4 / 7 , c ) 5 , d ) 5 / 7 , e ) none
Rationale: "let the required fraction be x . then 1 - x = 9 x 20 1 - x 2 = 9 x 20 20 - 20 x 2 = 9 x 20 x 2 + 9 x - 20 = 0 20 x 2 + 25 x - 16 x - 20 = 0 5 x ( 4 x + 5 ) - 4 ( 4 x + 5 ) = 0 ( 4 x + 5 ) ( 5 x - 4 ) = 0 x = 4 / 5 option a"
Answer: a
Problem: a man can swim in still water at 1.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 0.5 , c ) 1.1 , d ) 1.5 , e ) 1.9
Rationale: "m = 1.5 s = x ds = 1.5 + x us = 1.5 + x 1.5 + x = ( 1.5 - x ) 2 1.5 + x = 3 - 2 x 3 x = 1.5 x = 0.5 answer : b"
Answer: b
Problem: by using the numbers 1 , 2 , 3 , 7 and 9 only once , how many 5 digit numbers can be made that are divisible by 25 ?
Options: a ) 5 , b ) 4 , c ) not possible , d ) 3 , e ) 6
Rationale: a number to be divisible by 25 must end with 00 , 25 , 50 , or 75 . so , not possible . answer : c .
Answer: c
Problem: double of quarter of 5 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.0005 , c ) 0.025 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 5 % = 0.025 answer : c"
Answer: c
Problem: a car is purchased on hire - purchase . the cash price is $ 25 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 500 , b ) $ 504 , c ) $ 505 , d ) $ 560 , e ) $ 600
Rationale: "explanation : cash price = $ 25 000 deposit = 10 % ã — $ 25 000 = $ 2500 loan amount = $ 25000 â ˆ ’ $ 2500 number of payments = 60 = $ 22500 i = p * r * t / 100 i = 13500 total amount = 22500 + 13500 = $ 36000 regular payment = total amount / number of payments = 600 answer : e"
Answer: e
Problem: the average salary of 15 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 15,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 19,100 , e ) $ 12,300
Rationale: "total salary . . . 15 * 20 k = 300 k 5 emp @ 25 k = 125 k 4 emp @ 15 k = 60 k remaing 6 emp sal = 300 k - 125 k - 60 k = 115 k average = 115 k / 6 = 19100 ans : d"
Answer: d
Problem: a jar contains 5 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 21 , c ) 4 / 21 , d ) 3 / 7 , e ) 1 / 2
Rationale: p ( 1 st black , 2 nd white ) = 5 / 7 * 2 / 6 = 10 / 42 ; p ( 1 st white , 2 nd black ) = 2 / 7 * 5 / 6 = 10 / 42 . p = 10 / 42 + 10 / 42 = 20 / 84 = 10 / 42 = 5 / 21 answer : b .
Answer: b
Problem: there are 2 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 7 / 9 , e ) 4 / 10
Rationale: "w = m + 2 w + m = 16 m + 2 + m = 16 2 m = 14 m = 7 w = 9 ratio : 7 : 9 ans : d"
Answer: d
Problem: the regular price per can of a certain brand of soda is $ 0.40 . if the regular price per can is discounted 15 percent when the soda is purchased in 24 - can cases , what is the price of 100 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 34 , e ) $ 28.80
Rationale: "the discounted price of one can of soda is ( 0.85 ) ( $ 0.40 ) , or $ 0.34 . therefore , the price of 72 cans of soda at the discounted price would be ( 100 ) ( $ 0.34 ) = 34 answer : d ."
Answer: d
Problem: a lady has fine gloves and hats in her closet - 18 blue , 32 red , and 25 yellow . the lights are out and it is totally dark . in spite of the darkness , she can make out the difference between a hat and a glove . she takes out an item out of the closet only if she is sure that if it is a glove . how many gloves must she take out to make sure she has a pair of each color ?
Options: a ) 50 , b ) 8 , c ) 60 , d ) 42 , e ) 32
Rationale: in the first case the lady takes up 32 red colour then he takes up 24 y ( cause he should take up pair ) then he takes up 1 y + 1 blue then 2 blue ( cause to make sure he has a pair of each color in hand ) 32 + 24 + 2 + 2 = 60 answer : c
Answer: c
Problem: in a 2000 census , 51.27 % of the population are male , and 48.73 % are female . what is the ratio of men to every 100 women ?
Options: a ) 110 : 100 , b ) 105 : 100 , c ) 95 : 100 , d ) 85 : 100 , e ) 120 : 100
Rationale: the ratio of a to b , where a = the percent of males , and b = the percent of females . a = 51.27 b = 48.73 a : b = 51.27 : 48.73 so , 100 ( 5,127 / 4,873 ) : 100 giving a male to female ratio of 105.20 men for every 100 women . answer is b
Answer: b
Problem: the radius of a semi circle is 14 cm then its perimeter is ?
Options: a ) 32.8 , b ) 32.4 , c ) 72 , d ) 32.2 , e ) 32.9
Rationale: "diameter = 28 cm 1 / 2 * 22 / 7 * 28 + 28 = 72 answer : c"
Answer: c
Problem: a large field of 900 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 435 hectares . , b ) 425 hectares . , c ) 445 hectares . , d ) 415 hectares . , e ) 405 hectares .
Rationale: "let the areas of the parts be x hectares and ( 900 - x ) hectares . difference of the areas of the two parts = x - ( 900 - x ) = 2 x - 900 one - fifth of the average of the two areas = 1 / 5 [ x + ( 900 − x ) ] / 2 = 1 / 5 × ( 900 / 2 ) = 450 / 5 = 90 given that difference of the areas of the two parts = one - fifth of the average of the two areas = > 2 x - 900 = 90 = > 2 x = 990 ⇒ x = 990 / 2 = 495 hence , area of smaller part = ( 900 - x ) = ( 900 – 495 ) = 405 hectares . answer is e ."
Answer: e
Problem: a train passes a station platform in 60 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 420 m , c ) 168 m , d ) 197 m , e ) 691 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 36 = 15 = > x = 420 m answer : b"
Answer: b
Problem: 15 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required ?
Options: a ) 10 days , b ) 11 days , c ) 9 days , d ) 8 days , e ) 12 days
Rationale: "that is , 1 work done = 15 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 15 × 8 × 10 / 15 × 8 = 10 days a )"
Answer: a
Problem: a factory produces 4560 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1140 toys , b ) 2375 toys , c ) 3375 toys , d ) 4375 toys , e ) 5375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 4 days ) by 4 . 4560 / 4 = 1140 toys correct answer a"
Answer: a
Problem: the sum of four consecutive even numbers is 140 . what would be the largest number ?
Options: a ) 33 , b ) 38 , c ) 70 , d ) 123 , e ) 12
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x + 1 ) = 38 . answer : b"
Answer: b
Problem: a batsman makes a score of 82 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 34
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 82 = total runs scored in 17 innings = > 16 ( x - 3 ) + 82 = 17 x = > 16 x - 48 + 82 = 17 x = > x = 34 answer is e ."
Answer: e
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party a . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "assume the total pool of registered voters = 100 , so 35 of the country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and 20 had a favorable impression only of party a let x = # of voters with a favorable impression of both parties let 2 x = # of voters with a favorable impression only of party b so unfavorable a and favorable b # of voters = 2 x - x = x 35 + x = number of unfavorable a 20 + 35 + x = 100 55 + x = 100 x = 45 answer : e"
Answer: e
Problem: the length of a rectangle is reduced by 30 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 42.8 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 30 * 100 ) / ( 100 - 30 ) = 42.8 % a"
Answer: a
Problem: what is the remainder if 7 ^ 4 is divided by 100 ?
Options: a ) 5 , b ) 4 , c ) 1 , d ) 2 , e ) 10
Rationale: "7 * 7 * 7 * 7 / 100 = 2401 / 100 = 24 reminder 1 answer : c"
Answer: c
Problem: how many positive factors do 120 and 80 have in common ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 120 and 80 is 40 number of factors of 40 = 8 answer : a"
Answer: a
Problem: find value of x : ( 422 + 404 ) ^ 2 − ( 4 × 422 × 404 ) = x .
Options: a ) 234 , b ) 267 , c ) 324 , d ) 356 , e ) 577
Rationale: given equation is in the form ( a + b ) 2 − 4 ab where a = 422 and b = 404 hence answer = ( a + b ) 2 − 4 ab = ( a − b ) 2 = ( 422 − 404 ) 2 = 182 = 324 c
Answer: c
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6400 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9357 , e ) s . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6400 1 = 6400 / 68.4 100 = ( 6400 * 100 ) / 68.4 = rs . 9357 . answer : option d"
Answer: d
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14080 ?
Options: a ) 3200 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 4096
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14080 ã — 16 / 55 = rs . 4096 . share of z in the profit is rs . 4096 . option e"
Answer: e
Problem: 6 ) a marketing firm determined that , of 160 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 40 , e ) e ) 5
Rationale: "80 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 120 = > 4 x = 20 = > x = 5 answer - e"
Answer: e
Problem: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 54 , how many more green disks than blue disks are in the bag ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 54 - - > x = 3 . g - b = 8 x - 3 x = 5 x = 15 . the answer is a ."
Answer: a
Problem: what will be the fraction of 6 %
Options: a ) 1 / 20 , b ) 3 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 6 * 1 / 100 = 3 / 50 . option b"
Answer: b
Problem: among 250 viewers interviewed who watch at least one of the 3 tv channels namely a , bc . 116 watch a , 127 watch c , while 107 watch b . if 90 watch exactly two channels . how many watch exactly one channel ?
Options: a ) 155 , b ) 160 , c ) 175 , d ) 190 , e ) 195
Rationale: 250 = n ( exactly 1 channel ) + n ( exactly 2 channels ) + n ( exactly 3 channels ) 250 = n ( exactly 1 channel ) + 90 + n ( exactly 3 channels ) let ' s find the value of n ( exactly 3 channels ) = x 250 = n ( a ) + n ( b ) + n ( c ) - n ( a and b ) - n ( b and c ) - n ( c and a ) + n ( a and b and c ) note that each of n ( a and b ) is the sum of ' number of people watching exactly two channels a and b ' and ' number of people watching all three channels ' . 250 = 116 + 127 + 107 - n ( exactly 2 channels ) - 3 x + x 250 = 116 + 127 + 107 - 90 - 2 x x = 25 250 = n ( exactly 1 channel ) + 90 + 25 n ( exactly 1 channel ) = 155 answer ( a )
Answer: a
Problem: some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "let total paint = 1 let amount replaced = x 50 ( 1 - x ) + 25 x = 30 x = 4 / 5 answer : e"
Answer: e
Problem: 9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height . what is the diameter of each sphere ?
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 9 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 12 = 64 cm ^ 3 r = 4 cm d = 8 cm the answer is c ."
Answer: c
Problem: working simultaneously and independently at an identical constant rate , 6 machines of a certain type can produce a total of x units of product p in 5 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 4 x units of product p in 10 days ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 18
Rationale: "the rate of 6 machines is rate = job / time = x / 5 units per day - - > the rate of 1 machine 1 / 6 * ( x / 5 ) = x / 30 units per day ; now , again as { time } * { combined rate } = { job done } then 10 * ( m * x / 30 ) = 4 x - - > m = 12 . answer : c ."
Answer: c
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 220 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "answer d ( a + b ) ( a - b ) = 220 6 cases for ( a + b ) , ( a - b ) 220 , 1 110 , 2 55 , 4 44,5 22 , 10 20,11 answer d"
Answer: d
Problem: a boat goes 100 km downstream in 4 hours , and 75 km upstream in 15 hours . the speed of the stream is ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 35 , e ) 15
Rationale: "100 - - - 10 ds = 25 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 25 - 5 ) / 2 = 10 kmph . answer : a"
Answer: a
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 10 ) ?
Options: a ) 0 , b ) 5 , c ) 2 , d ) 14 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 10 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , and - 10 now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 = 30 - 30 = 0 hence the correct answer choice is a ."
Answer: a
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 60,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 2 a * 1 + a * 5 ) / 6 = 7 a / 6 = 35000 answer is a . $ 35,000"
Answer: a
Problem: along a road lie an odd number of stones placed at intervals of 10 m . these stones have to be assembled around the middle stone . a person can carry only one stone at a time . a man carried out the job starting with the stone in the middle , carrying stones in succession , thereby covering a distance of 4.8 km . then the number of stones is
Options: a ) 35 , b ) 15 , c ) 29 , d ) 31 , e ) 29
Rationale: explanation : if he travels 10 m for the first stone he has to travel that dist back as well . . . so he travels 2 * 10 m dist for the first stone and so on . = > 2400 = 2 * ( 10 + 20 + 30 . . . . 10 n ) using formula for ap = > 2400 = 2 * n / 2 * ( 2 * 10 + ( n - 1 ) * 10 ) . = > 2400 = 10 n 2 + 10 n . on solving this , we get n = 15 as the positive root , so total numer of stones on both sides = 30 . and including the one which he was at = 31 . answer : d
Answer: d
Problem: 850 - ( 1500 ÷ ? ) × 8 / 15 = 770
Options: a ) a ) 31 , b ) b ) 10 , c ) c ) 15 , d ) d ) 26 , e ) e ) 17
Rationale: "explanation : = > 850 - ( 1500 ÷ ? ) × 8 / 15 = 770 = > 850 - 770 = ( 1500 ÷ ? ) × 8 / 15 = > 80 = ( 1500 ÷ ? ) × 8 / 15 = > 80 × 15 / 8 = ( 1500 ÷ ? ) = 150 = > 1 / ? = 150 / 1500 = 1 / 10 = > ? = 10 answer : option b"
Answer: b
Problem: the contents of two vessels containing copper and tin in the ratio 2 : 3 and 5 : 7 are mixed in the ratio 3 : 5 . the resulting mixture will have copper and tin in the ratio ?
Options: a ) 210 : 283 , b ) 312 : 433 , c ) 178 : 213 , d ) 197 : 283 , e ) 145 : 256
Rationale: the ratio of copper and tin the new vessel = ( 2 / 5 * 3 / 8 + 5 / 12 * 5 / 8 ) : ( 3 / 5 * 3 / 8 + 7 / 12 * 5 / 8 ) = 197 / 480 : 283 / 480 = 197 : 283 answer is d
Answer: d
Problem: a and b together can do a work in 8 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 24 days , e ) 25 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 8 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 8 ) - ( 1 / 12 ) = 24 days answer : option d"
Answer: d
Problem: what is the unit ’ s digit of 7 ^ 4
Options: a ) 3 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) therefore , last digit of 7 ^ 4 = 1 answer b"
Answer: b
Problem: x and y are positive integers . when x is divided by 15 , the remainder is 2 , and when x is divided by 10 , the remainder is 7 . when y is divided by 9 , the remainder is 5 , and when y is divided by 7 , the remainder is 2 . what is the least possible value of x * y ?
Options: a ) 389 , b ) 390 , c ) 388 , d ) 391 , e ) 392
Rationale: "when x is divided by 15 , the remainder is 2 : so , the possible values of x are : 2 , 17 , 32 , 47 , etc . when x is divided by 10 , the remainder is 7 : so , the possible values of x are : 7,17 . . . stop . since both lists include 17 , the smallest possible value of x is 17 . when y is divided by 9 , the remainder is 5 : so , the possible values of y are : 5 , 14 , 23,32 etc . when y is divided by 7 , the remainder is 2 : so , the possible values of y are : 2 , 9 , 16 , 23 . . . stop . since both lists include 23 , the smallest possible value of y is 23 since the smallest possible values of x and y are 17 and 23 respectively , the smallest possible value of x * y is 391 . so , d is the correct answer to the original question ."
Answer: d
Problem: what is the minimum percentage increase in the mean of set s { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %
Rationale: mean of s is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of s , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( 4 - 2 ) / 2 * 100 = 100 % . answer : d .
Answer: d
Problem: marla starts running around a circular track at the same time nick starts walking around the same circular track . marla completes 20 laps around the track per hour and nick completes 10 laps around the track per hour . how many minutes after marla and nick begin moving will marla have completed 4 more laps around the track than nick ?
Options: a ) 5 , b ) 8 , c ) 24 , d ) 15 , e ) 20
Rationale: "maria ' s rate - 20 laps per hour - - > 20 / 60 laps / min nick ' s rate - 10 laps per hour - - > 10 / 60 laps / min lets set equations : 20 / 60 * t = 4 ( since maria had to run 4 laps before nick would start ) 10 / 60 * t = 0 ( hick has just started and has n ' t run any lap yet ) ( 20 / 60 - 10 / 60 ) * t = 4 - 0 ( since nick was chasing maria ) t = 24 min needed maria to run 4 laps answer : c"
Answer: c
Problem: in a renowned city , the average birth rate is 6 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 129,500 , b ) 129,600 , c ) 129,700 , d ) 129,800 , e ) 129,900
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 6 - 3 = 3 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 3 = 129,600 . hence b ."
Answer: b
Problem: how many times in a day , are the hands of a clock in straight line but opposite in direction ?
Options: a ) 21 , b ) 22 , c ) 17 , d ) 26 , e ) 25
Rationale: b 22 the hands of a clock point in opposite directions ( in the same straight line ) 11 times in every 12 hours . ( because between 5 and 7 they point in opposite directions at 6 o ' clcok only ) . so , in a day , the hands point in the opposite directions 22 times .
Answer: b
Problem: add 11 % of 36 and 12 % of 64 .
Options: a ) 9.5 , b ) 10.5 , c ) 11.5 , d ) 12 , e ) 15
Rationale: "11 % of 36 + 12 % of 64 36 * 11 / 100 + 64 * 12 / 100 3.9 + 7.6 = 11.5 answer c"
Answer: c
Problem: if the cost price of 55 articles is equal to the selling price of 50 articles , then what is the percent profit ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 50 y = 55 x y = 1.1 x the answer is b ."
Answer: b
Problem: in a certain quiz that consists of 8 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 360 points , how many points is the third question worth ?
Options: a ) 39 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 8 x + 112 = 360 8 x = 248 x = 31 3 rd question = 31 + 8 = 31 + 8 = 39 answer a
Answer: a
Problem: line l passes through the points ( - 2,0 ) and ( 0 , a ) . line ll passes through the points ( 4,0 ) and ( 6,2 ) . what value of a makes the two lines parallel ?
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: find slopes first slope of l = ( a - 0 ) / ( 0 - ( - 2 ) ) = a / 2 slope of ll = ( 2 - 0 ) / ( 6 - 4 ) = 1 for l and ll to be parallel , their slopes must be equal a / 2 = 1 , a = 2 correct answer b
Answer: b
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 6 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 72 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 6 books / month = 72 books a year total number of books = 72 cs"
Answer: c
Problem: debony normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if debony averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ?
Options: a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45
Rationale: debony normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d
Answer: d
Problem: if the average ( arithmetic mean ) of a and b is 40 and the average of b and c is 60 , what is the value of c − a ?
Options: a ) 25 , b ) 40 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 80 ) b + c = 120 c - a = 40 b . 40"
Answer: b
Problem: a 6 - liter solution is 25 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 2.1 , b ) 2.4 , c ) 2.7 , d ) 3.0 , e ) 3.3
Rationale: "let x be the amount of pure alcohol required . 0.25 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.5 x = 3 liters the answer is d ."
Answer: d