regisss/math_qa huggingface dataset:
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 14 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: total distance = 14 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 10 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 10 / 10 = 1 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 1 = 4 + 4 = 8 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 8 / 4 = 2 hrs . . . answer a
Answer: a
Problem: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 2 / 5 of that total . what was the price of the basic computer ?
Options: a ) 1300 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 2 / 5 of that new total price : p = 2 / 5 * $ 3,000 = $ 1200 . plug this value in the first equation : c + 1200 = $ 2,500 - - > c = $ 1,300 . answer : a ."
Answer: a
Problem: in a lottery there are 20 prizes and 35 blanks . a lottery is drawn at random . what is the probability of getting a prize
Options: a ) 2 / 13 , b ) 4 / 11 , c ) 5 / 11 , d ) 6 / 11 , e ) 3 / 13
Rationale: "total draws = prizes + blanks = 20 + 35 = 55 probability of getting a prize = 20 / 55 = 4 / 11 correct option is b"
Answer: b
Problem: lloyd normally works 7.5 hours per day and earns $ 3.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 42.00 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 3.5 + 3 * 3.5 * 1.5 = 42 answer b"
Answer: b
Problem: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many e kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5
Answer: c
Problem: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 462 the other is
Options: a ) 330 , b ) 300 , c ) 270 , d ) 150 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 462 = 150 answer is d ."
Answer: d
Problem: a reduction of 22 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.82 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 22 / 100 ) = 22 - - - 10 ? - - - 1 = > rs . 2.2 100 - - - 78 ? - - - 2.2 = > rs . 2.82 answer : a"
Answer: a
Problem: a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit .
Options: a ) rs . 1200 , b ) rs . 1230 , c ) rs . 1260 , d ) rs . 1290 , e ) rs . 1270
Rationale: explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 951 / 140 = 105 / x ) = > x = 1260 answer is c
Answer: c
Problem: patanjali 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 the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: patanjali walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e
Answer: e
Problem: the current in a river is 10 mph . a boat can travel 50 mph in still water . how far up the river can the boat travel if the round trip is to take 5 hours ?
Options: a ) 120 , b ) 100 , c ) 96 , d ) 85 , e ) 150
Rationale: upstream speed = 50 - 10 = 40 mph downstream speed = 50 + 10 = 60 mph d / 40 + d / 60 = 5 hours solving for d we get d = 120 answer : a
Answer: a
Problem: 60 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33 , b ) 45 , c ) 26 , d ) 28 , e ) 19
Rationale: "explanation : let the two parts be ( 60 - x ) and x . then , 10 ( 60 - x ) + 22 x = 780 = > 12 x = 180 = > x = 15 . bigger part = ( 60 - x ) = 45 . answer : b ) 45"
Answer: b
Problem: the sum of two number is 25 and their difference is 13 . find their product .
Options: a ) 114 , b ) 104 , c ) 315 , d ) 350 , e ) 400
Rationale: "let the numbers be x and y . then , x + y = 25 and x - y = 13 . 4 xy = ( x + y ) 2 - ( x - y ) 2 = ( 25 ) 2 - ( 13 ) 2 = ( 625 - 169 ) = = 456 = > 114 answer a"
Answer: a
Problem: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 5 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 36 % , e ) 73.6 %
Rationale: fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,101 non transferred fiction novels = 4,407 percent of the remaining collection was fiction novels = 4,407 / ( 18360 - 6120 ) * 100 = > 36.004 . . . % hence answer will be ( d )
Answer: d
Problem: there is one 4 - digit whole number n , such that the last 4 digits of n 2 are in fact the original number n
Options: a ) 8476 , b ) 7376 , c ) 9376 , d ) 7378 , e ) 9466
Rationale: c 9376 looking at the last digit , the last digit must be either 0 , 1 , 5 or 6 . then looking at the last two digits , the last two digits must be either 0001 , 25 or 76 . then looking at the last three digits , the last three digits must be either 00001 , 625 or 376 . then looking at the last four digits , the last four digits must be either 0000001 , 0625 or 9376 . out of those , only 9376 is a 4 digit number
Answer: c
Problem: when two dice are tossed , what is the probability that the total score is a prime number ?
Options: a ) 1 / 6 , b ) 3 , c ) 5 / 12 , d ) 7 / 12 , e ) 9 / 12
Rationale: total number of outcomes possible = 36 probability of total score is a prime number = 15 p ( e ) = 15 / 36 = 5 / 12 answer : c
Answer: c
Problem: running at the same constant rate , 6 identical machines can produce a total of 420 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2800 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 420 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 420 x = ( 10 x 4 x 420 ) / ( 6 ) x = 2800 . answer : c"
Answer: c
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 5 days more ?
Options: a ) 2280 , b ) 2240 , c ) 2299 , d ) 2288 , e ) 2266
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 5 x * 5 = 760 * 20 x = 3040 760 - - - - - - - 2280 answer : a"
Answer: a
Problem: the ratio of the volumes of two cubes is 216 : 343 . what is the ratio of their total surface areas ?
Options: a ) 81 : 12 , b ) 31 : 36 , c ) 81 : 22 , d ) 8 : 19 , e ) 1 : 11
Rationale: "ratio of the sides = ³ √ 216 : ³ √ 343 = 6 : 7 ratio of surface areas = 62 : 72 = 31 : 36 answer : b"
Answer: b
Problem: the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ?
Options: a ) 43.0 , b ) 44.0 , c ) 43.5 , d ) 45.0 , e ) 42.0
Rationale: "100 * 100 = 10000 110 * 130 = 14300 - - - - - - - - - - 4300 10000 - - - - - - - 4300 100 - - - - - - - 43.00 answer a"
Answer: a
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 11 a . m . and travels towards b at 100 km / hr . another starts from b at 12 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 4 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 11 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 11 + 5 = 4 p . m . answer is d"
Answer: d
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 65 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 65 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 2 = 10 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : c ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . c"
Answer: c
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 15 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: for solving this type of tasks we can use such approach 15 / 3 = 5 15 / 3 ^ 2 = 1 and remainder and 3 ^ 3 is more than 15 so we stop on second exponent 5 + 1 = 6 so maximum value of k = 6 and answer is d
Answer: d
Problem: how many of the integers between 15 and 55 are even ?
Options: a ) 21 , b ) 20 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 15 to 55 is 40 numbers half of them is even . . which is 20 answer : b"
Answer: b
Problem: count the numbers between 10 - 99 which yield a remainder of 5 when divided by 8 and also yield a remainder of 1 when divided by 6 ?
Options: a ) one , b ) three , c ) two , d ) five , e ) four
Rationale: "answer = e ) four numbers between 10 - 99 giving remainder 5 when divided by 8 = 13 , 21 , 29 , 37 , 45 , 53 , 61 , 69 , 77 , 85 , 93 the above numbers giving remainder 1 when divided by 6 = 13 , 37 , 61 , 85 = 4"
Answer: e
Problem: a train 510 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 52 , c ) 26 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 510 + 140 = 650 m required time = 650 * 2 / 25 = 52 sec answer : b"
Answer: b
Problem: if ryan and smith car ratio is 5 : 8 . ryan bought 6 new car and smith bought 2 new car . now , smith has 18 car . what is their car ratio now ?
Options: a ) 5 : 4 , b ) 3 : 2 , c ) 8 : 9 , d ) 6 : 5 , e ) 7 : 5
Rationale: current no . of smith car = 8 x + 2 = 18,8 x = 16 , x = 2 . current car ratio = 10 + 6 / 18 = 16 / 18 = 8 : 9 . answer c
Answer: c
Problem: a ( 7 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 15 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 15 w ^ 3 = 7 ^ 2 + 15 w ^ 3 = 64 w = 4 answer b"
Answer: b
Problem: the timing of a college is from 12 p . m to 4.10 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 46 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 10 minutes = 250 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 250 â € “ 20 ) / 5 = 46 minutes answer c"
Answer: c
Problem: the grade point average of one third of the classroom is 45 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ?
Options: a ) 54 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: let n = total students in class total points for 1 / 3 class = 45 n / 3 = 15 n total points for 2 / 3 class = 60 * 2 n / 3 = 40 n total points for whole class = 15 n + 40 n = 55 n 63 n total class points / n total students = 55 grade point average for total class answer : b
Answer: b
Problem: 63 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 21 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 63 x 12 x 5 = 30 x 6 x x x = 21 hence , the number of days = 21 . answer : a"
Answer: a
Problem: marcella has 24 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 24 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 24 pairs of shoes minus the 5 ' destroyed ' pairs yields 19 pairs that still fulfill the requirements . answer : c"
Answer: c
Problem: the sum of the squares of three numbers is 138 , while the sum of their products take two at a time is 131 . find the sum ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 50 , e ) 40
Rationale: "formula is ( a + b + c ) ^ 2 = ( a ^ 2 ) + ( b ^ 2 ) + ( c ^ 2 ) + 2 ( ab + bc + ca ) = 138 + ( 2 * 131 ) the sum of the three numbers a + b + c = √ 400 = 20 answer is option c"
Answer: c
Problem: two trains are approaching each other at 60 mph each . the length of each train is 1 / 6 miles . when the two locomotives ( engines ) meet , how many seconds will it take for them to pass each other completely ?
Options: a ) 8 sec , b ) 11 sec , c ) 12 sec , d ) 10 sec , e ) 15 sec
Rationale: total distance to cover = 2 * ( 1 / 6 ) = 2 / 6 miles relative speed = 60 + 60 = 120 mph time taken = ( 2 / 6 ) / 120 * 3600 = 10 sec . answer : d
Answer: d
Problem: a courtyard is 25 meter long and 15 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 18750 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1500 / 20 × 10 ) = 18750 answer : c"
Answer: c
Problem: a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 70 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 75 , b ) 90 , c ) 120 , d ) 150 , e ) 180
Rationale: "70 % is 20 % - points above 50 % and 10 % - points below 80 % . thus the ratio of ` ` the first 60 games ' ' to ` ` remaining games ' ' is 1 : 2 . so the team played a total of 60 + 120 = 180 games . the answer is e ."
Answer: e
Problem: if k and w are the dimensions of a rectangle that has area 48 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) four , b ) three , c ) two , d ) five , e ) six
Rationale: "kw = 48 = 48 * 1 = 24 * 2 = 16 * 3 = 12 * 4 - - > k can take 4 values . answer : a"
Answer: a
Problem: a number when divided by 5 , gives 45 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 10
Options: a ) a ) 5 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 5 = 45 = > p = 45 * 5 = 225 p / 10 = 225 / 10 = 22 , remainder = 5 answer : option a"
Answer: a
Problem: a certain elevator has a safe weight limit of 1950 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "lets assume there are 2 x people . half of them have average weight of 190 and other half has 200 . maximum weight is = 1950 so 190 * x + 200 * x = 1950 = > 390 x = 1950 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 answer d ."
Answer: d
Problem: a and b invests rs . 8000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 82 : 31 , c ) 8 : 15 , d ) 34 : 89 , e ) 35 : 21
Rationale: a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 64000 : 120000 8 : 15 answer : c
Answer: c
Problem: the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 86436 cu . m . its width is
Options: a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 86436 x = 7 answer : d"
Answer: d
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2000 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 18,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2000 triples to $ 6000 , in 28 years , it will again triple to $ 6000 * 3 = $ 18,000 answer d"
Answer: d
Problem: a man buys rs . 44 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 33
Rationale: "dividend on rs . 44 = rs . 9 / 100 x 44 = rs . 3.96 . rs . 12 is an income on rs . 100 . rs . 3.96 is an income on rs . 100 / 12 x 3.96 = rs . 33 . answer : option e"
Answer: e
Problem: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 16 meters . what is value of the radius in meters ?
Options: a ) 1 / 4 , b ) 2 , c ) 4 , d ) 8 , e ) 12
Rationale: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 16 ) which is about 16 r = 4 the answer is c ."
Answer: c
Problem: the duplicate ratio of 4 : 5 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 16 : 25
Rationale: 4 ^ 2 : 5 ^ 2 = 16 : 25 answer : e
Answer: e
Problem: how many different ways can 2 students be seated in a row of 5 desks , so that there is always at least one empty desk between the students ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "6 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 6 x 2 = 12 e"
Answer: e
Problem: he average weight of 8 persons increases by 2.5 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 ) 90 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 70 + 20 ) kg = 90 kg . answer : a"
Answer: a
Problem: if the function q is defined by the formula q = 5 w / ( 4 h ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , h is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: "we just need to find the factor thats all , w - > quadrupled - > 4 w h - > doubled - > 2 h z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and h * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"
Answer: b
Problem: ( 856942 x 555 ) = ?
Options: a ) 484638125 , b ) 474638130 , c ) 474638135 , d ) 475602810 , e ) 484638145
Rationale: 856942 x 555 = 475602810 ans d
Answer: d
Problem: the radius of a wheel is 20.4 cm . what is the distance covered by the wheel in making 400 resolutions ?
Options: a ) 512.448 m , b ) 704 m , c ) 510.448 m , d ) 706 m , e ) 204 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 400 resolutions . = 400 * 2 * 22 / 7 * 20.4 = 51244.8 cm = 512.448 m answer : 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 . 2490 ?
Options: a ) s . 332 , b ) s . 498 , 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 c ' s share in the profit of rs . 2490 = 12 ( 2490 / 60 ) = rs . 498 . answer : b"
Answer: b
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 20 % . what was its profit on the items sold in february ?
Options: a ) 20 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.8 * 150 x = 120 x hence total profit = 20 % option a"
Answer: a
Problem: if the cost price of 50 articles is equal to the selling price of 20 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 150
Rationale: "percentage of profit = 30 / 20 * 100 = 150 % answer : e"
Answer: e
Problem: what is rate of interest if principal . amount be 400 , simple interest 160 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 20 , d ) 12 , e ) 14.5
Rationale: s . i = ( p * r * t ) / 100 160 = 800 r / 100 r = 160 / 8 = 20 % answer c
Answer: c
Problem: on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 2 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 200 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
Options: a ) 250 , b ) 300 , c ) 800 , d ) 400 , e ) 550
Rationale: "let d = total distance traci traveled 1 / 2 = d / 2 i . e . remaining distance = d / 2 she traveled 1 / 4 th of d / 2 = d / 8 thus : d = ( d / 2 ) + ( d / 8 ) + 200 d = 800 answer : c"
Answer: c
Problem: the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is :
Options: a ) 168 , b ) 125 , c ) 186 , d ) 197 , e ) 191
Rationale: "explanation : take radius 100 . then surface area is 4 × π π × 100 × 100 . after increase radius by 50 % the radius becomes 100 + 50 % of 100 = 150 then new surface area is 4 × π π × 150 × 150 then put the values into formula of percentage = 4 π 1502 − 4 π 10024 π 1002 × 1004 π 1502 − 4 π 10024 π 1002 × 100 = 125 % answer : b"
Answer: b
Problem: a man can row 4 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.98 , b ) 3.98 , c ) 3.54 , d ) 3.87 , e ) 3.82
Rationale: "m = 4 s = 1.2 ds = 4.8 us = 2.8 x / 4.8 + x / 2.8 = 1 x = 1.77 d = 1.77 * 2 = 3.54 answer : c"
Answer: c
Problem: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive difference w between n and m ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result w will be 8 - 5 = 3 and answer b"
Answer: b
Problem: h is a positive integer and 225 and 216 are both divisors of h . if h = ( 2 ^ a ) * ( 3 ^ b ) * ( 5 ^ c ) , where a , b and c are positive integers , what is the least possible value of a + b + c ?
Options: a ) 4 , b ) 8 , c ) 6 , d ) 7 , e ) 5
Rationale: lets make factorization of 225 and 216 . . 225 = 5 x 5 x 3 x 3 x 3 216 = 2 x 2 x 2 x 3 x 3 x 3 h would have to have 3 two ' s , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once . . . 225 has 2 fives . . . so we had them together and we get 3 + 3 + 2 = 8 ( b ) ( answer ) . . .
Answer: b
Problem: if p and q are both odd prime numbers andp < q , then how many different positive integer factors does 2 pqhave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: p and q are both odd prime numbers - it means either p or q is not 2 and since prime numbers have only two factors - 1 and the number itself p and q each will have ( 1 + 1 ) = 2 factors hence 2 pq will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Problem: the average age of 25 students in a class is 12 years . 15 students whose average age is 10 years joined them . what is the present average age .
Options: a ) 13 , b ) 12.6 , c ) 11.25 , d ) 12 , e ) 13
Rationale: "explanation : solution : present average = ax + by / a + b = 25 * 12 + 15 * 10 / 25 + 15 years = 300 + 150 / 40 = > 450 / 40 = > 11.25 . answer : c"
Answer: c
Problem: ? x 12 = 173 x 240
Options: a ) 3460 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 12 = 173 x 240 then y = ( 173 x 240 ) / 12 = 3460 answer : a"
Answer: a
Problem: a man goes to shopkeeper and says that if u give me as much as i have , i will spend rs . 10 / - on ur shop . shopkeeper agrees and man moves to another shopkeeper ans asked same . at 3 rd shop after all the transaction , he was left with no money . find the initial amount with the man
Options: a ) 5.75 , b ) 6.75 , c ) 7.75 , d ) 8.75 , e ) 9.75
Rationale: man has rs . x he leaves - 1 st shop wid rs . ( 2 x - 10 ) 2 nd shop wid rs . [ 2 ( 2 x - 10 ) - 10 ] 3 rd shop wid rs . { 2 [ 2 ( 2 x - 10 ) - 10 ] - 10 } = 0 ( since he has no money left ) so solving the eqn x = 8.75 answer : d
Answer: d
Problem: what is the average ( arithmetic mean ) of the numbers 15 , 16 , 17 , 17 , 18 , and 19 ?
Options: a ) 14.2 , b ) 16.5 , c ) 17 , d ) 17.5 , e ) 18
Rationale: "the average of 15 , 16,17 , 18,19 ( sequence numbers ) is 17 & now average of 17 & 17 ( remaining digit from given list ) is 17 . hence answer is 17 . answer : c"
Answer: c
Problem: a starts a business with $ 3500 . after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . b ' s contribution in the capital is
Options: a ) 7000 , b ) 9000 , c ) 8000 , d ) 9900 , e ) 7900
Rationale: ratio in which profit is divided = 2 : 3 assume that b ' s contribution to the capital = b 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 × 3 = 2 × b × 7 ⇒ b = 3500 × 12 × 3 / 2 × 7 = 500 × 6 × 3 = 9000 answer : b
Answer: b
Problem: two trains of length 180 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 22 sec , b ) 23 sec , c ) 76 sec , d ) 20 sec , e ) 66 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 180 + 280 = 400 m . the time required = d / s = 460 / 20 = 23 sec . answer : b"
Answer: b
Problem: a train running at the speed of 60 km / hr crosses a pole in 7 sec . what is the length of the train ?
Options: a ) 112.21 , b ) 27.21 , c ) 117.66 , d ) 277 , e ) 116.66
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 7 = 116.66 answer : e"
Answer: e
Problem: sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour . if the empty rectangular box is 7 feet long , 6 feet wide , and 2 feet deep , approximately how many hours does it take to fill the box ?
Options: a ) 20
b ) 21
c ) 22
d ) 23
e ) 24
Rationale: the volume the box is : length * width * depth = 7 * 6 * 2 = 84 cubic feet . 84 cubic feet / 4 cubic feet per hour = 21 hours . it will take 21 hours to fill the box . the answer is b .
Answer: b
Problem: a train 150 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 22 , b ) 50 , c ) 99 , d ) 288 , e ) 59
Rationale: speed of the train relative to man = ( 150 / 10 ) m / sec = ( 15 ) m / sec . [ ( 15 ) * ( 18 / 5 ) ] km / hr = 54 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 54 = = > x = 59 km / hr . answer : e
Answer: e
Problem: last year a worker saved 4 % of her annual salary . this year , she made 10 % more money than last year and she saved 5 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 137.5 % , b ) 142.5 % , c ) 147.5 % , d ) 152.5 % , e ) 157.5 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.04 x . this year , she saved 0.05 ( 1.1 x ) = 0.055 x 0.055 x / 0.04 x = 55 / 40 = 137.5 % the answer is a ."
Answer: a
Problem: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 40 km and the other at the rate of 50 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 11.04 , b ) 10.0 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: "t = ( 111 + 165 ) / ( 40 + 50 ) * 18 / 5 t = 11.04 answer : a"
Answer: a
Problem: a corporation paid $ 10 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 0 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 43 %
Rationale: "difference in ratios = ( 30 / 150 ) - ( 10 / 50 ) = 0 % change = 0 % answer - a"
Answer: a
Problem: a and b walk around a circular track . they start at 8 a . m from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 9 a . m
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: explanation : relative speed = ( 2 + 3 ) = 5 rounds per hour so , they cross each other 5 times in an hour hence , they cross 5 times before 9 a . m answer : option a
Answer: a
Problem: the product x of two prime numbers is between 17 and 100 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 95
Rationale: "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 51 = 5 * 19 > > answer answer = e"
Answer: e
Problem: 10 men and 15 women together can complete a work in 6 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 225 days
Rationale: 1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 6 15 women ' s 1 day work = ( 1 / 6 - 10 / 100 ) = 1 / 15 1 woman ' s 1 day work = 1 / 225 1 woman alone can complete the work in 225 days . answer : e
Answer: e
Problem: in a basket of apples , 12 % of them are rotten and 66 are in good condition . find the total number of apples in the basket .
Options: a ) 33 , b ) 75 , c ) 23 , d ) 20 , e ) 287
Rationale: let the total number of apples in the basket be m 12 % of the apples are rotten , and apples in good condition are 66 therefore , according to the question , 88 % of m = 66 88 / 100 × m = 66 m = ( 66 × 100 ) / 88 m = 3 × 25 m = 75 therefore , total number of apples in the basket is 75 . answer : b
Answer: b
Problem: a distributor sells a product through an on - line 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 $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 25 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 24
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 25 % of the final price - - > ( final price ) * 0.75 = $ 18 - - > ( final price ) = $ 24 . answer : e ."
Answer: e
Problem: a piece of cloth cost rs 35 . if the length of the piece would have been 4 m longer and each meter cost re 1 less , the cost would have remained unchanged . how long is the piece ?
Options: a ) 5 mtrs , b ) 10 mtrs , c ) 12 mtrs , d ) 15 mtrs , e ) 18 mtrs
Rationale: if length of piece is x and cost per mtr is c , then x * c = 35 or c = 35 / x ( x + 4 ) * ( c - 1 ) = 35 or x * c + 4 c - x - 4 = 35 or 35 + 4 c - x - 4 = 35 4 c - x = 4 4 * ( 35 / x ) - x = 4 x = 10 mtrs answer : b
Answer: b
Problem: what is the average of 4 tenths and 5 thousandths ?
Options: a ) 0.2022 , b ) 0.2012 , c ) 0.2025 , d ) 0.2021 , e ) 0.2029
Rationale: four tenths = 0.4 five thousandths = 0.005 the average is ( 0.4 + 0.005 ) / 2 = 0.2025 answer : c
Answer: c
Problem: the average weight of a , b and c is 43 kg . if the average weight of a and b be 48 kg and that of b and c be 42 kg , then the weight of b is :
Options: a ) 55 kg , b ) 53 kg , c ) 49 kg , d ) 52 kg , e ) 51 kg
Rationale: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 43 x 3 ) = 129 â € ¦ . ( i ) a + b = ( 48 x 2 ) = 96 â € ¦ . ( ii ) b + c = ( 42 x 2 ) = 84 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 180 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 51 . b â € ™ s weight = 51 kg . answer e"
Answer: e
Problem: pipe p can fill a tank in 3 hours , pipe q in 9 hours and pipe r in 18 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.4 hours , c ) 3 hours , d ) 3.5 hours , e ) 4.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 3 + 1 / 9 + 1 / 18 ) = 1 / 2 all the three pipes together will fill the tank = 2 / 1 = 2 hours answer a"
Answer: a
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 25 minutes ?
Options: a ) 80 , b ) 100 , c ) 150 , d ) 240 , e ) 300
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 25 minutes the population increases by 25 x 4 = 100 people . answer . b ."
Answer: b
Problem: a monkey ascends a greased pole 10 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options: a ) 10 th minute , b ) 21 st minute , c ) 17 th minute , d ) 22 nd minute , e ) 13 th minute
Rationale: the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 10 meters . i mean this will continue for first 8 * 2 = 16 mins . he would have reached 8 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 16 + 1 = 17 mins . so , asnwer will be c
Answer: c
Problem: the number 35 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 6 , b ) 15 , c ) 21 , d ) 27 , e ) 39
Rationale: "2 ^ 3 + 3 ^ 3 = 35 therefore product is 2 * 3 = 6 a"
Answer: a
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 13 %
Rationale: "let x be the percentage decrease in fox jeans pony jeans = 22 - x ( 15 * x / 100 ) * 3 + ( 18 ( 22 - x ) / 100 ) * 2 = 9 . . . . . . . . . . . given 45 x / 100 + 792 - 36 x / 100 = 9 9 x + 792 / 100 = 9 9 x + 792 = 900 9 x = 108 x = 12 = fox jeans hence pony jeans = 22 - 12 = 10 answer : b"
Answer: b
Problem: two pipes a and b can separately fill a tank in 12 and 15 minutes respectively . a third pipe c can drain off 42 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 542 , b ) 504 , c ) 548 , d ) 829 , e ) 279
Rationale: "1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 42 = 504 answer : b"
Answer: b
Problem: if i walk at 4 km / h , i miss the bus by 10 minutes . if i walk at 5 km / h , i reach 5 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 5 km , b ) 4.5 km , c ) 5 1 ⁄ 4 km / h , d ) can not be determined , e ) none of these
Rationale: "d = product of speed difference of time / difference of speed d = 4 × 5 / 60 [ 10 − ( − 5 ) / 5 − 4 ] [ here , – ve sign indicates before the schedule time ] ⇒ d = 5 km answer a"
Answer: a
Problem: a jogger running at 9 kmph along side a railway track is 260 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 38 sec , c ) 36 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 260 + 120 ) m = 380 m . ∴ time taken = ( 380 ⁄ 10 ) sec = 38 sec . answer b"
Answer: b
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 2 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 5.5 % , d ) 3.3 % , e ) 2.8 %
Rationale: 33.33 / 6 = 5.5 answer : c
Answer: c
Problem: find the quotient when total no . of divisors of 16 ! is divided by right most non - zero digit of 15 !
Options: a ) 672 , b ) 682 , c ) 692 , d ) 745 , e ) 845
Rationale: first find the factors of 16 ! and then divide with non zero digit of 15 ! factors of 16 ! prime no below 16 are 2 3 5 7 11 13 now highest power of 2 in 16 ! is 15 3 is 65 is 37 is 211 , is 113 is 1 so no of factors is 16 * 7 * 4 * 3 * 2 * 2 = 5376 now last digit in 15 ! it can be written as 2 ^ 11 * 3 ^ 6 * 5 ^ 3 * 7 ^ 2 * 11 ^ 1 * 13 * 1 5 ^ 3 * 2 ^ 3 gives 0 so remaining is 2 ^ 3 = 8 therefore 5376 / 8 = 672 answer : a
Answer: a
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1408 cm is ?
Options: a ) a ) 16 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 1408 = > x = 16 answer : a"
Answer: a
Problem: calculate the area of a triangle , if the sides of are 65 cm , 60 cm and 25 cm , what is its area ?
Options: a ) 850 cm 2 , b ) 750 cm 2 , c ) 450 cm 2 , d ) 550 cm 2 , e ) 650 cm 2
Rationale: "the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b"
Answer: b
Problem: if an object travels at 9 feet per second , how many feet does it travel in one hour ?
Options: a ) 32400 , b ) 30000 , c ) 32000 , d ) 1800 , e ) 22000
Rationale: "if an object travels at 5 feet per second it covers 9 x 60 feet in one minute , and 9 x 60 x 60 feet in one hour . answer = 32400 answer : a"
Answer: a
Problem: the admission charge in a water park is $ 1 by adult and $ 0.75 by child accompanying an adult . how much was there of child with an adult who paid in quite $ 3.25 to have access to the water park ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: a = # of adults price for on adult = $ 1.00 e = # of kids price for on kid ( accompanying an adult ) = $ 0.75 t = total ( $ ) $ 3.25 t = price for an adult * a + price for on kid * e 3.25 = $ 1 * a + $ 0.75 * e 3.25 = a + $ 0.75 * e because the kids have to be accompanying by an adult , a = 1 $ 3.25 = 1 + $ 0.75 * e $ 3.25 - 1 = 1 - 1 + $ 0.75 * e $ 2.25 = $ 0.75 * e $ 2.25 / $ 0.75 = ( $ 0.75 * e ) / $ 0.75 3 = e = number of kids accompanying an adult . correct option : c ) 3 kids
Answer: c
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 3 children and 5 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 5.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "25 / 5 = 5 answer : c"
Answer: c
Problem: the l . c . m of two numbers is 495 and their h . c . f is 5 . if the sum of the numbers is 100 , then their difference is
Options: a ) 19 , b ) 10 , c ) 28 , d ) 27 , e ) 29
Rationale: "let the numbers be x and ( 100 - x ) . then , \ inline \ fn _ jvn \ rightarrow \ inline \ fn _ jvn x ^ { 2 } - 100 x + 2475 = 0 \ inline \ fn _ jvn \ rightarrow ( x - 55 ) ( x - 45 ) = 0 \ inline \ fn _ jvn \ rightarrow x = 55 or x = 45 \ inline \ fn _ jvn \ therefore the numbers are 45 and 55 required difference = ( 55 - 45 ) = 10 answer : b"
Answer: b
Problem: what is the sum of the greatest common factor and the lowest common multiple of 48 and 72
Options: a ) 126 , b ) 184 , c ) 168 , d ) 154 , e ) 186
Rationale: "prime factorization of 72 = 2 x 2 x 2 x 3 x 3 prime factorization of 48 = 2 x 2 x 2 x 2 x 3 gcf = 24 lcm = 144 sum = 168 ans : c"
Answer: c
Problem: the area of a square is 4225 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 41 : 130
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4225 a = 65 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 41 : 130 answer : e"
Answer: e
Problem: jisha 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 the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: jisha walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e
Answer: e
Problem: the spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls . the diameters of two of these are 1 1 / 2 cm and 2 cm respectively . the diameter of third ball is ?
Options: a ) 2.8 , b ) 2.5 , c ) 2.2 , d ) 2.0 , e ) 2.1
Rationale: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π [ ( 3 / 2 ) 3 + 23 + r 3 ] r = 1.25 d = 2.5 answer : b"
Answer: b
Problem: thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 21 have taken the preparatory course and 42 have not taken the course . how many members are there in the swim club ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 90 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 42 + 21 = 63 members have not passed the test , thus 0.7 * total = 63 - - > total = 90 . answer : d ."
Answer: d
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) 228 , b ) 288 , c ) 500 , d ) 200 , e ) 881
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 500 was made . answer : c"
Answer: c
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 28 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 12.2 , c ) 14.8 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 28 inch = ( 136 ã — 28 ) / 312 = 12.2 km answer : b"
Answer: b
Problem: positive integer y is 50 percent of 25 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?
Options: a ) 50 , b ) 125 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: y = 50 % of 25 % 0 f x = x / 8 and y / 100 of x = 100 y / 100 * 8 y = 100 y = 125 answer - b
Answer: b
Problem: in simple interest what sum amounts of rs . 1120 / - in 4 years and rs . 1200 / - in 5 years ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 800 , d ) rs . 900 , e ) rs . 700
Rationale: for 1 year interest = 1200 - 1120 = 80 for 4 year 320 then sum = 1120 - 320 = 800 answer : c
Answer: c