regisss/math_qa huggingface dataset:
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 5,5 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 26 / 143 , d ) 1 / 5 , e ) 31 / 220
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 5.5 * 2 = 11 hours ; in 1 hour 15 journeymen can finish 1 / 11 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 11 = 31 / 220 of the job . answer : e"
Answer: e
Problem: calculate the l . c . m of 1 / 5 , 6 / 7 , 5 / 6 , 3 / 5 is :
Options: a ) 15 , b ) 30 , c ) 20 , d ) 40 , e ) 10
Rationale: "required l . c . m = l . c . m . of 1 , 6 , 5 , 3 / h . c . f . of 5 , 7 , 6 , 5 = 30 / 1 = 30 answer is b"
Answer: b
Problem: find the average of all prime numbers between 1 and 10
Options: a ) 2.5 , b ) 1.35 , c ) 4.25 , d ) 6.12 , e ) 7.13
Rationale: "prime numbers between 1 and 10 are 2,3 , 5,7 required average = ( 2 + 3 + 5 + 7 ) / 4 = 17 / 4 = 4.25 answer is c"
Answer: c
Problem: the average age of a class of 20 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 19 , average would not have changed . since average increased by 2 , age of the teacher = 19 + 22 × 1 = 41 answer : b"
Answer: b
Problem: there were 35 students in a hostel . due to the admission of 7 new students , ; he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . wbat was the original expenditure of the mess ?
Options: a ) 520 , b ) 720 , c ) 425 , d ) 625 , e ) 420
Rationale: "let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 7 x = 84 x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . answer is e ."
Answer: e
Problem: evaluate : | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 73 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 7 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 7 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 7 + 72 | - | 5 - 11 | = | 79 | - | - 6 | = 79 - 6 = 73 correct answer c ) 73"
Answer: c
Problem: if 14 lions can kill 14 deers in 14 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 14 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 14 ( lions ) * 14 ( min ) / 14 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 14 answer : b"
Answer: b
Problem: in a 100 m race , sam beats john by 3 seconds . on the contrary , if sam allowed john to start 24 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 4 seconds , b ) 25.33 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: their difference is 3 second but this difference is 0 if john allows sam to start the race from 24 m ahead . that means jhon was 24 m away from finishing line when they started together . so he will cover 24 m in 3 seconds . so his speed = 24 / 3 = 8 metre / second . so time taken = 100 / 3 = 33.33 seconds . so sam took = 25.33 seconds . correct answer = b
Answer: b
Problem: if | x - 25 | = 50 what is the sum of all the values of x .
Options: a ) 0 , b ) - 100 , c ) - 50 , d ) 50 , e ) 100
Rationale: there will be two cases x - 25 = 50 and x - 25 = - 50 solve for x = > x = 50 + 25 = > x = 75 or x = - 50 + 25 = > x = - 25 the sum of both values will be 75 + - 25 = 50 answer is d
Answer: d
Problem: product of two co - prime numbers is 117 . their l . c . m should be :
Options: a ) 1 , b ) 117 , c ) 116 , d ) equal to their h . c . f , e ) can not be calculated
Rationale: "h . c . f of co - prime numbers is 1 . so , l . c . m = 117 / 1 = 117 . answer : b"
Answer: b
Problem: the price of a tv was increased by 30 percent . the new price was then increased by 40 percent . a single increase of what percent is equivalent to these two successive increases ?
Options: a ) 82 % , b ) 75 % , c ) 65 % , d ) 50 % , e ) 45 %
Rationale: "consider base price - $ 100 30 % increase = 1.30 * 100 = $ 130 another 40 % increase on new price = 1.4 * 130 = $ 182 so final price of radio - $ 182 therefore a 82 % increase correct option - a"
Answer: a
Problem: terry is having lunch at a salad bar . there are two types of lettuce to choose from , as well as 3 types of tomatoes , and 4 types of olives . he must also choose whether or not to have one of the two types of soup on the side . if terry has decided to have the salad and soup combo and he picks one type of lettuce , one type of tomato , and one type of olive for his salad , how many total options does he have for his lunch combo ?
Options: a ) 9 , b ) 11 , c ) 24 , d ) 48 , e ) 54
Rationale: terry can pick one lunch salad bar . . . . we can choose lettuce 2 c 1 , tomatoes - 3 c 1 and olives - 4 c 1 . . . two types of soups , if he picks one then 2 c 1 ways . terry decided to have the combo : soup + salad . . . hmmm . . . using the above information , we get ( 2 c 1 * 2 c 1 * 3 c 1 * 4 c 1 ) = 48 . . ans option d is correct answer . .
Answer: d
Problem: what will be the reminder when ( 31 ^ 31 + 31 ) is divided by 32 ?
Options: a ) 72 , b ) 43 , c ) 91 , d ) 40 , e ) 30
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 31 ^ 31 + 1 ) will be divisible by ( 31 + 1 ) ; ( 31 ^ 31 + 1 ) + 30 when divided by will give 30 as remainder . correct option : e"
Answer: e
Problem: if m equals the sum of the odd integers from 1 to 111 , inclusive , and t equals the sum of the even integers from 2 to 50 , inclusive , what is the value of m + t ?
Options: a ) 400 , b ) 5550 , c ) 6922 , d ) 3786 , e ) 5553
Rationale: use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 111 - 1 ) / 2 ] + 1 = 56 and [ ( 50 - 2 ) / 2 ] + 1 = 25 mean of integers = ( 111 + 1 ) / 2 = 56 and ( 50 + 2 ) / 2 = 26 sum of integers = ( 56 * 56 ) = 3136 and ( 25 * 26 ) = 650 thus their sum ( m + t ) = 3786 answer : d
Answer: d
Problem: a meeting has to be conducted with 6 managers . find the number of ways in which the managers be selected from among 10 managers , if 2 managers will not attend the meeting together ?
Options: a ) 120 , b ) 110 , c ) 105 , d ) 140 , e ) 135
Rationale: "we can either choose all 6 people from 8 manager who have no problems or choose 5 from the 8 and 1 from the 2 managers who have a problem sitting together so 8 c 6 + ( 8 c 5 * 2 c 1 ) this is 28 + 112 = 140 answer : d"
Answer: d
Problem: the smallest value of n , for which 2 n + 3 is not a prime number , is
Options: a ) 4,5 , b ) 3,4 , c ) 2,6 , d ) 5,6 , e ) 2,3
Rationale: "( 2 ã — 1 + 3 ) = 5 . ( 2 ã — 2 + 3 ) = 7 . ( 2 ã — 3 + 3 ) = 9 . ( 2 ã — 4 + 3 ) = 15 . which is not prime , n = 3,4 . answer : b"
Answer: b
Problem: the average age of a class of 12 students is 19 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 34 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 12 , average would not have changed . since average increased by 2 , age of the teacher = 12 + 22 × 1 = 34 answer : b"
Answer: b
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 14 wins and 6 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 1 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "14 wins , 6 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 6 games so it can lose another 1 at most . answer ( a )"
Answer: a
Problem: a train , 125 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 250 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 125 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 125 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 125 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 125 + x = > 45 ã — 10 ã — 10 / 12 = 125 + x = > 15 ã — 10 ã — 10 / 4 = 125 + x = > 15 ã — 25 = 125 + x = 375 = > x = 375 - 125 = 250 answer : option a"
Answer: a
Problem: in a division sum , the quotient is 36 , the divisor 85 and the remainder 26 , find the dividend ?
Options: a ) 3066 , b ) 3586 , c ) 3086 , d ) 3968 , e ) 3286
Rationale: "explanation : 36 * 85 + 26 = 3086 answer : c"
Answer: c
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number q of people surveyed by the company ?
Options: a ) 46 , b ) q . 80 , c ) q . 90 , d ) q . 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Problem: two trains 141 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.59 , c ) 7.12 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 141 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.59 answer : b"
Answer: b
Problem: a pharmaceutical company received $ 6 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 72 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 6 / 20 = 3 / 10 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 6 / 20 ) x 60 = 18 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 18 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 18 ) / 18 ] x 100 - 650 / 9 x 100 at this point we can stop and consider the answer choices . since we know that 650 / 9 is just a bit less than ½ , we know that - 650 / 9 x 100 is about a 72 % decrease . answer e ."
Answer: e
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 86 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 81 min , b ) 108 min , c ) 144 min , d ) 192 min , e ) none
Rationale: "solution let the slower pipe alone fill the tank in x minutes . then , faster pipes will fill it in x / 3 minutes . therefore , 1 / x + 3 / x = 1 / 36 ‹ = › 4 / x = 1 / 36 ‹ = › x = 144 min . answer c"
Answer: c
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 90 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 45 , e ) 14
Rationale: "10 x = 90 = > x = 9 therefore the secretary who worked the longest spent 9 x 5 = 45 hours on the project option ( c )"
Answer: c
Problem: one train is travelling 45 kmph and other is at 10 meters a second . ratio of the speed of the two trains is ?
Options: a ) 3 : 3 , b ) 5 : 7 , c ) 5 : 4 , d ) 7 : 2 , e ) 8 : 5
Rationale: c 5 : 4 45 * 5 / 18 = 10 25 : 20 = > 5 : 4
Answer: c
Problem: in the xy - plane , a triangle has vertices ( 00 ) , ( 40 ) and ( 410 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5
Rationale: the area of the right triangle is ( 1 / 2 ) * 4 * 10 = 20 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 20 = 2 / 5 the answer is e .
Answer: e
Problem: a train 150 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 75 kmph , b ) 85 kmph , c ) 95 kmph , d ) 105 kmph , e ) 115 kmph
Rationale: let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 150 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2700 x = 85 kmph answer is b
Answer: b
Problem: working together , wayne and his son can shovel the entire driveway in 3 hours . if wayne can shovel 6 times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 7 , e ) 12
Rationale: w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 6 and w = 6 s then we have 1 / ( 6 * s ) + 1 / s = 1 / 6 < = > 7 / ( 6 * s ) = 1 / 6 < = > s = 7 ans : d
Answer: d
Problem: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 21 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.8 , b ) 987.8 , c ) 877.8 , d ) 898.8 , e ) 667.4
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 21 = 2 r a = 12 / 5 r and r = 63 a = 151.2 required total cost = 4 * 151.2 + 3 * 63 + 5 * 21 = 604.8 + 189 + 105 = $ 898.80 d"
Answer: d
Problem: how many pieces of 85 cm length can be cut from a rod of 25.5 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 2550 / 85 = 30 the answer is c ."
Answer: c
Problem: a father is 4 times as old as his son . in 20 years , he ' ll be twice as old . how old are they now ?
Options: a ) 540 , b ) 1040 , c ) 2040 , d ) 1030 , e ) 15,30
Rationale: if f is age of father and s is age of son f = 4 s f + 20 = 2 * ( s + 20 ) 4 s + 20 = 2 s + 40 2 s = 20 s = 10 f = 40 answer : b
Answer: b
Problem: how many positive integers h less than 10000 are such that the product of their digits is 210 ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 72
Rationale: 210 is the answer when 2 , 3 , 5 and 7 are multiplied . 210 can also be arrive using 56 and 7 and 1 , 5 , 6 and 7 . so sum of arrangements of 2357 , 567 and 1567 . this translates to 4 ! + 3 ! + 4 ! , this equals to 24 + 6 + 24 = 54 , d is the answer .
Answer: d
Problem: two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km / hr and 36 km / hr . the time of crossing each other , if they run in the opposite direction is
Options: a ) 322 sec , b ) 14 sec , c ) 11 sec , d ) 13 sec , e ) 34 sec
Rationale: explanation : total distance to be covered = 156.62 + 100 = 256.62 m trains are running in opposite directions , hence relative speed = 30 + 36 = 66 km / hr = 18.33 m / sec time = distance / relative speed = 256.62 / 18.33 sec = 14 sec therefore , the time of crossing each other in the opposite direction is 14 seconds . answer : b
Answer: b
Problem: the length of the bridge , which a train 170 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 388 , b ) 267 , c ) 205 , d ) 288 , e ) 261
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 170 + x ) / 30 = 25 / 2 = = > 2 ( 170 + x ) = 750 = = > x = 205 m . answer : c"
Answer: c
Problem: on multiplying a number a by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number a is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Problem: andrew purchased 11 kg of grapes at the rate of 98 per kg and 7 kg of mangoes at the rate of 50 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1428 , d ) 1500 , e ) 1080
Rationale: "cost of 11 kg grapes = 98 × 11 = 1078 . cost of 7 kg of mangoes = 50 × 7 = 350 . total cost he has to pay = 1078 + 350 = 1428 c"
Answer: c
Problem: two numbers are in the ratio of 3 : 4 . if 12 be subtracted from each , they are in the ratio of 9 : 8 . find the numbers ?
Options: a ) 6,9 , b ) 3,8 , c ) 6,7 , d ) 3,5 , e ) 3,4
Rationale: "( 3 x - 12 ) : ( 4 x - 12 ) = 9 : 8 x = 1 = > 3,4 answer : e"
Answer: e
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1380 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1380 20 x / 100 = 1380 x = 1380 * 100 / 20 = 6900 answer is c"
Answer: c
Problem: rounded to 3 decimal places , 1.003 ^ 4 =
Options: a ) 1.004 , b ) 1.006 , c ) 1.008 , d ) 1.012 , e ) 1.016
Rationale: as compared to 1 , 0.003 is a very small quantity . thus , we can write ( 1 + 0.003 ) ^ 4 is nearly equal to ( 1 + 4 * 0.003 ) = 1.012 . as the question asks for approximation to three decimal places , the further terms will anyways not come into picture . d .
Answer: d
Problem: the banker ' s gain of a certain sum due 2 years hence at 10 % per annum is rs . 24 . what is the present worth ?
Options: a ) rs . 600 , b ) rs . 500 , c ) rs . 400 , d ) rs . 300 , e ) none of these
Rationale: "explanation : t = 2 years r = 10 % td = ( bg × 100 ) / tr = ( 24 × 100 ) / ( 2 × 10 ) = 12 × 10 = rs . 120 td = ( pw × tr ) / 100 ⇒ 120 = ( pw × 2 × 10 ) / 100 ⇒ 1200 = pw × 2 pw = 1200 / 2 = rs . 600 answer : option a"
Answer: a
Problem: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 50 ) * 100 = 4 % so , x * 4 % = 50 x = 1250 answer : c"
Answer: c
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 10 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 10 k waiters . 14 k = 10 k + 12 k = 3 there are 9 cooks . the answer is c ."
Answer: c
Problem: the profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 1020 , e ) none of these
Rationale: "let the profit or loss be x and 912 – x = 448 + x or , x = 464 ⁄ 2 = 232 \ cost price of the article = 912 – x = 448 + x = 680 \ sp of the article = 680 × 150 ⁄ 100 = 1020 answer d"
Answer: d
Problem: working individually , julie can peel potatoes in 10 hours and ted can peel potatoes in 8 hours . if julie and ted work together but independently at the task for 4 hours , at which point ted leaves , how many remaining hours will it take julie to complete the task alone ?
Options: a ) 3 / 15 , b ) 2 / 11 , c ) 1 / 4 , d ) 1 / 3 , e ) 1
Rationale: in first 4 hrs ted will finish 4 / 8 = 1 / 2 of work and julie will finish 4 / 10 work so total 1 / 2 + 2 / 5 = 9 / 10 work is finished and 1 - 9 / 10 = 1 / 10 work remaining . now julie will take ( 1 / 10 ) * 10 = 1 hrs to finish it . so answer is e .
Answer: e
Problem: x is able to do a piece of work in 8 days and y can do the same work in 12 days . if they can work together for 3 days , what is the fraction of work left ?
Options: a ) 8 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "explanation : amount of work x can do in 1 day = 1 / 8 amount of work y can do in 1 day = 1 / 12 amount of work x and y can do in 1 day = 1 / 8 + 1 / 12 = 5 / 24 amount of work x and y can together do in 3 days = 3 × ( 5 / 24 ) = 5 / 8 fraction of work left = 1 – 5 / 8 = 3 / 5 answer : option d"
Answer: d
Problem: an article is bought for rs . 1450 and sold for rs . 1420 , find the loss percent ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 12 %
Rationale: "1450 - - - - 30 100 - - - - ? = > 2 % answer : a"
Answer: a
Problem: in a group of 28 junior high school students , 7 take french , 9 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
Rationale: "e 8 add 7 + 9 + 4 to get 20 . then subtract 21 from the total students ⇒ 28 – 20 = 8 . answer is e"
Answer: e
Problem: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in r hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of r ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * r = 1 = > x = 1 / z when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / r = 4 / 3 = > 1 / r = ( 8 - 3 ) / 6 = 5 / 6 = > r = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Problem: if 36 men can do a piece of work in 15 hours , in how many hours will 15 men do it ?
Options: a ) 22 , b ) 36 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 15 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 15 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 15 } { 15 } = 36 hence , 15 men can do it in 36 hours . answer : b ) 36"
Answer: b
Problem: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 60 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 132 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 180 min e"
Answer: e
Problem: dawson is going with 14 friends on a trip to washington d . c for spring break . airfare and hotel costs a total of $ 13500.00 for the group of 15 friends . how much does each person have to pay for their hotel and airfare ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 850 , d ) $ 950 , e ) $ 920
Rationale: answer = a the total cost of the trip ( $ 13500.00 ) divided by 15 equals $ 900.00 .
Answer: a
Problem: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 367 , c ) 269 , d ) 177 , e ) 199
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 190 x + ( x - 190 ) = 208 2 x = 398 x = 199 runs answer : e"
Answer: e
Problem: the point a and point b is 30 miles apart , the point b and point c is 25 miles apart . a car travels from point a to point b in 30 min and point b to point c in 40 min . what is the average speed of the car ?
Options: a ) 34.15 , b ) 40.35 , c ) 47.14 , d ) 50.12 , e ) 56.66
Rationale: average speed = total distance covered / total time taken = 55 miles / 70 min = 0.79 miles / min = 47.14 miles / hour answer : c
Answer: c
Problem: 0.009 / x = 0.025 . find the value of x
Options: a ) 0.0003 , b ) 0.36 , c ) 0.3 , d ) 36 , e ) 90
Rationale: "x = 0.009 / 0.36 = 0.25 answer : c"
Answer: c
Problem: at the moment there are 54210 tagged birds in a certain wildlife refuge . if exactly 30 percent of all birds in the refuge are tagged , what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged ?
Options: a ) 66.67 , b ) 66 , c ) 67 , d ) 65.99 , e ) 67.26
Rationale: all birds = 54210 currently tagged = 54210 * 30 / 100 = 16263 so untagged birds = 54210 - 16263 = 37947 half of all birds = 27105 the number of birds to be tagged to make half of all birds tagged = 27105 - 16263 = 10842 so now the question remains - 10842 is how much percentage of untagged birds ( 16263 ) = 10842 * 100 / 16263 = 66.67 answer ( a )
Answer: a
Problem: find the cost of fencing around a circular field of diameter 70 m at the rate of rs . 1 a meter ?
Options: a ) 288 , b ) 132 , c ) 220 , d ) 592 , e ) 261
Rationale: "2 * 22 / 7 * 35 = 220 220 * 1 = rs . 220 answer : c"
Answer: c
Problem: the area of a square is equal to four times the area of a rectangle of dimensions 25 cm * 16 cm . what is the perimeter of the square ?
Options: a ) 80 cm , b ) 100 cm , c ) 120 cm , d ) 140 cm , e ) 160 cm
Rationale: "area of the square = s * s = 4 ( 25 * 16 ) = > s * s = 2 * 2 * 5 * 5 * 4 * 4 = > s = 2 * 5 * 4 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : e"
Answer: e
Problem: a train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min . find the length of train ?
Options: a ) 100.1 m , b ) 223.1 m , c ) 111.1 m , d ) 120.3 m , e ) 133.4 m
Rationale: explanation : we know , speed = distance / time speed = 10 / 50 x 60 = 40 x 5 / 18 m / sec = 11.1 m / sec length of train = ( speed x time ) = ( 11.11 x 10 ) = 111.1 m answer is c
Answer: c
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 6 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 900
Rationale: explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 6 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 1800 . hence , ( r - p ) = ( 1800 - 900 ) = 900 answer : e
Answer: e
Problem: a farmer spent $ 34 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.40 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 34 = $ 13.6 on chicken feed , thus he spent the remaining 34 - 13.6 = $ 20.4 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 13.6 - - > x = $ 17 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 17 + 20.4 = $ 37.4 . answer : a ."
Answer: a
Problem: a sum of rs . 312 was divided among 100 boys and girls in such a way that each boy gets rs . 3.60 and each girl rs . 2.40 .
Options: a ) 45 , b ) 49 , c ) 52 , d ) 60 , e ) 74
Rationale: let number of boys = x then number of girls = ( 100 - x ) 3.60 x + 2.40 ( 100 - x ) = 312 ¡ ê 1.2 x = 312 - 240 = 72 ¡ ê x = 60 answer : d
Answer: d
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 6 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 67 , e ) 50
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 6 oz can = 300 oz / 6 oz = 50 answer e , 50 cans"
Answer: e
Problem: if the average ( arithmetic mean ) of a and b is 30 and the average of b and c is 60 , what is the value of c − a ?
Options: a ) 25 , b ) 60 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: - ( a + b = 60 ) b + c = 120 c - a = 60 b . 60
Answer: b
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on november 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 40 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 nov 1 = c - 40 difference between stock on november 1 than were in stock on january 1 will be - c - ( c - 40 ) = 40 hence answer will be ( c )"
Answer: c
Problem: what is the minimum percentage increase in the mean of set f { - 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 f is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of f , 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: the volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3 . what is the ratio of their heights ?
Options: a ) a ) 3 : 4
b ) b ) 2 : 7
c ) c ) 2 : 2
d ) d ) 2 : 1
e ) e ) 2 : 9
Rationale: the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 12 = ( 1 ) 2 h 1 / ( 3 ) 2 h 2 = > h 1 / h 2 = 3 / 4 i . e . h 1 : h 2 = 3 : 4 answer : a
Answer: a
Problem: two numbers are 35 % and 42 % are less than a third number . how much percent is the second number less than the first ?
Options: a ) 11.769 % , b ) 10.769 % , c ) 12.769 % , d ) 11.69 % , e ) 11.89 %
Rationale: "explanation : i ii iii 65 58 100 65 - - - - - - - - 7 100 - - - - - - ? = > 10.769 % answer b"
Answer: b
Problem: john and roger can finish the work 24 days if they work together . they worked together for 16 days and then roger left . john finished the remaining work in another 16 days . in how many days john alone can finish the work ?
Options: a ) 30 days , b ) 48 days , c ) 70 days , d ) 80 days , e ) 90 days
Rationale: amount of work done by john and roger in 1 day = 1 / 24 amount of work done by john and roger in 16 days = 16 ã — ( 1 / 24 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 16 days amount of work john can do in 1 day = ( 1 / 3 ) / 16 = 1 / 48 = > john can complete the work in 48 days answer : b
Answer: b
Problem: there are 43 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 1980 , b ) 1920 , c ) 1990 , d ) 1890 , e ) 1900
Rationale: "the total number of stations = 45 from 45 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 45 p 2 ways . 45 p 2 = 45 * 44 = 870 answer : a"
Answer: a
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 12 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 18 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 12 - 6 = 6 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 6 + 12 = 18 . answer : c ."
Answer: c
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 6 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 6 ) ( 4 + 4 x ) or , x = 1 / 2 answer c"
Answer: c
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 3 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 360 km , b ) 480 km , c ) 278 km , d ) 297 km , e ) 671 km
Rationale: let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 3 2 x / 15 - x / 8 = 3 = > x = 360 km . answer : a
Answer: a
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers q are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Problem: what is the remainder when 1271 * 1275 * 1277 * 1285 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 11 , d ) 9 , e ) 7
Rationale: "in this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 . . . the remainder which comes now will be the answer . 1271 div by 12 = = > remainder = 11 1275 div by 12 = = > rema = 3 1285 div by 12 = = > remain = 1 1277 div by 12 = = > rema = 5 now multiply the remainder = 165 165 div by 12 rem = 9 answer : d"
Answer: d
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 500 grams per kg , what is his percent ?
Options: a ) 20 % , b ) 25 % , c ) 29 % , d ) 55 % , e ) 100 %
Rationale: "500 - - - 500 100 - - - ? = > 100 % answer : e"
Answer: e
Problem: ( 7895632 x 881 ) = ?
Options: a ) 6846381250 , b ) 6584638130 , c ) 6584638135 , d ) 6584638140 , e ) 6956051792
Rationale: 7895632 x 881 = 6956051792 ans e
Answer: e
Problem: solve the equation for x : 8 x - 40 + 2 x = 5 + 10 - x
Options: a ) 4 , b ) 10 , c ) 7 , d ) 5 , e ) 3
Rationale: "d 5 10 x + x = 15 + 40 11 x = 55 = > x = 5"
Answer: d
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 9 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 9 / 13 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9
Rationale: her tips were 9 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 9 / 4 ) ( $ 4 ) = $ 9 so , her total income = $ 4 + $ 9 = $ 13 what fraction of her income for the week came from tips $ 9 $ 13 = 9 / 13 = a
Answer: a
Problem: a can do a piece of work in 8 days . b can do it in 12 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 16 days , d ) 24 days , e ) 36 days
Rationale: "c = 1 / 4 - 1 / 8 - 1 / 12 = 1 / 24 = > 24 days answer : d"
Answer: d
Problem: find the value of m 62519 x 9999 = m ?
Options: a ) 724533811 , b ) 625127481 , c ) 545463251 , d ) 725117481 , e ) 677899932
Rationale: "62519 x 9999 = 62519 x ( 10000 - 1 ) = 62519 x 10000 - 62519 x 1 = 625190000 - 62519 = 625127481 b"
Answer: b
Problem: the difference between compound interest and simple interest on a sum for 3 years at 10 % p . a . is rs . 124 find the sum .
Options: a ) rs . 5000 , b ) rs . 4000 , c ) rs . 6000 , d ) rs . 8000 , e ) rs . 7000
Rationale: "for 3 years , we know c . i - s . i = p ( r / 100 ) ^ 3 + 3 ( r / 100 ) ^ 2 so , putting all values we have , 124 = p ( ( 10 / 100 ) ^ 3 + 3 ( 10 / 100 ) ^ 2 ) = 4000 answer : b"
Answer: b
Problem: an italian sausage is 8 inches long . how many pieces of sausage can be cut from the 8 - inch piece of sausage if each piece is to be 2 / 3 of an inch ?
Options: a ) 12 , b ) 32 , c ) 22 , d ) 15 , e ) 20
Rationale: number of pieces = italian sausage ÷ 2 / 3 of an inch = 8 ÷ 2 / 3 = 8 / 1 ÷ 2 / 3 = 8 / 1 * 3 / 2 = 24 / 2 = 12 . answer is a .
Answer: a
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 3500 and b rs . 2500 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4200 , e ) 6000
Rationale: "35 : 25 = > 7 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 12 = 5040 + 960 = 6000 answer : e"
Answer: e
Problem: what is the dividend . divisor 20 , the quotient is 8 and the remainder is 6
Options: a ) a ) 145 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 166
Rationale: "d = d * q + r d = 20 * 8 + 6 d = 160 + 6 d = 166 answer : e"
Answer: e
Problem: a train 550 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 30 , b ) 60 , c ) 25 , d ) 40 , e ) 10
Rationale: speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 550 * 3 / 55 ] sec = 30 sec answer : a
Answer: a
Problem: given that 268 x 74 = 19732 , find the value of 2.68 x . 74 .
Options: a ) 1.9732 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9732 answer a"
Answer: a
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 70 more . what was his original selling price ?
Options: a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840
Rationale: "let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 70 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 70 = > 0.07 x = 70 = > x = $ 1000 original purchase price = $ 1000 hence , original selling price ( at 10 % of profit ) = 1.1 ( 1000 ) = $ 1100 option d"
Answer: d
Problem: george baked a total of 50 pizzas for 5 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: 3 / 5 of the 50 pizzas cooked on saturday = 30 pizzas 3 / 5 of the remaining pizzas on sunday = 12 pizzas we ' re left with ( 50 - 30 - 12 ) = 8 pizzas for the remaining 3 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w 5 2 1 = 8 w = 1 e
Answer: e
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "explanatory answer let the original number be x . let a be the value obtained when x is increased by 12.5 % . therefore , a = x + 12.5 % of x let b be the value obtained when x is decreased by 25 % . therefore , b = x - 25 % of x the question states that a - b = 30 i . e . , x + 12.5 % of x - ( x - 25 % of x ) = 30 x + 12.5 % of x - x + 25 % of x = 30 37.5 % of x = 30 x = 30 / 37.5 * 100 = 80 the correct choice is ( b )"
Answer: b
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 1492 , c ) 1667 , d ) 2500 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 15 minutes = 50 / 18 * 15 * 60 = 2500 m answer is d"
Answer: d
Problem: in a company of 12 employees , 5 employees earn $ 36000 , 4 employees earn $ 45000 , and the 3 highest - paid employees earn the same amount . if the average annual salary for the 12 employees is $ 47500 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 60,000 , b ) $ 65,000 , c ) $ 70,000 , d ) $ 75,000 , e ) $ 80,000
Rationale: 5 * 36,000 + 4 * 45,000 + 3 x = 12 * 47,500 3 x = 570,000 - 180,000 - 180,000 3 x = 210,000 x = 70,000 the answer is c .
Answer: c
Problem: dames school has 2000 boys and 5000 girls . what is the percentage increase from boys to total attendance and girls to total attendance ?
Options: a ) a ) 40 % , b ) b ) 10 % , c ) c ) . 4 % , d ) d ) 50 % , e ) e ) 12 %
Rationale: ratio of boys to total attendance ( 2 / 7 ) ratio of girls to total attendance ( 5 / 7 ) percentage increase is ( difference / initial quantity ) * 100 ( 2 / 7 ) / ( 5 / 7 ) * 100 = 40 % correct answer is a
Answer: a
Problem: a man swims downstream 76 km and upstream 48 km taking 4 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 1.5 kmph , c ) 3.5 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 76 - - - 4 ds = 19 ? - - - - 1 48 - - - - 4 us = 12 ? - - - - 1 s = ? s = ( 19 - 12 ) / 2 = 3.5 answer : option c"
Answer: c
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 16000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 35 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 16000 x 7 ) + 6000 ( x - 7 ) x = 35 . answer c"
Answer: c
Problem: n = 1 / 3 + 1 / 4 what is the value of n ?
Options: a ) 7 / 12 , b ) 1 / 6 , c ) 1 / 8 , d ) 5 / 17 , e ) 12 / 7
Rationale: to sum 1 / 3 and 1 / 4 multiply both sides by 12 12 * n = 12 * 1 / 3 + 12 * 1 / 4 12 * n = 4 + 3 n = 7 / 12 ans : a
Answer: a
Problem: how many even multiples of 55 are there between 549 and 1101 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "550 = 10 * 55 1100 = 20 * 55 the even multiples are 55 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Problem: sum of two numbers prime to each other is 15 and their l . c . m . is 56 . what are the numbers ?
Options: a ) 9 and 8 , b ) 5 and 10 , c ) 7 and 9 , d ) 7 and 8 , e ) 10 and 8
Rationale: "as two numbers are prime , only options satisfy ie option a and d and c but option d will make the product of numbers i . e 56 answer : d"
Answer: d
Problem: if - 3 x + 2 y = 28 and 3 x + 6 y = 84 , what is the product of x and y ?
Options: a ) 264 . , b ) 428 , c ) 0 , d ) 462 , e ) 642
Rationale: "given - 3 x + 2 y = 28 - - - eq 1 3 x + 6 y = 84 - - eq 2 sum both eqns we get 8 y = 112 = > y = 14 sum 2 y in eq 1 = > - 3 x - 28 = 28 . = > x = 0 now xy = 0 * 14 = 0 . option c is correct answer ."
Answer: c
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 10 , d ) 1 / 45 , e ) 1 / 60
Rationale: "pete covered 5 * 60 = 300 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 300 = 1 / 60 . answer : e ."
Answer: e
Problem: a sphere is inscribed in a cube with an edge of 10 . what is the shortest possible distance from one of the vertices of the cube to the surface of the sphere ?
Options: a ) 10 ( √ 3 - 1 )
b ) 5
c ) 10 ( √ 2 - 1 )
d ) 5 ( √ 3 - 1 )
e ) 5 ( √ 2 - 1 )
Rationale: as sphere is inscribed in cube then = > the edge of the cube equals to the diameter of a sphere - - > diameter = 10 diagonal of a cube equals to diagonal = square _ root ( 10 ^ 2 + 10 ^ 2 + 10 ^ 2 ) = 10 √ 3 . half of diagonal - diameter is gap between the vertex of a cube and the surface of the sphere = ( 10 √ 3 - 10 ) / 2 = 5 ( √ 3 - 1 ) answer : d
Answer: d
Problem: by selling 20 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 80 , b ) 60 , c ) 50 , d ) 30 , e ) 10
Rationale: "80 % - - - 20 120 % - - - ? 80 / 120 * 20 = 30 answer : d"
Answer: d
Problem: 25.25 / 2000 is equal to :
Options: a ) 1.012526 , b ) 0.012625 , c ) 0.12526 , d ) 0.12625 , e ) 0.12725
Rationale: "25.25 / 2000 = 2525 / 200000 = 0.012625 answer : b"
Answer: b
Problem: on a sum of money , the simple interest for 2 years is rs . 660 , while the compound interest is rs . 696.30 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 10 % , b ) 11 % , c ) 12 % , d ) 10.5 % , e ) none
Rationale: "solution difference in c . i and s . i for 2 years = rs ( 696.30 - 660 ) = rs . 36.30 . s . i for one years = rs 330 . s . i on rs . 330 for 1 year = rs . 36.30 rate = ( 100 x 36.30 / 330 x 1 ) % = 11 % . answer b"
Answer: b