regisss/math_qa huggingface dataset:
Problem: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses t at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) t = 256 , d ) t = 384 , e ) t = 480
Rationale: "most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 200 before any discount ?
Options: a ) $ 112.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 100.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 200 would be . . . . . ( $ 200 ) ( . 7 ) ( . 8 ) = ( $ 200 ) ( . 56 ) = 112 final answer : a"
Answer: a
Problem: a train 550 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 30
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 550 * 3 / 55 = 30 sec . answer : option e"
Answer: e
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 186 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 5 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 186 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 186 m ) / ( w + m ) = 180 170 w + 186 m = 180 w + 180 m 6 m = 10 w 3 m = 5 w m / w = 5 / 3 the ratio of men to women is 5 to 3 . c"
Answer: c
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 50 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3.19 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 50 / 60 47 x / 60 = 50 / 60 = > x = 1.06 . total distance = 3 * 1.06 = 3.19 km ."
Answer: c
Problem: how many digits are used to number a book containg 300 pages .
Options: a ) 694 , b ) 792 , c ) 698 , d ) 784 , e ) 789
Rationale: explanation : number of digits in 1 digit numbers = 1 to 9 = 9 number of digits in 2 digit numbers = 10 to 99 = 90 ( 2 ) = 180 number of digits in 3 digit numbers = 100 to 300 = 201 ( 3 ) = 603 total = 792 answer : option b
Answer: b
Problem: barbata invests $ 2800 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 1400 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2800 + 0.05 * 2800 + x + 0.08 x = 2800 + x + 0.06 ( 2800 + x ) 0.05 * 2800 + 0.08 x = 0.06 x + 0.06 * 2800 0.02 x = 2800 ( 0.06 - 0.05 ) x = 2800 * 0.01 / 0.02 = 1400 ans : ` ` d ' '"
Answer: d
Problem: at what rate percent on simple interest will rs . 600 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 9.33 % , e ) 11.67 %
Rationale: "350 = ( 600 * 5 * r ) / 100 r = 11.67 % answer : e"
Answer: e
Problem: a , b and c can do a work in 90 , 45 and 6 days respectively . if they work together , in how many days will they complete the work ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 11
Rationale: one days ' s work of a , b and c = 1 / 90 + 1 / 45 + 1 / 6 = ( 1 + 2 + 15 ) / 90 = 1 / 5 a , b and c together can do the work in 5 days . answer : a
Answer: a
Problem: a man can row upstream at 25 kmph and downstream at 41 kmph , and then find the speed of the man in still water ?
Options: a ) 33 , b ) 67 , c ) 30 , d ) 15 , e ) 17
Rationale: "us = 25 ds = 41 m = ( 41 + 25 ) / 2 = 33 answer : a"
Answer: a
Problem: i bought two books ; for rs . 450 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337 , b ) 262.5 , c ) 299.5 , d ) 266.5 , e ) 299
Rationale: "x * ( 85 / 100 ) = ( 450 - x ) 119 / 100 x = 262.5 answer : b"
Answer: b
Problem: how many multiples of 5 are there between 1 and 100 ( both are inclusive ) ?
Options: a ) 1.2 , b ) 20.8 , c ) 2.3 , d ) 6.7 , e ) 8.2
Rationale: "the answer is ( 100 - 1 ) / 5 + 1 = 20.8 answer is b"
Answer: b
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 2 / 5 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 ) 4 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 2 / 5 ) ( 4 + 4 x ) or , x = 4 answer d"
Answer: d
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 14 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 98 %
Rationale: 0,098 r = x / 100 * 0.1 r answer e
Answer: e
Problem: the speed of a train is 110 kmph . what is the distance covered by it in 11 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 88 kmph , d ) 20 kmph , e ) 12 kmph
Rationale: "110 * 11 / 60 = 20 kmph answer : d"
Answer: d
Problem: a sum of money at simple interest amounts to rs . 2240 in 2 years and to rs . 2600 in 5 years . the sum is :
Options: a ) rs . 1500 , b ) rs . 2000 , c ) rs . 1000 , d ) rs . 1200 , e ) rs . 1800
Rationale: "s . i . for 3 years = rs . ( 2600 - 2240 ) = rs . 360 . s . i . for 1 year = rs . 360 / 3 = rs . 120 . s . i . for 2 years = rs . ( 120 x 2 ) = rs . 240 . principal = rs . ( 2240 - 240 ) = rs . 2000 . answer : option b"
Answer: b
Problem: mother , her daughter and her grand child weighs 120 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 120 kg daughter + child = 60 kg mother = 120 - 60 = 60 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 60 = 12 kg so now daughter = 120 - ( mother + child ) = 120 - ( 60 + 12 ) = 48 kg answer : c"
Answer: c
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if 2 managers will not attend the meeting together .
Options: a ) 1.35 , b ) 2.91 , c ) 3.12 , d ) 4.36 , e ) 5.15
Rationale: "8 managers , but two of them can not attend the meeting together . we can split it into two cases . 1 . meeting without these two managers in it . that would mean selecting 5 , from the remaining 6 which is 6 c 5 = 6 2 . meeting with one of the two managers . select 1 manager from two , and then select 4 from the remaining 6 , which is 2 c 1 x 6 c 4 = 15 . so , answer is 30 + 6 = 36 . answer : d"
Answer: d
Problem: 150 is what percent of 60 ?
Options: a ) 250 % , b ) 20 % , c ) 50 % , d ) 200 % , e ) 500 %
Rationale: "60 * x = 150 - - > x = 2.5 - - > 2.5 expressed as percent is 250 % . answer : a ."
Answer: a
Problem: if each edge of cube increased by 25 % , the percentage increase in
Options: a ) 55 , b ) 52.25 , c ) 59.75 , d ) 51.75 , e ) 56.25
Rationale: "100 × ( 125 ) / 100 × ( 125 ) / 100 = 156.25 = > 56.25 % answer is e ."
Answer: e
Problem: in a class of students , 1 / 2 of the number of girls is equal to 1 / 5 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 3 / 2 , c ) 1 / 3 , d ) 2 / 3 , e ) 4 / 3
Rationale: "( 1 / 2 ) g = ( 1 / 5 ) ( b + g ) 5 g = 2 b + 2 g 3 g = 2 b b / g = 3 / 2 . the answer is b ."
Answer: b
Problem: how many 3 - digit positive integers are there , where each digit is positive , and no 3 adjacent digits are same ?
Options: a ) 1236 , b ) 504 , c ) 4096 , d ) 4608 , e ) 6561
Rationale: "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities 9 * 8 * 7 = 504 . b"
Answer: b
Problem: if n = ( 33 ) ^ 43 + ( 23 ) ^ 33 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 33 ) ^ 23 is the same as that of 3 ^ 23 and the units digit of ( 23 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 23 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 23 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 23 + ( 23 ) ^ 33 is 3 + 3 = 6 . answer : d ."
Answer: d
Problem: for a positive integer n , if 5 ^ n is a factor of 20 ! , but 5 ^ n + 1 is not a factor of 20 ! , what is the value of n ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: 20 ! has four 5 ' s 20 / 5 = 4 thus 5 ^ 4 can completely divide 20 ! and 5 ^ 5 can not divide 20 ! so , answer will be ( a ) 4
Answer: a
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 570 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 876 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 570 = > x = ( 570 * 100 ) / 65 = 876 answer d"
Answer: d
Problem: the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate r , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Problem: in what time will a railway train 96 m long moving at the rate of 45 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 8 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 96 / 45 * 18 / 5 = 8 sec answer : b"
Answer: b
Problem: what is x if x + 2 y = 10 and y = 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 3 in x + 2 y = 10 x + 2 ( 3 ) = 10 x + 6 = 10 if we substitute x by 4 in x + 6 = 10 , we have 4 + 6 = 10 . hence x = 4 correct answer d"
Answer: d
Problem: if 10 a = 6 b = 20 , then 120 ab =
Options: a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "10 a * 6 b = 20 * 20 = 400 60 ab = 400 i . e . 120 ab = 800 answer : option a"
Answer: a
Problem: which number need to add to 7844213 to get a number exactly divisible by 549 ?
Options: a ) 418 , b ) 148 , c ) 448 , d ) 248 , e ) 348
Rationale: "7844213 / 549 = 14288 and reminder = 101 . 549 - 101 = 448 so , the next number divisible by 549 is 448 places in front of 7844213 which means 448 + 7844213 = 7844661 448 should be added to 7844213 c"
Answer: c
Problem: a scale 7 ft . 12 inches long is divided into 4 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 24 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 7 * 12 ) + 12 = 96 inches length of each of the 4 parts = 96 / 4 = 24 inches answer : c"
Answer: c
Problem: the population of a town increases 10 % and 20 % respectively in two consecutive years . after the growth the present population of the town is 1320 . then what is the population of the town 2 years ago ?
Options: a ) 1100 , b ) 1001 , c ) 1010 , d ) 1000 , e ) 1002
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1320 * 100 / 110 * 100 / 120 = 1000 answer : option d"
Answer: d
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 408 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 1054 , c ) 788 , d ) 298 , e ) 177
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 408 62 % - - - - - - - - ? = > 1054 answer : b"
Answer: b
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 1104 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 2145 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 1104 ) ( x - 8 ) ^ 2 = t + 1104 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 2145 + 1104 = 3249 = 57 ^ 2 = ( x - 8 ) ^ 2 hence , x = 65 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 65 * 66 / 2 = 2145 hence , answer is a ."
Answer: a
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many v hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) v = 4 . , c ) v = 5 . , d ) v = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double v = 6 hrs . . so closest to that option is 5 ."
Answer: c
Problem: one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 10 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 20 , c ) 12 , d ) 8 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 10 r = 20 b"
Answer: b
Problem: the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 47 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.02 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 48 - 47 ) = 1801 . correct mean = 1801 / 50 = 36.02 answer : d"
Answer: d
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 5000 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1000 ft short of the summit and then descends at a rate of 1000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 11.0 , b ) 12.0 , c ) 13.0 , d ) 14.0 , e ) 15.0
Rationale: solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b
Answer: b
Problem: $ 200 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 80 , b ) $ 50 , c ) $ 25 , d ) $ 200 , e ) $ 50
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 200 * 2 / 5 = $ 80 answer is a"
Answer: a
Problem: if a ( a + 6 ) = 27 and b ( b + 6 ) = 27 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 6 , c ) 2 , d ) 46 , e ) 48
Rationale: "a ( a + 6 ) = 27 and b ( b + 6 ) = 27 = > a , b must be integers and if a is - 9 or 3 , b will be 3 and - 9 respectively = > a + b = - 6 ans : b"
Answer: b
Problem: the base of a right triangle is 8 and hypotenuse is 10 . its area is ?
Options: a ) 12
b ) 80
c ) 59
d ) 24
e ) 25
Rationale: explanation : h 2 = ( 10 ) 2 - ( 8 ) 2 - ( 6 ) 2 - > h = 6 1 / 2 * 8 * 6 = 24 answer is d
Answer: d
Problem: jack and jill work at a hospital with 3 other workers . for an internal review , 2 of the 5 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 10 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3
Rationale: 1 / 5 c 2 = 1 / 10 . answer : b .
Answer: b
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 6000 m 3 , b ) 4580 m 3 , c ) 18500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 4000 * 2 * 45 ) / 60 = 6000 m 3 answer : option a"
Answer: a
Problem: the ratio of two quantities is 5 to 6 . if each of the quantities is increased by 15 , what is the ratio of these 2 new quantities ?
Options: a ) 5 : 6 , b ) 25 : 27 , c ) 15 : 16 , d ) 20 : 21 , e ) it can not be determined from the information given
Rationale: the ratio can not be straight way added any quantity . . . 5 : 6 means 5 x : 6 x . . . so when you add a quantity , it becomes 5 x + 15 : 6 x + 15 . . so value of x is must . . ans e
Answer: e
Problem: a sum of $ 1000 amounts to $ 1500 in 5 years at simple interest . if the interest rate is increased by 5 % it would amount to how much ?
Options: a ) $ 1000 , b ) $ 750 , c ) $ 1541 , d ) $ 1478 , e ) $ 1750
Rationale: "s . i = 1500 - 1000 = 500 p = $ 1000 t = 5 years r = 100 * 500 / 1000 * 5 = 10 % new rate = 10 + 5 = 15 % new s . i . = 1000 * 15 * 5 / 100 = $ 750 new amount = 1000 + 750 = $ 1750 answer is e"
Answer: e
Problem: if f ( x ) = ax ^ 5 – 3 x ^ 2 + ax ^ 2 – x , then f ( b ) – f ( - b ) will equal :
Options: a ) 0 , b ) 2 ab , c ) 2 ab ^ 4 – 6 , d ) 2 ab ^ 5 - 2 b , e ) ab ^ 5
Rationale: "f ( x ) = ax ^ 5 – 3 x ^ 2 + ax ^ 2 – x f ( b ) = ab ^ 5 – 3 b ^ 2 + ab ^ 2 – b f ( - b ) = - ab ^ 5 – 3 b ^ 2 + ab ^ 2 + b f ( b ) - f ( - b ) = ab ^ 5 – 3 b ^ 2 + ab ^ 2 – b + ab ^ 5 + 3 b ^ 2 - ab ^ 2 – b = 2 ab ^ 5 - 2 b answer d"
Answer: d
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.3 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 4 : 5 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.3 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.3 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.5 = 4 / 5 required ratio = 4 / 5 : 1 = 4 : 5 . answer : d"
Answer: d
Problem: a man whose bowling average is 12.4 , takes 8 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 173 , b ) 174 , c ) 175 , d ) 176 , e ) 177
Rationale: "12.4 * x + 26 = ( 8 + x ) 12 solve equation x = 175 answer : c"
Answer: c
Problem: a number when divided by 342 gives a remainder 47 . when the same number is divided by 19 what would be the remainder ?
Options: a ) 0 , b ) 9 , c ) 19 , d ) 29 , e ) 18
Rationale: number = 342 k + 47 = 19 * 18 k + 19 * 2 + 9 = 19 ( 18 k + 2 ) + 9 . the given number when divided by 19 gives 18 k + 2 as quotient and 9 as remainder . answer b 9
Answer: b
Problem: a train passes a station platform in 62 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 615 m , b ) 240 m , c ) 168 m , d ) 444 m , e ) 691 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 62 = 15 = > x = 444 m answer : d"
Answer: d
Problem: a , b and c enter into a partnership by investing $ 7000 , $ 11000 and $ 18000 respectively . at the end of 8 months , b receives $ 2200 as his share . find the share of a .
Options: a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1500 , e ) $ 1600
Rationale: "the ratio of capital of a , b and c = 7000 : 11000 : 18000 = 7 : 11 : 18 a ' s share = ( 7 / 11 ) * 2200 = $ 1400 the answer is c ."
Answer: c
Problem: if 40 % of a certain number is 160 , then what is 10 % of that number ?
Options: a ) 100 , b ) 40 , c ) 80 , d ) 120 , e ) 110
Rationale: explanation : 40 % = 40 * 4 = 160 10 % = 10 * 4 = 40 answer : option b
Answer: b
Problem: a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 2100 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 600 , b ) 715 , c ) 600 , d ) 875 , e ) 900
Rationale: "principal = ( 100 * 2100 ) / ( 12 * 20 ) = rs . 875 answer : d"
Answer: d
Problem: the average ( arithmetic mean ) of 24 , 35 , and 58 is 6 more than the average of 19 , 51 , and x . what is x ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "the average of 24 , 35 , and 58 is 39 . the average of 19 , 51 and x is 33 . then 19 + 51 + x = 99 . x = 29 . the answer is d ."
Answer: d
Problem: instead of multiplying a number by 5 , the number is divided by 5 . what is the percentage of error obtained ?
Options: a ) 98 % , b ) 97 % , c ) 96 % , d ) 99 % , e ) 95 %
Rationale: "let the number be x the right number is 5 x the wrong number is x / 5 error is ( 5 x - x / 5 ) = 24 x / 5 percentage of error is ( ( 24 x / 5 ) / 5 x ) * 100 = 96 % answer : c"
Answer: c
Problem: a person crosses a 600 m long street in 5 minutes , what is his speed in km per hour ?
Options: a ) 4.3 , b ) 7.2 , c ) 2.3 , d ) 3.2 , e ) 1.1
Rationale: "explanation : speed = { \ color { blue } \ left ( \ frac { 600 } { 5 \ times 60 } \ right ) m / sec = 2 m / sec = \ left ( 2 \ times \ frac { 18 } { 5 } \ right ) km / hr = 7.2 km / hr } answer : b"
Answer: b
Problem: the length of a train and that of a platform are equal . if with a speed of 72 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 750 , e ) 600
Rationale: "speed = [ 72 * 5 / 18 ] m / sec = 20 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 20 = > x = 20 * 60 / 2 = 600 answer : e"
Answer: e
Problem: square a has an area of 81 square centimeters . square b has a perimeter of 32 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 17 / 64
b ) 17 / 81
c ) 16 / 25
d ) 3 / 5
e ) 6 / 25
Rationale: i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 32 , then its side is 32 / 4 = 8 and the area is 4 ^ 2 = 64 ; empty space between the squares is 81 - 64 = 17 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 17 / 81 . answer : b
Answer: b
Problem: one hour after yolanda started walking from x to y , a distance of 60 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 5 miles per hour and bob â s was 6 miles per hour , how many miles had bob walked when they met ?
Options: a ) 40 , b ) 25 , c ) 28 , d ) 30 , e ) 30.5
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 5 ( t + 1 ) miles . these distances must sum to 60 miles , so 6 t + 5 ( t + 1 ) = 60 , which may be solved for t as follows 6 t + 5 ( t + 1 ) = 60 6 t + 5 t + 5 = 60 11 t = 55 t = 5 ( hours ) therefore , bob had walked 6 t = 6 ( 5 ) = 30 miles when they met . the best answer is d ."
Answer: d
Problem: in a class of 25 students , 15 play hockey and 16 play basketball . if there are 4 students who play neither sport , determine the number of students who play both hockey and basketball ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: let the number of who play both be x number of students who play sports 25 - 4 = 21 use venn diagram ( 15 - x ) + x + ( 16 - x ) = 21 which gives x = 10 answer is a 10 play both sport
Answer: a
Problem: what is the difference between 80 % of 170 and 35 % of 300 .
Options: a ) 30 , b ) 29 , c ) 37 , d ) 36 , e ) 31
Rationale: "( 80 / 100 ) * 170 â € “ ( 35 / 100 ) * 300 136 - 105 = 31 answer : e"
Answer: e
Problem: a car travels first 160 km at 90 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 84.7 , c ) 71.1 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 90 km / hr time taken to travel first 160 km = distancespeed = 160 / 90 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 90 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 90 + 160 / 80 ) = 84.7 km / hr answer : b"
Answer: b
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 37 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 370 , c ) 266 , d ) 299 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 37 sec = 37 * 10 = 370 m . the length of the faster train = 370 m . answer : b"
Answer: b
Problem: a water tank which could be filled in 5 hours takes one more hour to be filled as a result of a leak in its bottom . if the tank is full calculate the time it will take for the leak empty it ?
Options: a ) 32 hours , b ) 30 hours , c ) 34 hours , d ) 31 hours , e ) 33 hours
Rationale: part filled without leak in 1 hour = 1 / 5 part filled with leak in 1 hour = 1 / 6 work done by leak in 1 hour = 1 / 5 â ˆ ’ 1 / 6 = 30 hours answer : b
Answer: b
Problem: country x taxes each of its citizens an amount equal to 10 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 60,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.10 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 12,000 - - > x = 60,000 . answer : c ."
Answer: c
Problem: two trains of length 100 m and 200 m are 70 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ?
Options: a ) 2 sec , b ) 32 / 3 sec , c ) 20 / 7 sec , d ) 32 / 3 sec , e ) 53 / 2 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 70 / 35 = 2 sec . answer : a"
Answer: a
Problem: the area of a rectangular plot is 24 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 14 metres
b ) 5 metres
c ) 7.5 metres
d ) data inadequate
e ) none of these
Rationale: l × b = 24 × b ∴ l = 24 m and l – b = 10 ∴ b = 24 – 10 = 14 m answer a
Answer: a
Problem: peter ' s average ( arithmetic mean ) test score on 4 tests is 78 . what must be the student ' s score on a 5 th test for the peter ' s average score on the 5 tests to be 80 ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: e . 88 peter must score at least an 80 for sure . if he scores an 8 , then he will need to score 2 pots for each of the 4 other tests tomake upthe difference . they each were at 78 ( at least the average is , but this is a small point and does n ' t matter to the answer ) . so 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average , so 80 + 8 = 88 .
Answer: e
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 14 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 350 m , c ) 267 m , d ) 535.71 m , e ) 656 m
Rationale: "speed = 300 / 14 = 150 / 7 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 150 / 7 = > x = 535.71 m . answer : d"
Answer: d
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 21 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 256 , e ) 312
Rationale: "so 12.2 * 21 = 256 . . imo option d is correct answer . ."
Answer: d
Problem: find the 15 th term of an arithmetic progression whose first term is 2 and the common difference is 3 .
Options: a ) 45 , b ) 38 , c ) 44 , d ) 40 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 2 + ( 15 - 1 ) * 3 , = 2 + 42 = 44 . answer : c"
Answer: c
Problem: a fill pipe can fill 1 / 2 of cistern in 15 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 1 min , b ) 5 min , c ) 10 min , d ) 15 min , e ) 20 min
Rationale: "required time = 15 * 2 * 1 / 2 = 15 minutes answer is d"
Answer: d
Problem: a train passes a platform in 30 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 150 meter , b ) 240 meter , c ) 200 meter , d ) 260 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 30 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 30 = > 300 + l = 15 × 30 = 450 = > l = 450 - 300 = 150 meter answer : option a"
Answer: a
Problem: kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ?
Options: a ) 1900 , b ) 3500 , c ) 4000 , d ) 4200 , e ) 4450
Rationale: "let the number of 50 – rupee notes be x . then , the number of 100 - rupee notes = ( 85 – x ) 50 x + 100 ( 85 – x ) = 5000 = x + 2 ( 85 – x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : option b"
Answer: b
Problem: a 250 meter long train crosses a platform in 40 seconds while it crosses a signal pole in 20 seconds . what is the length of the platform ?
Options: a ) 500 , b ) 1000 , c ) 350 , d ) 250 , e ) 20
Rationale: "speed = [ 250 / 20 ] m / sec = 25 / 2 m / sec . let the length of the platform be x meters . then , x + 250 / 40 = 25 / 2 2 ( x + 250 ) = 1000 è x = 250 m . answer : d"
Answer: d
Problem: in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many different victory circles are possible ?
Options: a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648
Rationale: gold can be awarded in 4 ways , then silver can be awarded in 3 ways and bronze in 2 ways . therefore the total number of ways are : 4 * 3 * 2 = 24 ways of awarding the medals and the same number of ways of forming the circle . this is when there is no tie . and if there is tie , for example all three receive the gold or the silver or the bronze , then there are 4 more cases . which implies 24 * 4 = 96 . ans : c
Answer: c
Problem: a goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 140 m , c ) 160 m , d ) 170 m , e ) none of these
Rationale: explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , [ ( x + 350 ) / 26 ] = 20 = > x + 350 = 520 = > x = 170 . answer : d
Answer: d
Problem: the population of a town increased from 1 , 62,500 to 2 , 62,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5 % , c ) 6.154 % , d ) 8.75 % , e ) none of these
Rationale: "solution increase in 10 year = ( 262500 - 162500 ) = 100000 . increase % = ( 100000 / 162500 x 100 ) % = 61.54 % â ˆ ´ required average = ( 61.54 / 10 ) % = 6.154 % answer c"
Answer: c
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 45 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 45 , b ) 14 / 45 , c ) 8 / 45 , d ) 3 / 45 , e ) 7 / 45
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41,43 } n ( x ) = 14 , n ( s ) = 45 hence , the required probability is 14 / 45 . answer : b"
Answer: b
Problem: on increasing the price of t . v . sets by 80 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 44 , b ) 5 , c ) 56 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 180 × 80 ) = rs . 14400 increase % = 4400 / 10000 × 100 = 44 % answer : a"
Answer: a
Problem: in a hostel , the number of students decreased by 15 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 1.96 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 15 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.85 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.85 * 1.2 ) = > f ( new ) = 0.9804 f therefore the new cost of food must be 98.04 % of the old cost , or the cost of food must decrease by 1.96 % ( option e )"
Answer: e
Problem: a family pays $ 800 per year for an insurance plan that pays 70 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 800 $ family needs to pay 30 % of first 1000 $ in expense = 300 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 300 = 1100 $ total amount paid by insurance plan for first 1000 $ = 800 $ total amount paid by family will equal amount paid by plan when medical expense = 1400 $ ( since insurance plan will pay 100 % of amount that exceeds 1100 $ ) answer c"
Answer: c
Problem: a bag contains 5 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 5 / 26 , d ) 3 / 29 , e ) 4 / 27
Rationale: p ( both are red ) , = 5 c 215 c 2 = 5 c 215 c 2 = 10 / 105 = 2 / 21 b
Answer: b
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 27 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 13.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 27 % 0.4 x + ( m - x ) 0.25 = 0.27 m 0.15 x = 0.02 m x = 0.1333 m x = 13.33 % of m b"
Answer: b
Problem: a , b , c , d , e , f are the only 6 families in indira nagar . a , b , c , d , e and f has 7 , 8 , 10 , 13 , 6 , and 10 member in their families respectively . if 1 member from all the 6 families left their respective families to accommodate themselves in the hostel of iim lucknow , then the average number of member now in each family of indira nagar is
Options: a ) 8 , b ) 9 , c ) 10 , d ) 13 , e ) 15
Rationale: answer required average = ( ( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + ( 6 - 1 ) + ( 10 - 1 ) ) / 6 = ( 7 + 8 + 10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6 = 9 - 1 = 8 correct option : a
Answer: a
Problem: a rectangular grass field is 75 m * 40 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350
b ) s . 1327
c ) s . 1200
d ) s . 1397
e ) s . 1927
Rationale: area = ( l + b + 2 d ) 2 d = ( 75 + 40 + 2.5 * 2 ) 2 * 2.5 = > 600 600 * 2 = rs . 1200 answer : c
Answer: c
Problem: if - 2 x + 3 y = 8 and 4 x - 3 y = 20 , what is the sum of x and y ?
Options: a ) 24 , b ) 28 , c ) 18 , d ) 26 , e ) 32
Rationale: "given - 2 x + 3 y = 8 - - - eq 1 4 x - 3 y = 20 - - eq 2 sum both eqns we get 2 x = 28 = > x = 14 sub 2 x in eq 1 = > - 28 + 3 y = 8 . = > y = 12 now x + y = 12 + 14 = 26 option d is correct answer ."
Answer: d
Problem: in a river flowing at 2 km / hr , a boat travels 72 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 27 hours , e ) none of these
Rationale: explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 72 km total time taken = time taken downstream + time taken upstream = ( 72 / 8 ) + ( 72 / 4 ) = 27 hr . answer : option d
Answer: d
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 3.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 999 , d ) s . 1085 , e ) s . 2331
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 3.5 = 2331 answer : e"
Answer: e
Problem: if a - b = 5 and a 2 + b 2 = 29 , find the value of ab .
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 2
Rationale: 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 25 = 4 ab = 2 . answer : e
Answer: e
Problem: how many miles is 320 km ?
Options: a ) 150 miles , b ) 175 miles , c ) 200 miles , d ) 225 miles , e ) 250 miles
Rationale: "200 miles 320 / 1.6 = 200 answer : c"
Answer: c
Problem: 60 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 12 days
Rationale: "1 women ' s 1 day work = 1 / 420 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 420 + 10 / 140 ) = 1 / 12 5 women and 10 children will complete the work in 12 days . answer : e"
Answer: e
Problem: how many seconds will it take for a car that is traveling at a constant rate of 14 miles per hour to travel a distance of 96 yards ? ( 1 mile = 1,160 yards )
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: "speed = 14 miles / hr = 6.84 yard / s distance = 96 yards time = distance / speed = 96 / 6.84 = 14 sec ans - d"
Answer: d
Problem: in how many years rs 200 will produce the same interest at 10 % as rs . 400 produce in 5 years at 12 %
Options: a ) 16 , b ) 13 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 400 , time 5 years and rate 12 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 200 * 10 ) = 12 option c"
Answer: c
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 196 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 1000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1028 , e ) s : 1400
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 196 100 % - - - - ? = > rs : 1400 answer : e"
Answer: e
Problem: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 37 % ryegrass , what percent of the weight of the mixture is from mixture x ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "37 % is 12 % - points above 25 % and 3 % - points below 40 % . thus the ratio of mixture y to mixture x is 1 : 4 . the percent of mixture x is 4 / 5 = 80 % . the answer is e ."
Answer: e
Problem: how many cubes of 10 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 10000 cubes , b ) 1000 cubes , c ) 100 cubes , d ) 50 cubes , e ) none of these
Rationale: "explanation : number of cubes = 100 ∗ 100 ∗ 100 / 10 ∗ 10 ∗ 10 = 1000 note : 1 m = 100 cm option b"
Answer: b
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 35 kms . what was the total distance travelled in 12 hours ?
Options: a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these
Rationale: "explanation : total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . . . upto 12 terms ) this is an a . p with first term , a = 35 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 × 35 + { 12 - 1 ) × 2 ] = 6 ( 70 + 23 ) = 552 kms . answer : c"
Answer: c
Problem: a and b together can do a piece of work in 10 days . b alone can finish it in 20 days . in how many days can a alone finish the work ?
Options: a ) 20 , b ) 10 , c ) 15 , d ) 5 , e ) 7
Rationale: time taken by a to finish the work = xy / ( y - x ) = 10 x 20 / ( 20 - 10 ) = 200 / 10 = 20 days answer : a
Answer: a
Problem: the ratio of pens to pencils is 5 to 6 . there are 7 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 55 , e ) 64
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 7 x = 7 the number of pencils is 42 . the answer is b ."
Answer: b
Problem: the average score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 42 , then find the average for the last 4 matches .
Options: a ) 33.5 , b ) 33.5 , c ) 34.25 , d ) 35 , e ) none of these
Rationale: solution required average = ( 38.9 x 10 ) - ( 42 x 6 ) / 4 = 137 / 4 = 34.25 answer c
Answer: c
Problem: the area of a square is equal to seven times the area of a rectangle of dimensions 25 cm * 343 cm . what is the perimeter of the square ?
Options: a ) 810 cm , b ) 800 cm , c ) 980 cm , d ) 718 cm , e ) 860 cm
Rationale: "area of the square = s * s = 7 ( 343 * 25 ) = > s = 5 * 7 * 7 = 245 cm perimeter of the square = 4 * 245 = 980 cm . answer : c"
Answer: c
Problem: the distance between a & b is 600 km . a person is traveling from a to b at 70 km / hr started at 10 am and another person is traveling from b to a at 80 km / hr and started at same time . then at what time they meet together .
Options: a ) 2 pm , b ) 4 pm , c ) 1 pm , d ) 3 pm , e ) 5 pm
Rationale: let x hours be they will meet together distance covered by 1 st person + distance covered by 2 nd person = 600 km 70 x + 80 x = 600 x = 4 hr they will meet = 10 am + 4 hr = 2 pm answer is a
Answer: a
Problem: a train running at 1 / 4 of its own speed reached a place in 12 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 9 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 4 * 12 = 3 hrs time saved = 12 - 3 = 9 hrs answer : a"
Answer: a
Problem: when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 67.50 , what was the total value of the item ?
Options: a ) $ 1,150 , b ) $ 1,450 , c ) $ 1,750 , d ) $ 2,150 , e ) $ 2,450
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 67.5 x = $ 750 the total value was $ 750 + $ 1,000 = $ 1,750 . the answer is c ."
Answer: c