regisss/math_qa huggingface dataset:
Problem: by selling 10 pens for a rupee a woman loses 18 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 6 , e ) 7
Rationale: "d 82 % - - - 10 130 % - - - ? 82 / 130 * 10 = 6"
Answer: d
Problem: what is the greatest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?
Options: a ) 9800 , b ) 9600 , c ) 9400 , d ) 9500 , e ) 9200
Rationale: greatest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , greatest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : b
Answer: b
Problem: a one - foot stick is marked in 1 / 3 and 1 / 4 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "lcm of 12 = 12 1 / 3 marking are ( table of 4 ) 0 . . . . . . 4 . . . . . . 8 . . . . . 12 ( total = 4 ) 1 / 4 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 ( total = 5 ) overlapping markings are 0 . . . . . . . . 12 ( total = 2 ) total markings = 4 + 5 - 2 = 7 answer = c"
Answer: c
Problem: a company has a hierarchical system where for every 10 workers , there is one team lead , and for every 3 teams leads , there is one supervisor . if the company has 13 supervisors , how many workers does it have ?
Options: a ) 140 , b ) 321 , c ) 390 , d ) 500 , e ) 130
Rationale: some students may initially answer 130 to this question , especially if answering similar problems . however , that would be incorrect , as this is not a straight - forward ratio of 1 : 3 : 10 . the ratio of supervisors to team leads is 1 : 3 , and the ratio of team leads to workers is 1 : 10 . therefore , the ratio of supervisors to workers is 1 : 30 . therefore , 13 * 30 = 390 answer : c )
Answer: c
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 9 km / hr completes one round in 5 min , then the area of the park ( in sq . m ) is ?
Options: a ) 337500 m , b ) 300000 m , c ) 153600 m , d ) 33750 m , e ) 9000 m
Rationale: "perimeter = distance covered in 5 min . = ( 9000 x 5 ) / 60 m = 750 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 750 or x = 75 . length = 225 m and breadth = 150 m . area = ( 225 x 150 ) m 2 = 33750 m d"
Answer: d
Problem: a train 120 m long is running with a speed of 66 km / hr . in what time will it pass a man who is roller skating at 12 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.92 , b ) 6.92 , c ) 7.92 , d ) 4.92 , e ) 2.92
Rationale: "speed of train relative to man = 66 + 12 = 78 km / hr . = 78 * 5 / 18 = 65 / 3 m / sec . time taken to pass the man = 150 * 3 / 65 = 6.92 sec . answer : b"
Answer: b
Problem: paul ' s income is 20 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?
Options: a ) 26 / 27 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.8 r = 8 q = 0.8 p = 6.4 s = 0.6 p = 4.8 for that we get s = 10.8 and q 10.4 so 10.4 / 10.8 = 2.6 / 2.7 ans : a"
Answer: a
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 20 * 16 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 20 and 16 is 4 . hence 20 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 20 * 16 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Problem: how many quarters are equal to 2 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7
Rationale: b . 8 quarters
Answer: b
Problem: a person borrows 7000 for 3 years at 6 % p . a . simple interest . he immediately lends it to another person at 31 % p . a . for 3 years . find his gain in the transaction per year .
Options: a ) 1600 , b ) 1700 , c ) 1550 , d ) 1650 , e ) 1750
Rationale: "gain in 3 years = [ ( 7000 ã — 31 ã — 3 / 100 ) â ˆ ’ ( 7000 ã — 6 ã — 3 / 100 ) ] = ( 6510 â € “ 1260 ) = 5250 . â ˆ ´ gain in 1 year = ( 5250 â  „ 3 ) = 1750 answer e"
Answer: e
Problem: david obtained 86 , 85 , 82 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 276 , c ) 87 , d ) 85 , e ) 11
Rationale: "explanation : average = ( 86 + 85 + 82 + 87 + 85 ) / 5 = 425 / 5 = 85 . answer : d"
Answer: d
Problem: how many of the positive factors of 56 , 96 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 56 - 1 , 2 , 4 , 7 , 8 , 14 , 28 , 56 factors of 96 - 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 32 , 48 , 96 comparing both , we have three common factors of 56 and 96 - 1 , 2,4 answer ( c )"
Answer: c
Problem: it takes joey the postman 1 hours to run a 4 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 5 mile / hour , what is the speed with which joey returns ?
Options: a ) 6 2 / 3 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 4 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 4 * x / 4 + x = 5 8 x = 5 x + 20 = > 3 x = 20 = > x = 6 2 / 3 a"
Answer: a
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 43.15 $
Rationale: "let x be the amount the most their food can cost . x + 0.07 x + 0 . 15 x = 50 solving for x , x = 40.98 $ , this is the maximum amount that can be used for food . hence 40.63 $ is the maximum value less than 40.98 $ hence option b"
Answer: b
Problem: the sum of present age of abe and the age before 7 years is 37 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 37 2 x - 7 = 37 2 x = 37 + 7 x = 44 / 2 x = 22 z = x + 7 = 22 + 7 = 29 answer : e"
Answer: e
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price w of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price w = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 12 % solution ?
Options: a ) a ) 6.7 , b ) b ) 2.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 12 / 100 250 + 25 x = 300 + 3 x 22 x = 50 x = 2.3 answer is b"
Answer: b
Problem: what is the total number of integers between 111 and 222 that are divisible by 9 ?
Options: a ) 12 , b ) 10 , c ) 11 , d ) 14 , e ) 13
Rationale: "117 , 126 , 135 , . . . , 207,216 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 216 - 117 ) / ( 9 ) + 1 = 99 / 9 + 1 = 11 + 1 = 12 answer is a"
Answer: a
Problem: 350 is increased by 50 % . find the final number .
Options: a ) 725 , b ) 625 , c ) 225 , d ) 525 , e ) 425
Rationale: explanation final number = initial number + 50 % ( original number ) = 350 + 50 % ( 350 ) = 350 + 175 = 525 . answer d
Answer: d
Problem: a train 240 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 54 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: "s = 240 / 16 * 18 / 5 = 54 kmph answer : c"
Answer: c
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 2400 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 300 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 2400 × ( 1 / 8 ) = 300 answer : option a"
Answer: a
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 15 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 19 % , b ) 21 % , c ) 23 % , d ) 25 % , e ) 27 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 0.6 x = 1.05 x 1.05 x / 5 x = 0.21 the answer is b ."
Answer: b
Problem: pr is tangent to a circle at point p . q is another point on circle such that pq is diameter of circle and rq cuts circle at m . if radius of circle is 4 units and pr = 6 units . find ratio of triangle pmr to pqr .
Options: a ) 11 / 20
b ) 3 / 5
c ) 13 / 20
d ) 18 / 25
e ) 18 / 26
Rationale: let pm = y qm = x mr = 10 - x in triangle pqm , pm ^ 2 + qm ^ 2 = pq ^ 2 = > x ^ 2 + y ^ 2 = 64 . . . . . ( 1 ) in triangle pmr , pm ^ 2 + mr ^ 2 = pr ^ 2 y ^ 2 + ( 10 - x ) ^ 2 = 36 . . . . . . ( 2 ) solving for x and y x = 6.4 y = 4.8 taking permineter of triangle pqr = 24 perimeter of triangle pmr = 14.4 take ratio 14.4 / 24 = 0.6 answer : c
Answer: c
Problem: if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by :
Options: a ) 6 , b ) 12 , c ) 24 , d ) 6 only , e ) 6 and 12 both
Rationale: explanation : ( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . e
Answer: e
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 17 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 391 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 17 ) . larger number = ( 23 x 17 ) = 391 . answer : option c"
Answer: c
Problem: a rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet . if the surface of the rug does not extend beyond the area of the floor , what fraction of the area of the floor is not covered by the rug ?
Options: a ) a . 3 / 16
b ) 1 / 4
c ) c . 1 / 2
d ) 25 / 32
e ) 7 / 8
Rationale: area of the rectangular rug = 2 * 7 = 14 fraction not covered by the rug = ( total area - rug area ) / total area = ( 64 - 14 ) / 64 = 25 / 32 = d
Answer: d
Problem: find the value of ( 55 + 113 / 78 ) × 78
Options: a ) 4423 , b ) 4403 , c ) 4413 , d ) 2403 , e ) 4375
Rationale: "= ( 55 + 113 / 78 ) × 78 = ( 4290 + 113 ) / 78 × 78 = 4403 / 78 × 78 = 4403 answer is b ."
Answer: b
Problem: if two typists can type two pages in two minutes , how many typists will it take to type 25 pages in 5 minutes ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 12 , e ) 36
Rationale: in 2 minutes 2 typists type 2 pages which means that in 5 minutes they will type 5 pages but to type 25 pages ( 5 times ) we need 5 times more typists i . e . 2 x 5 = 10 typists . c
Answer: c
Problem: the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 11 years
Rationale: "given that a + b = 11 + b + c = > a â € “ c = 11 + b â € “ b = 11 = > c is younger than a by 11 years answer : e"
Answer: e
Problem: n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 12 ?
Options: a ) 12 , b ) 6 , c ) 14 , d ) 16 , e ) 10
Rationale: n ^ ( n / 2 ) = 12 apply log n / 2 logn = log 12 nlogn = 2 log 12 = log 12 ^ 2 = log 144 logn = log 144 now apply antilog n = 144 / n now n = 12 answer : a
Answer: a
Problem: a sum of money at simple interest amounts to rs . 800 in 3 years and to rs . 850 in 4 years . the sum is :
Options: a ) rs . 670 , b ) rs . 690 , c ) rs . 600 , d ) rs . 625 , e ) rs . 654
Rationale: "explanation : s . i . for 1 year = rs . ( 850 - 800 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 800 - 150 ) = rs . 600 . answer : option c"
Answer: c
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? e"
Answer: e
Problem: if y is the smallest positive integer such that 4410 multiplied by y is the square of an integer , then y must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 10
Rationale: 4410 = 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 2 * 5 = 10 . the answer is e .
Answer: e
Problem: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 20 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 35 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 20 / 17 - - > the least positive value of p + 1 is 20 , so the least value of p is 19 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 19 + 16 = 35 . answer : a"
Answer: a
Problem: a portion of the 80 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 50 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.8 ( 1 - x ) + 0.2 * x = 0.5 - - > x = 1 / 2 . answer : b ."
Answer: b
Problem: the maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 16 , b ) 18 , c ) 36 , d ) 19 , e ) 32
Rationale: "number of pens = 1008 number of pencils = 928 required number of students = h . c . f . of 1008 and 928 = 16 answer is a"
Answer: a
Problem: lilly has 10 fish and rosy has 12 fish . in total , how many fish do they have in all ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: 10 + 12 = 22 the answer is c .
Answer: c
Problem: what is the least common multiple of 6 , 18 , and 24 ?
Options: a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 6 = 2 * 3 18 = 2 * 3 ^ 2 24 = 2 ^ 3 * 3 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"
Answer: a
Problem: the ratio of number of boys and girls in a school is 2 : 5 . if there are 420 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 420 number of girls in the school = 5 * 420 / 7 = 300 answer is c"
Answer: c
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 20 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 15 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: speed = 100 / 1 = 100 km / hr new speed = 100 - 20 = 80 km / hr time taken = 100 / 80 = 1 hr 15 min answer is b
Answer: b
Problem: a bag contains 3 red , 4 black and 2 white balls . what is the probability of drawing a red and a white ball in two successive draws , each ball being put back after it is drawn ?
Options: a ) 2 / 27 , b ) 1 / 9 , c ) 1 / 3 , d ) 4 / 27 , e ) 2 / 9
Rationale: p = 2 ∗ 39 ∗ 29 = 427 p = 2 ∗ 39 ∗ 29 = 427 we are multiplying by 2 as there are two possible wining scenarios rw and wr . answer : d .
Answer: d
Problem: last year sandy saved 10 % of her annual salary . this year , she made 10 % more money than last year , and she saved 15 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 142 % , b ) 150 % , c ) 165 % , d ) 176 % , e ) 188 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.15 * 1.1 x = 0.165 x 0.165 x / 0.1 x = 1.65 = 165 % the answer is c ."
Answer: c
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 t , 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: the difference between the place values of 7 and 3 in the number 527435 is
Options: a ) 4 , b ) 5 , c ) 45 , d ) 6970 , e ) none
Rationale: "sol . = ( place value of 7 ) – ( place value of 3 ) = ( 700 - 30 ) = 6970 answer d"
Answer: d
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container m ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Problem: a and b together can do a work in 2 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 2.4 days , b ) 8 days , c ) 1.2 days , d ) 1.0 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 2 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 2 ) - ( 1 / 12 ) = 2.4 days answer : option a"
Answer: a
Problem: list k consists of 12 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = c = 7 if least = - 3 , then largest = 8 range = 8 - 1 = 7"
Answer: c
Problem: let a , b , c be distinct digits . consider a two - digit number ‘ ab ’ and a 3 - digit number ‘ ccb ’ , both defined under the usual decimal number system , if ( ab ) 2 = ccb > 300 , then the value of b is
Options: a ) 1 , b ) 0 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : given , ( ab ) 2 = ccb . [ only 1 , 5 and 6 on squaring will result with same digits in units place . ] taking a = 2 , b = 1 , = > ( 21 ) ^ 2 = 441 > 300 . hence , the required value of b = 1 answer : a
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 21 seconds . find the length of the train .
Options: a ) 350 m , b ) 145 m , c ) 240 m , d ) 135 m , e ) 255 m
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 350 meter answer : a"
Answer: a
Problem: instead of multiplying a number by 7 , the number is divided by 7 . what is the percentage of error obtained ?
Options: a ) 97.959 % , b ) 98.959 % , c ) 99.959 % , d ) 96.959 % , e ) 95.959 %
Rationale: "let the number be x the right number is 7 x the wrong number is x / 7 error is ( 7 x - x / 7 ) = 48 x / 7 percentage of error is ( ( 48 x / 7 ) / 7 x ) * 100 = 97.959 % answer : a"
Answer: a
Problem: find how many 4 digits no . is less then 1239 such that all 4 digits are distinct .
Options: a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72
Rationale: case 1 - 1000 - 1099 - there are 56 distinct digits case 2 - 1200 - 1209 - there are 7 distinct digits case 3 - 1230 - 1239 ( excluding 1239 ) - there are 6 distinct digits hence , 56 + 7 + 6 = 69 answer : b
Answer: b
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 3 times , what is the probability that it will land tails up on the first flip and not on the last 2 flips ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 3 / 4
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 8 answer : a
Answer: a
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 360 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 43 , c ) 50 , d ) 53 , e ) 62
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 360 / 9 = 40 , so the median is also 40 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 43 . option b"
Answer: b
Problem: a factory produces 4340 toys per week . if the workers at this factory work 2 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2170 toys , c ) 2375 toys , d ) 2175 toys , e ) 5375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 2 days ) by 2 . 4340 / 2 = 2170 toys correct answer b"
Answer: b
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 9 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 65.25 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 91 / 100 ) = 59.375 mp = 65.25 answer : a"
Answer: a
Problem: the mean of 50 observations was 36 . it was found later that an observation 34 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.0 , b ) 36.5 , c ) 36.24 , d ) 36.12 , e ) 36.22
Rationale: "explanation : correct sum = ( 36 * 50 + 434 - 23 ) = 1825 . correct mean = = 1811 / 50 = 36.5 answer : e ) 36.22"
Answer: e
Problem: in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 3 and a y - intercept of - 3 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 3 x - 3 3 x - 3 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Problem: if - 11 and - 8 are negative integers , then - 11 * - 8 + 5 is
Options: a ) - 14 , b ) 14 , c ) 33 , d ) 83 , e ) 93
Rationale: answer : e
Answer: e
Problem: if there are 20 apples and the apples have to be shared equally among 3 babies . what number of apples are to be added ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given there are 20 apples . if 1 extra apple is added , then it becomes 21 which can be divided equally that is 7 apples to each baby . option a is correct .
Answer: a
Problem: 8 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire rest of the car , then the share of each of the remaining persons increased by ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 7 , d ) 7 / 8 , e ) 8 / 7
Rationale: when there are eight people , the share of each person is 1 / 8 th the total cost answer : b
Answer: b
Problem: a box contains 3 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 7 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: my complicated version of your simple approach let the 5 black balls be bbbbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 7 ! ) / ( 4 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 3 red ( rrr ) they can be arranged in ( 6 ! ) / ( 3 ! x 3 ! ) hence required probability = [ ( 7 ! ) / ( 4 ! x 3 ! ) ] / [ ( 6 ! ) / ( 3 ! x 3 ! ) ] ans = 7 / 4 a
Answer: a
Problem: in kaya ' s teacher ' s desk there are 4 pink highlighters , 2 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 4 + 2 + 5 = 11 . answer is a ."
Answer: a
Problem: the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 50 kg , c ) 85 kg , d ) 90 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 10 ã — 2.5 = 25 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 25 = x - 65 = > x = 25 + 65 = 90 answer : option d"
Answer: d
Problem: on a map , 1 inch represents 28 miles . how many z inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "z inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c"
Answer: c
Problem: a train 150 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 ) 9 , e ) 8
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 = 150 * 3 / 55 = 8 sec . answer : e"
Answer: e
Problem: the h . c . f . of two numbers is 40 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 600 , c ) 699 , d ) 722 , e ) 745
Rationale: "the numbers are ( 40 x 11 ) and ( 40 x 15 ) . larger number = ( 40 x 15 ) = 600 . answer : b"
Answer: b
Problem: excluding stoppages , the speed of a train is 54 kmph and including stoppages it is 40 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 13.55 , b ) b ) 14.55 , c ) c ) 15.55 , d ) d ) 16.55 , e ) e ) 17.55
Rationale: "explanation : t = 14 / 54 * 60 = 15.55 answer : option c"
Answer: c
Problem: a train 385 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 ) 5 , b ) 21 , c ) 7 , d ) 8 , e ) 9
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 = [ 385 * 3 / 55 ] sec = 21 sec answer : option b"
Answer: b
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 15 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 61 % , b ) 70 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: "find the product of the two increases : ( 1.4 ) * ( . 15 ) , which is 1.61 and a 61 % increase . a"
Answer: a
Problem: a mixture contains alcohol and water in the ratio 4 : 3 . if 9 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 22 litres , e ) 18 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 9 ) = 4 / 5 20 x = 4 ( 3 x + 9 ) 8 x = 36 x = 4.5 quantity of alcohol = ( 4 x 4.5 ) litres = 18 litres . answer is e"
Answer: e
Problem: if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 39 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 39 women = 15 women + 39 women = 54 women 20 women can do the work in 54 days . so , 54 women can do it in ( 20 * 54 ) / 54 = 20 days .
Answer: c
Problem: in an election , candidate a got 79 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate .
Options: a ) 357003 , b ) 357090 , c ) 37667 , d ) 379888 , e ) 287761
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357090 answer : b"
Answer: b
Problem: if a car had traveled 35 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 105 km , at what speed did it travel ?
Options: a ) 50 kmh , b ) 55 kmh , c ) 60 kmh , d ) 65 kmh , e ) 70 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 105 / x - 105 / ( x + 35 ) = 1 / 2 substitute the value of x from the options . - - > x = 70 - - > 105 / 70 - 105 / 105 = 3 / 2 - 1 = 1 / 2 answer : e"
Answer: e
Problem: the base of pyramid p is an isosceles right triangle whose leg is 3 . if the height of p is 4 , what is the volume of p ?
Options: a ) 36
b ) 18
c ) 12
d ) 8
e ) 6
Rationale: volume of a pyramid is given by v = 1 / 3 ah , where a is the area of the triangular base and h is the height of the pyramid . area of triangular base = 1 / 2 * 3 * 3 = 9 / 2 so , v = 1 / 3 * 9 / 2 * 4 = 6 option e
Answer: e
Problem: 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 6514 , how much was it in the beginning ?
Options: a ) 8545 , b ) 8770 , c ) 8515 , d ) 7999 , e ) 7989
Rationale: "x * ( 90 / 100 ) * ( 85 / 100 ) = 6514 x = 8515 answer : c"
Answer: c
Problem: if each year the population of the country grows by 10 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 7 , e ) 8
Rationale: till year 2000 , population is 100 . year 2001 : population becomes 110 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 121 . . . . . . . . . . . . . 2 year elapsed year 2003 : population becomes > 133 . . . . . . . . . . . . . 3 year elapsed year 2004 : population becomes > 146 . . . . . . . . . . . . . . . . . . 4 year elapsed year 2005 : population becomes > 160 . . . . . . . . . . . . . . . . . . 5 year elapsed year 2006 : population becomes > 176 . . . . . . . . . . . . . . . . . . 6 year elapsed year 2007 : population becomes > 193 . . . . . . . . . . . . . . . . . . 7 year elapsed year 2008 : population > 200 . . . . . . . . . . . . . . . . . . 8 year elapsed answer : e
Answer: e
Problem: 5 percent of a certain grass seed is timothy . if the amount of the mixture needed to plant one acre contains 2 pounds of timothy , how many acres can be planted with 600 pounds of the seed mixture ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 120
Rationale: if the mixture contains 2 pounds of timothy , the mixture must be 40 pounds . thus we need 40 pounds of mixture per acre . 600 / 40 = 15 acres the answer is b .
Answer: b
Problem: we invested a total of $ 1,000 . we invested one part of the money at 5 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1 , 054.50 . how much money did we invest at 5 % ?
Options: a ) $ 400 , b ) $ 450 , c ) $ 500 , d ) $ 550 , e ) $ 600
Rationale: "let x be the money invested at 5 % . 1.05 x + 1.06 ( 1000 - x ) = 1054.50 . 0.01 x = 1060 - 1054.50 . 0.01 x = 5.50 . x = 550 . the answer is d ."
Answer: d
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 19 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 19 a – d = 3 a + d = 19 2 d = 16 d = 8 answer d"
Answer: d
Problem: if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ?
Options: a ) 105 , b ) 120 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 16 c 2 = 16 * 15 / 2 = 120 . therefore , the answer is b ."
Answer: b
Problem: a cistern 8 m long and 6 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 80 m 2 , b ) 50 m 2 , c ) 83 m 2 , d ) 86 m 2 , e ) 55 m 2
Rationale: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 6 x 1.25 + 8 x 1.25 ) + 8 x 6 ] m 2 = 83 m 2 . answer : c
Answer: c
Problem: in a certain accounting class of 90 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 70 % , what was the average score for the entire class ?
Options: a ) 63 % , b ) 64 % , c ) 65 % , d ) 66 % , e ) 67 %
Rationale: "70 % of the class scored 60 % and 30 % of the class scored 70 % . the difference between 60 % and 70 % is 10 % . the average will be 60 % + 0.3 ( 10 % ) = 63 % . the answer is a ."
Answer: a
Problem: a sum fetched a total simple interest of 4016.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 4462.5 , b ) 8032.5 , c ) 8925 , d ) none of these , e ) can not be determined
Rationale: "explanation : principal = ( 100 x 4016.25 ) / ( 9 x 5 ) = 401625 / 45 = 8925 answer : option c"
Answer: c
Problem: a bag consists of 20 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 20 - 5 - 9 = 6 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 20 + 6 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ."
Answer: a
Problem: how many different positive integers exist between 10 ^ 6 and 10 ^ 7 , the sum of whose digits is equal to 2 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 18
Rationale: "total cases = > 1000000 = > 6 cases for 1 being present at any of the 6 zero and last case 2000000 hence & cases answer : c"
Answer: c
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 65 , c ) 98 , d ) 107 , e ) 198
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 1 x 60 ) = 60 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 60 x + 20 x + 15 x + 12 x ) = 107 x . for minimum number of pencils x = 1 . the person should have at least 107 pencils . d )"
Answer: d
Problem: a sum of rs . 1550 was lent partly at 5 % and partly at 8 % p . a . simple interest . the total interest received after 3 years was rs . 300 . the ratio of the money lent at 5 % to that lent at 8 % is :
Options: a ) 16 : 15 , b ) 15 : 16 , c ) 15 : 8 , d ) 8 : 15 , e ) 8 : 17
Rationale: explanation : let the partial amount at 5 % be x and the partial amount at 8 % be ( 1550 - x ) interest on x at 5 % for 3 years + interest on ( 1550 - x ) at 8 % for 3 years = 300 x × 5 × 3 / 100 + ( 1550 - x ) × 8 × 3 / 100 = 300 x × 5 / 100 + ( 1550 - x ) × 8 / 100 = 100 5 x + 8 ( 1550 − x ) = 10000 5 x + 12400 − 8 x = 10000 3 x = 2400 x = 800 required ratio = x : ( 1550 - x ) = 800 : ( 1550 - 800 ) = 800 : 750 = 16 : 15 answer : option a
Answer: a
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.20 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the third day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.2 2 nd day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value ) 3 rd day fine - 0.4 + 3 = 0.7 ( as doubling gives higher value ) answer : b ."
Answer: b
Problem: a part - time employee ’ s hourly wage was increased by 15 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 13 % , b ) 15 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 15 % wage increase , the employee makes $ 1.15 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.15 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.15 to get : new # of hours = 100 / 1.15 ≈ 87 hours so , the number of hours decreases from 100 hours to ( approximately ) 87 hours . this represents a 13 % decrease ( approximately ) . answer : a"
Answer: a
Problem: if y is 60 % greater than x , than x is what % less than y ?
Options: a ) 29.3 % , b ) 33.4 % , c ) 37.5 % , d ) 41.6 % , e ) 45.7 %
Rationale: "y = 1.6 x x = y / 1.6 = 10 y / 16 = 5 y / 8 x is 3 / 8 less which is 37.5 % less than y . the answer is c ."
Answer: c
Problem: a student gets 50 % in one subject , 70 % in the other . to get an overall of 70 % how much should get in third subject .
Options: a ) 90 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 50 + 70 + x = 3 * 70 120 + x = 210 x = 210 - 120 = 90 answer : a"
Answer: a
Problem: the product of two successive numbers is 2652 . which is the smaller of the two numbers ?
Options: a ) 51 , b ) 68 , c ) 57 , d ) 55 , e ) 37
Rationale: "a 51 from the given alternatives , 51 × 52 = 2652 ∴ smaller number = 51"
Answer: a
Problem: a sum of money deposited at c . i . amounts to rs . 2560 in 3 years and to rs . 2989 in 4 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 20 % , d ) 16 % , e ) 50 %
Rationale: "2560 - - - 429 100 - - - ? = > 16 % answer : d"
Answer: d
Problem: if k is a non - negative integer and 30 ^ k is a divisor of 929,260 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520
Rationale: 9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b .
Answer: b
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 18 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 23 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.82 * 150 x = 123 x hence total profit = 23 % option d"
Answer: d
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 5500 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 1980 , c ) 2900 , d ) 2200 , e ) 2300
Rationale: "b number of valid votes = 80 % of 5500 = 4400 . valid votes polled by other candidate = 45 % of 4400 = ( 45 / 100 x 4400 ) = 1980 ."
Answer: b
Problem: there are 7 players in a bowling team with an average weight of 103 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 95 kg . , b ) 99 kg . , c ) 89 kg . , d ) 90 kg . , e ) 92 kg .
Rationale: "the new average will be = ( 103 * 7 + 110 + 60 ) / 9 = 99 kgs b is the answer"
Answer: b
Problem: find the average of all numbers between 3 and 86 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 + 80 + 85 ) / 17 = 765 / 17 = 45 answer : option e"
Answer: e
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 14000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 16940 , e ) 10002
Rationale: "the required population is = 14000 ( 1 + 10 / 100 ) ^ 2 = 14000 * 11 / 10 * 11 / 10 = 16940 answer is d"
Answer: d
Problem: the average of 21 numbers is 44 . average of the first 11 of them is 48 and that of the last 11 is 41 . find the 11 th number ?
Options: a ) 48 , b ) 51 , c ) 47 , d ) 49 , e ) 55
Rationale: sum of all the 21 numbers = 21 * 44 = 924 sum of the first 11 of them = 11 * 48 = 528 sum of the last 11 of them = 11 * 41 = 451 so , the 11 th number = 528 + 451 - 924 = 55 . answer : e
Answer: e
Problem: a train running at the speed of 30 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 75 m , b ) 180 m , c ) 324 m , d ) can not be determined , e ) none of these
Rationale: "speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 9 = 75 m answer : a"
Answer: a
Problem: three unbiased coins are tossed , what is the probability of ge ƫ ng at least 2 tails ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 8 , e ) none of these
Rationale: "explanation : total cases are = 2 * 2 * 2 = 8 , which are as follows [ ttt , hhh , tth , tht , htt , thh , hth , hht ] favoured cases are = [ tth , tht , htt , ttt ] = 4 so required probability = 4 / 8 = 1 / 2 answer : c"
Answer: c
Problem: in the next cricket world cup t - 20 , team t has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team t score these 200 runs ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: team t can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d
Answer: d
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 5 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 5 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 5 = 4 / 5 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 4 / 5 = 4 / 10 = 2 / 5 - - - > p ( of burning out in a six mnth period ) = 1 - 2 / 5 = 3 / 5 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 4 / 5 * 3 / 5 = 1 / 2 ans c"
Answer: c
Problem: the perimeter of an isosceles right triangle is 8 + 8 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 4 , b ) 5.656 , c ) 5 , d ) 6 , e ) 7
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 8 + 8 sqrt 2 or , a . ( 2 + sqrt 2 ) = 8 ( 1 + sqrt 2 ) , a = 8 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 8 * 2.414 / 3.414 = 0.707 * 8 then hypotenuse = 5.656 b"
Answer: b
Problem: when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 18 = 26 - x or , 4 x = 44 or , x = 11 . c answer ."
Answer: c