regisss/math_qa huggingface dataset:
Problem: if x is an integer and 2.134 × 10 ^ x is less than 220,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 220,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 220,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5"
Answer: c
Problem: calculate 469157 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none
Rationale: "answer 469157 x 9999 = 469157 x ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 . option : c"
Answer: c
Problem: the area of a square field is 400 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 4 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 400 km 2 . then , each side of field = √ 400 = 20 km distance covered by the horse = perimeter of square field = 20 × 4 = 80 km ∴ time taken by horse = distances / peed = 80 / 20 = 4 h answer c
Answer: c
Problem: there are 10 dozen mangoes in a box . if there are 36 such boxes , how many mangoes are there in all the boxes together ?
Options: a ) 516 , b ) 3096 , c ) 6192 , d ) 628 , e ) 4320
Rationale: number of mangoes = 12 dozens = 12 × 10 = 120 ∴ number of mangoes in 36 boxes = 36 × 120 = 4320 answer e
Answer: e
Problem: if a and b are in the ratio 3 : 4 , and b and c in the ratio 12 : 13 , then a and c will be in the ratio
Options: a ) 3 : 13 , b ) 9 : 13 , c ) 36 : 13 , d ) 13 : 9 , e ) none
Rationale: solution : ( a / b ) * ( b / c ) = ( 3 / 4 ) * ( 12 / 13 ) ; or , a / b = 36 / 39 = 9 : 13 . answer : option b
Answer: b
Problem: the sum of a number and the number preceding it is 33 . by how much is two less than 6 times the number ?
Options: a ) 196 , b ) 94 , c ) 90 , d ) 100 , e ) 120
Rationale: two numbers must be 16 and 17 16 + 17 = 33 required number is 17 six times of this number = 6 * 17 = 102 two less than 102 = 102 - 2 = 100 answer : d
Answer: d
Problem: 4,18 , 100,294 , ___
Options: a ) 1000 , b ) 1100 , c ) 1210 , d ) 1452 , e ) 1552
Rationale: "2 ^ 3 - 2 ^ 2 = 4 ; 3 ^ 3 - 3 ^ 2 = 18 ; 5 ^ 3 - 5 ^ 2 = 100 ; 7 ^ 3 - 7 ^ 2 = 294 ; so , 11 ^ 3 - 11 ^ 2 = 1210 answer : c"
Answer: c
Problem: a bag holds 5 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 6 , b ) 2 / 5 , c ) 3 / 10 , d ) 2 / 9 , e ) 1 / 2
Rationale: "probability of selecting first red marble = 5 / 10 probability of selecting second red marble without replacement = 4 / 9 final probability = 5 / 10 * 4 / 9 = 2 / 9 the correct answer is d ."
Answer: d
Problem: what is the smallest integer x for which 27 ^ x > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ x > 3 ^ 24 converting into the same bases : 27 ^ x > 27 ^ 8 therefore for the equation to hold true , x > 8 or x = 9 option c"
Answer: c
Problem: a man can row downstream at 16 kmph and upstream at 12 kmph . find the speed of the man in still water .
Options: a ) 14 , b ) 13 , c ) 12 , d ) 16 , e ) 15
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 16 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 28 = > x = 14 , y = 2 . answer : a"
Answer: a
Problem: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 38 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 44
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 138 let marked price be rs . x . then , 96 / 100 x = 138 x = 13800 / 96 = rs . 143.75 now , s . p . = rs . 143.75 , c . p . = rs . 100 profit % = 44 % . answer : e"
Answer: e
Problem: two trains of length 160 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 82 sec , d ) 24 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 160 + 320 = 480 m . the time required = d / s = 480 / 20 = 24 sec . answer : d"
Answer: d
Problem: solve ( 0.76 × 0.76 × 0.76 − 0.008 ) / ( 0.76 × 0.76 + 0.76 × 0.2 + 0.04 )
Options: a ) 0.56 , b ) 0.62 , c ) 0.5 , d ) 0.48 , e ) 0.52
Rationale: 0.56 option ' a '
Answer: a
Problem: what is the maximum area that can be enclosed by a wire 44 cm long ?
Options: a ) 77
b ) 154
c ) 308
d ) 318
e ) none of these
Rationale: perimeter of circle = 2 * 22 / 7 * r = 44 cm from this r = 7 then area of circle = 22 / 7 * r ^ 2 = 154 answer : b
Answer: b
Problem: if the average ( arithmetic mean ) of 2 x , 4 x , and 8 x is 140 , what is the value of x ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 33 , e ) 31
Rationale: "am of 2 x , 4 x and 8 x = 2 x + 4 x + 8 x / 3 = 14 x / 3 given that 14 x / 3 = 140 x = 30 answer is b"
Answer: b
Problem: if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 10 inclusive ?
Options: a ) 7 / 32 , b ) 11 / 64 , c ) 35 / 128 , d ) 49 / 128 , e ) 65 / 128
Rationale: "one possible case is : rainy - rainy - rainy - not rainy - not rainy - not rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 7 = 1 / 128 the number of possible cases is 7 c 3 = 35 . p ( exactly 3 rainy days ) = 35 * 1 / 128 = 35 / 128 the answer is c ."
Answer: c
Problem: what is the positive difference between the sum of the squares of the first 5 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 = 55 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 55 is 14 . so the answer is ( d ) ."
Answer: d
Problem: find the value of 80641 x 9999 = m ?
Options: a ) 807518799 , b ) 806436469 , c ) 807538799 , d ) 806329359 , e ) 817431046
Rationale: "80641 x 9999 = 80641 x ( 10000 - 1 ) = 80641 x 10000 - 80641 x 1 = 806410000 - 80641 = 806329359 d"
Answer: d
Problem: 3889 + 12.952 – ? = 3854.002
Options: a ) 47.095 , b ) 47.752 , c ) 47.932 , d ) 47.95 , e ) none
Rationale: explanation let 3889 + 12.952 – x = 3854.002 . then x = ( 3889 + 12.952 ) – 3854.002 = 3901.952 – 3854.002 = 47.95 . answer d
Answer: d
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 9 inches on a side and costs $ 10 , and a large pizza that measures 14 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches
b ) 10 square inches
c ) 15 square inches
d ) 25 square inches
e ) 34 square inches
Rationale: in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 9 * 9 = 81 ) for the small pizza and ( 14 * 14 = 196 ) for the large pizza . in total sq inches that would be ( 81 + 196 ) * 2 = 554 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 196 = 588 sq inches . hence , the difference is 34 square inches more ( 588 - 554 ) . the correct answer is e
Answer: e
Problem: which number is a factor of 20 ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 18 , e ) 9
Rationale: a whole number that divides exactly into another whole number is called a factor 20 / 5 = 4 answer b
Answer: b
Problem: there are 2 sections a and b in a class , consisting of 24 and 16 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?
Options: a ) 35.29 kg , b ) 37.25 kg , c ) 42 kg , d ) 38 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 24 * 40 + 16 * 35 = 1520 average weight of the class is = 1520 / 40 = 38 kg answer is d"
Answer: d
Problem: if n divided by 5 has a remainder of 4 , what is the remainder when 3 times n is divided by 5 ?
Options: a ) 1 , b ) 4 , c ) 3 , d ) 2 , e ) 0
Rationale: "as per question = > n = 5 p + 4 for some integer p hence 3 n = > 15 q + 12 but again , 12 can be divided by 5 to get remainder 2 for some integer q hence d"
Answer: d
Problem: a man can row downstream at 18 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 2
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 28 = > x = 14 , y = 4 . answer : d"
Answer: d
Problem: if four machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 48 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 4 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 8 / 3 = 10 / 3 * x x = 4 / 5 hour so 48 minutes answer : a"
Answer: a
Problem: the ratio of number of boys and girls in a school is 2 : 5 . if there are 210 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 = 210 number of girls in the school = 5 * 210 / 7 = 150 answer is a"
Answer: a
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 10 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 5020
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , and 2 * 5 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 = 2520 the answer is d ."
Answer: d
Problem: there are two positive integers a and b . what is the probability that a + b is odd /
Options: a ) 3 / 2 , b ) 6 / 7 , c ) 1 / 2 , d ) 7 / 2 , e ) 4 / 5
Rationale: s = adding two numbers is ( even + even ) , ( even + odd ) , ( odd + odd ) , ( odd + even ) n ( s ) = 4 e = ( even + odd ) , ( odd + even ) are the points in the event . n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 4 = 1 / 2 answer is option c
Answer: c
Problem: of the 150 employees at company x , 60 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 80 answer : option d"
Answer: d
Problem: if f is the smallest positive integer such that 3,150 multiplied by f is the square of an integer , then f must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by f is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x f = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , y = 7 x 2 = 14 answer is e .
Answer: e
Problem: what is the least number . which should be added to 0.0355 to make it a perfect square ?
Options: a ) 0.0005 , b ) 0.0016 , c ) 0.0056 , d ) 0.0066 , e ) 0.0006
Rationale: "0.0355 + 0.0006 = 0.0361 ( 0.19 ) ^ 2 answer : e"
Answer: e
Problem: if x + 4 y = 5 and 5 x + 6 y = 7 , then 3 x + 5 y = ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: add the left terms and right terms of the two equation to obtain a new equation x + 5 x + 4 y + 6 y = 5 + 7 group and simplify 6 x + 10 y = 12 divide all terms of the above equation by 2 to obtain a new equation 3 x + 5 y = 6 correct answer a
Answer: a
Problem: the distance from steve ' s house to work is 10 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 10 km = > speed = 5 kmph a"
Answer: a
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 35 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 35 % = 63 responded as satisfied , so remaining satisfied are 120 - 63 = 57 so 57 is what percentage of 300 - 19 % so the answer should be a
Answer: a
Problem: a work can be finished in 30 days by 30 women . the same work can be finished in fifteen days by 15 men . the ratio between the capacity of a man and a woman is
Options: a ) 1 : 3 , b ) 4 : 3 , c ) 2 : 3 , d ) 4 : 1 , e ) 2 : 4
Rationale: "work done by 30 women in 1 day = 1 / 30 work done by 1 woman in 1 day = 1 / ( 30 × 30 ) work done by 15 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 × 15 ) ratio of the capacity of a man and woman = 1 / ( 15 × 15 ) : 1 / ( 30 × 30 ) ) = 1 / 225 : 1 / 900 = 1 / 1 : 1 / 4 = 4 : 1 option d"
Answer: d
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 8 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 16 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 8 = 8 c 2 total possible outcomes - 2 ^ 8 ( each child can be either a girl or a boy ) probability = 2 c 1 * 8 c 2 / 2 ^ 8 = 2 * 8 / 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 16 / 256 = 1 / 16 ans = d"
Answer: d
Problem: ? % of 360 = 126
Options: a ) 277 , b ) 35 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 126 or , ? = 126 × 100 / 360 = 35 answer b"
Answer: b
Problem: the area of a circle of radius 5 is numerically what percent of its circumference ?
Options: a ) 200
b ) 225
c ) 240
d ) 250
e ) none
Rationale: solution required % = [ π x ( 5 ) 2 / 2 π x 5 x 100 ] % ‹ = › 250 % . answer d
Answer: d
Problem: jony walks along sunrise boulevard daily . he starts walking at 07 : 00 from block 10 and walks to block 90 where he turns around and walks back to block 70 , where he stops at 07 : 40 . the blocks along the boulevard are numbered sequentially ( 1 , 2,3 ) , and each block measures 40 meters . what is jony ' s speed in meters per minute ?
Options: a ) 88 , b ) 100 , c ) 198 , d ) 216 , e ) 252
Rationale: total distance from 10 to 90 = 80 + from 90 to 70 = 20 so the dist is 100 × 40 ( per block dist ) speed = 4000 mts / 40 min = 100 m / min b is the answer
Answer: b
Problem: car a is 40 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 5.5 , e ) 6.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 40 miles and drive 8 miles ahead so to drive 48 miles it ' ll need 48 / 8 = 6 hours . answer : b"
Answer: b
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , - 8 ) . what is the least possible value of the slope of line l ?
Options: a ) - 6.5 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 10
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 8 ) should satisfy the equation . hence x = t and y = - 8 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 8 - 5 ) / ( 4 - 2 ) = - 6.5 imo option a is correct answer ."
Answer: a
Problem: two fill taps a and b can separately fill a cistern in 45 and 40 minutes respectively . they started to fill a cistern together but tap a is turned off after few minutes and tap b fills the rest part of cistern in 23 minutes . after how many minutes , was tap a turned - off ?
Options: a ) 9 min , b ) 10 min , c ) 12 min , d ) 7 min , e ) none of these
Rationale: let a was turned off after x min . then , cistern filled by a in x min + cistern filled by b in ( x + 23 ) min = 1 ⇒ x / 45 + x + 23 / 40 = 1 ⇒ 17 x + 207 = 360 ⇒ x = 9 min . answer a
Answer: a
Problem: find the compound interest on $ 1200 for 4 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 1288 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 4 = $ 2488 ci = $ 1288 answer is c"
Answer: c
Problem: in a company 10 % of male staff are same in number as 1 / 4 th of the female staff . what is the ratio of male staff to female staff
Options: a ) 3 : 2 , b ) 5 : 2 , c ) 2 : 1 , d ) 4 : 3 , e ) 1 : 2
Rationale: 10 % of ms = 1 / 4 th of fs - > 10 ms / 100 = 1 / 4 fs - > ms = 5 / 2 fs : . ms / fs = 5 / 2 = ms : fs = 5 : 2 answer : b
Answer: b
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 25 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 75 / 2 , e ) 35
Rationale: "b : d : w = 2 : 25 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 25 ) = ( 2 / 75 ) dnew / wnew = ( 1 / 2 ) * ( 25 / 100 ) = ( 1 / 8 ) wnew = 300 dnew = wnew / 5 = 300 / 8 = 75 / 2 so , answer will be d"
Answer: d
Problem: the average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 176 kg , b ) 80 kg , c ) 185 kg , d ) 90 kg , e ) 128 kg
Rationale: "solution total weight increased = ( 10 x 6.3 ) kg = 63 kg . weight of new person = ( 65 + 63 ) kg = 128 kg . answer e"
Answer: e
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number t of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average t sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Problem: the speed of a car is 98 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 75 kmph , c ) 87 kmph , d ) 79 kmph , e ) 86 kmph
Rationale: "s = ( 98 + 60 ) / 2 = 79 kmph answer : d"
Answer: d
Problem: what is the least whole number that should be added to 625573 if it is to be divisible by 3 ?
Options: a ) 6 , b ) 1 , c ) 4 , d ) 3 , e ) 2
Rationale: a number is divisible by 3 if the sum of the digits is divisible by 3 . . here , 6 + 2 + 5 + 5 + 7 + 3 = 28 , the next multiple of 3 is 30 . 2 must be added to 625574 to make it divisible by 3 e
Answer: e
Problem: what least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
Options: a ) 9 , b ) 8 , c ) 5 , d ) 11 , e ) 15
Rationale: "on dividing 2000 by 17 , we get 11 as remainder . required number to be subtracted = 11 answer d"
Answer: d
Problem: v is the volume of a cylinder ; the radius r is 3.4 . the height is 350 % more than the radius . which of the following is true ?
Options: a ) 100 < v < 300
b ) 300 < v < 500
c ) 500 < v < 700
d ) 700 < v < 900
e ) 900 < v < 1100
Rationale: as we see the answers are in form of range we can use approximation volume of cylinder is π r ^ 2 h given π = 22 / 7 and r = 3.4 so r ^ 2 ~ 12 and h = 4.5 * 3.4 ~ 15 so 22 / 7 * 12 * 15 = 566 so answer should be c . 500 < v < 700 answer : c
Answer: c
Problem: how many 7 in between 1 to 120 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78,79 , 87,97 , 107,117 22 7 ' s between 1 to 120 answer : c"
Answer: c
Problem: in 1990 the budgets for projects q and v were $ 620,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 620 + 30 x = 780 - 10 x - - > 40 x = 160 and x = 4 . thus , it happens in 1994 . c ."
Answer: c
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 162.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 35 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 162.5 subtracting the first equation from the second gives us b + 3 s = 42.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 35 . in any case , there is no necessity to know each item ' s price , just the sum . answer : b"
Answer: b
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day at 1 mile faster than 2 nd day for same hours . how many miles in total did she walk ?
Options: a ) 63 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 5 hours - 25 miles total 18 + 20 + 25 = 63 answer : option a ."
Answer: a
Problem: simplify : ( 4 + 3 ) + ( 8 - 3 - 1 )
Options: a ) - 11 , b ) – 12 , c ) 11 , d ) 12 , e ) 10
Rationale: solution : ( 4 + 3 ) + ( 8 - 3 - 1 ) = 7 + ( 8 - 3 - 1 ) = 7 + 8 - 3 - 1 = 15 - 1 = 11 answer : ( c )
Answer: c
Problem: a train running at the speed of 56 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 140 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec length of train ( distance ) = speed * time ( 140 / 9 ) * 9 = 140 meter answer : a"
Answer: a
Problem: how many 9 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 123454321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 90000
Rationale: take the task of building palindromes and break it intostages . stage 1 : select the 9 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 8 th , 7 th , 6 th , 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 9 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 90000 ways ) answer : e
Answer: e
Problem: the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?
Options: a ) 37.2 %
b ) 37.5 %
c ) 30.2 %
d ) 37.7 %
e ) 33.2 %
Rationale: explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b
Answer: b
Problem: when sold at a 60 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 66.67 % , d ) 80 % , e ) 100 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 60 % of 100 = 40 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 40 or x = 33.33 . . . marked price was 100 so . . . so answer is 66.67 % . . c"
Answer: c
Problem: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 56,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 28,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 56,000 i . e . rs . 28,000 answer : a"
Answer: a
Problem: if the sides of a square are multiplied by sqrt ( 5 ) , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 5 %
b ) 20 %
c ) 50 %
d ) 100 %
e ) 120 %
Rationale: let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length sqrt ( 5 ) * x , so the area is 5 x ^ 2 . the area of the original square is 1 / 5 = 20 % times the area of the new square . the answer is b .
Answer: b
Problem: a start walking from a place at a uniform speed of 3 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 3.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 3 + 5 / 9 = 3.55 answer b"
Answer: b
Problem: find the 25 % of rs . 600 .
Options: a ) s . 150 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 600 = > 25 / 100 * 600 = rs . 150 answer : a"
Answer: a
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 60900 . what is his profit percent ?
Options: a ) 10.7 % , b ) 19 % , c ) 18 % , d ) 14 % , e ) 16 %
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 60900 profit ( % ) = ( 60900 - 55000 ) / 55000 * 100 = 10.7 % answer : a"
Answer: a
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 10 - meter platform and caught it after it had traveled 29.65 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 10 + 10 + 5 + 2.5 + 1.25 + 0.6 + 0.3 ans b"
Answer: b
Problem: if the length of the sides of two cubes are in the ratio 2 : 1 , what is the ratio of their total surface area ?
Options: a ) 2 : 1 , b ) 3 : 1 , c ) 4 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 2 x ) ^ 2 = 24 x ^ 2 . the ratio of surface areas is 4 : 1 . the answer is c ."
Answer: c
Problem: a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55
Rationale: "there 3 questions in part a out of which 4 question can be chosen as = 5 c 3 . similarly , 5 questions can be chosen from 10 questions of part b as = 5 c 4 . hence , total number of ways , = 5 c 3 * 5 c 4 = [ 5 ! / ( 2 ! 3 ! ) ] * [ 5 ! / ( 4 ! * 1 ) ] = { 10 } * { 5 * 4 ! / ( 4 ! ) } = 10 * 5 = 50 . a"
Answer: a
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 42 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3150 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 42 = 30 x = 3150 km answer is e"
Answer: e
Problem: what is the speed of the stream if a canoe rows upstream at 8 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 8 ) kmph = 2 kmph . answer d"
Answer: d
Problem: obra drove 150 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 %
b ) 12.5 %
c ) 18.75 %
d ) 25 %
e ) 31.25 %
Rationale: area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 150 π / 480 π = 31.25 % hence , answer is e .
Answer: e
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 305 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 610 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 305 ) = 2 + 2 ( extra ) = > 2 x - 610 = x = > x = 610 . answer : b"
Answer: b
Problem: at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 10 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000
Rationale: "let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 8 ) + 30 ( y - 8 ) = r - . 1 r = > 20 x + 160 + 30 y - 240 = . 9 r = > 20 x + 30 y = . 9 r + 80 . . . . . . . . . . . . ( 2 ) so , r = . 9 r + 80 = > r = 800 the answer is d ."
Answer: d
Problem: two pots are in side - by - side . one pot , which is 20 inches tall , casts a shadow that is 10 inches long . the other pot is 40 inches tall . compute , in inches , the length of the shadow that the taller pot casts .
Options: a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20
Rationale: the ratio of shadow to height is constant , so if x is the length of the shadow , then 20 / 10 = 40 / x and x = 20 . correct answer e
Answer: e
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 19000 , then find his savings ?
Options: a ) 3800 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 19000 = > x = 3800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3800 . answer : a"
Answer: a
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 7.0 = ?
Options: a ) - 0.61 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.61 answer a
Answer: a
Problem: if 9 a - b = 10 b + 60 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 8 , b ) - 4 , c ) 0 , d ) 4 , e ) 8
Rationale: "( i ) 9 a - 11 b = 60 ( ii ) 2 a + 22 b = - 60 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Problem: in a fuel station the service costs $ 2.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 462 $
Rationale: 12 * 2.75 + 0.65 * 12 * 55 = 462 hence - e
Answer: e
Problem: find 20 % of 240
Options: a ) 96 , b ) 94 , c ) 86 , d ) 74 , e ) 48
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 20 % of 240 20 / 100 × 240 = 48 answer : e"
Answer: e
Problem: if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 12 . what is the value of f ( 6 ) ?
Options: a ) 1 , b ) 0 , c ) - 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 12 then f ( 5 ) = 12 - 5 = 7 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 7 - 6 = 1 . answer : a . questions on funtions to practice :"
Answer: a
Problem: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 12.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 318 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286
Rationale: total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 12 = 16 * 12 = 192 $ total charge = 126 + 192 = 318 $ answer a
Answer: a
Problem: when a number is divided by 3 & then multiply by 12 the answer is 9 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 2.25 , d ) 5.7 , e ) 6.5
Rationale: "if $ x $ is the number , x / 3 * 12 = 9 = > 4 x = 9 = > x = 2.25 c"
Answer: c
Problem: an error 2 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 1.04 , b ) 2.04 , c ) 3.04 , d ) 4.04 , e ) none of these
Rationale: "explanation : 100 cm is read as 102 cm . a 1 = ( 100 × 100 ) cm 2 and a 2 = ( 102 × 102 ) cm 2 ( a 2 - a 1 ) = [ 1022 - 1002 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 answer : d"
Answer: d
Problem: juan and his five friends will sit on six fixed seats around a circular table . if juan must sit on the seat closest to the window and jamal must sit next to juan , in how many can juan and his five friends sit ?
Options: a ) 20
b ) 24
c ) 48
d ) 72
e ) 120
Rationale: j = juan , f = jamal since j is always fixed , set j , set f relative to j , then see how many options there are : j f 4 3 2 1 = 24 or f j 4 3 2 1 = 24 24 + 24 = 48 … c answer : c
Answer: c
Problem: lucia ' s sells kale at x dollar per pound for the first 20 pounds and . 8 x for every subsequent pound . amby ' s price is x per pound for the first 14 pounds and . 9 x for subsequent pounds . what is the minimum number of pounds over 15 for which lucia ' s becomes an equal or better deal ?
Options: a ) 24 , b ) 26 , c ) 25 , d ) 27 , e ) 28
Rationale: for amy ' s deal to be better , the cost has to be less or equal to lucia ' s assuming ' n ' is the number of pounds of kale , the equation is 20 x + ( n - 20 ) ( 0.8 x ) < = 14 x + ( n - 14 ) ( 0.9 x ) resolve it : = = > 20 x + 0.8 nx - 16 x < = 14 x + 0.9 nx - 12.6 x = = > 2.6 x < = 0.1 nx = = > 26 x < = nx = = > x ( n - 26 ) > = 0 as x can not be 0 , = = > n - 26 > = 0 = = > n > = 26 so the minimum value is 26 ' b ' would be the correct answer
Answer: b
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 1 . what is the value of 7 y – x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y - 3 = x 7 y - x = 3 the answer is c ."
Answer: c
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 140800 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 140800 = 1 * 5 ^ 2 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c .
Answer: c
Problem: evaluate 49 / . 07
Options: a ) 400 , b ) 500 , c ) 700 , d ) none of these , e ) 506
Rationale: "explanation : 49 / . 07 = 4900 / 7 = 700 option c"
Answer: c
Problem: an employee ’ s annual salary was increased 30 % . if her old annual salary equals $ 30,000 , what was the new salary ?
Options: a ) $ 28,000 , b ) $ 25,000 , c ) $ 20,000 , d ) $ 35,000 , e ) $ 39,000
Rationale: "old annual salary = $ 30,000 salary increase = 30 % . original salary = $ 30,000 * 30 / 100 = $ 9000 new salary = $ 30,000 + $ 9000 = $ 39,000 hence e ."
Answer: e
Problem: 1 , 3,5 , 7,9 , . . . . 50 find term of sequnce
Options: a ) 1000 , b ) 1200 , c ) 1300 , d ) 1800 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Problem: david deposited $ 5000 to open a new savings account that earned 6 percent annual interest , compounded semi - annually . if there were no other transactions in the account , what the amount of money in david account one year after the account was opened ?
Options: a ) $ 5306 , b ) $ 6120 , c ) $ 5136 , d ) $ 5405 , e ) $ 5500
Rationale: approach # 1 : 6 percent annual interest compounded semi - annually - - > 3 % in 6 moths . for the first 6 moths interest was 3 % of $ 5000 , so $ 150 ; for the next 6 moths interest was 3 % of $ 5000 , plus 3 % earned on previous interest of $ 150 , so $ 150 + $ 6 = $ 156 ; total interest for one year was $ 150 + $ 156 = $ 306 , hence balance after one year was $ 5000 + $ 306 = $ 5306 . answer : a .
Answer: a
Problem: ( 1000 ) 7 ÷ ( 10 ) 17 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: explanation : = ( 103 ) 7 / ( 10 ) 17 = ( 10 ) 21 / ( 10 ) 17 = 10 ( 4 ) = 10000 option d
Answer: d
Problem: how many multiples of 3 are there between 100 and 300 ( both are inclusive ) ?
Options: a ) 67.6 , b ) 1.58 , c ) 2.47 , d ) 3.54 , e ) 6.51
Rationale: "the answer is ( 300 - 100 ) / 3 + 1 = 67.6 answer is a"
Answer: a
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50
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 , 47 } n ( x ) = 15 , n ( s ) = 50 hence , the required probability is 15 / 50 . answer : b
Answer: b
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 10 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 1.250 kg , e ) none of these
Rationale: "the weight of non - water in 10 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 10 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 1.25 answer : d"
Answer: d
Problem: two trains , a and b , started simultaneously from opposite ends of a 200 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 200 - mile trip in 10 hours ; train b , traveling at a constant rate , completed the 200 - mile trip in 6 hours . how many miles had train a traveled when it met train b ?
Options: a ) 70 , b ) 75 , c ) 87.5 , d ) 90 , e ) 92.5
Rationale: "as the ratio of the rates of a and b is 6 to 10 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 6 / ( 6 + 10 ) = 6 / 16 of 200 miles : 200 * 6 / 16 = 75 miles . answer : b ."
Answer: b
Problem: a mixture of 200 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 11 liters , b ) 11.2 liters , c ) 12.5 liters , d ) 13.78 liters , e ) 13.33 liters
Rationale: "number of liters of water in 200 liters of the mixture = 20 % of 120 = 20 / 100 * 200 = 40 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 40 + p ) and total volume of mixture is ( 200 + p ) . ( 40 + p ) = 25 / 100 * ( 200 + p ) 160 + 4 p = 200 + p p = 13.33 liters . answer : e"
Answer: e
Problem: a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 5 from part a & 10 from part b , in how many ways can he choose the questions ?
Options: a ) 100 , b ) 120 , c ) 125 , d ) 350 , e ) 252
Rationale: "there 5 questions in part a out of which 10 question can be chosen as = 10 c 5 similarly , 10 questions can be chosen from 10 questions of part b as = 10 c 10 . hence , total number of ways , = 10 c 5 * 10 c 10 = [ 10 ! / ( 5 ! 5 ! ) ] * [ 10 ! / ( 0 ! * 10 ) ] = { 10 * 9 * 8 * 7 * 6 / ( 5 * 4 * 3 * 2 * 1 ) } * 10 ! / 1 * 10 ! = 252 e"
Answer: e
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 240,000 ?
Options: a ) 27 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 240 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 240,000 = 3 years total 27 years . answer a"
Answer: a
Problem: 14.02 ã — 0.001 = ?
Options: a ) 0.1402 , b ) 0.001402 , c ) 1.4021 , d ) 0.01402 , e ) none of these
Rationale: "14.02 ã — 0.001 = 0.01402 the answer is d ."
Answer: d
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 17 candidates . she plans to have one working interview with 3 of the 17 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 420 , c ) 300 , d ) 30 , e ) 333
Rationale: "420 . answer b"
Answer: b
Problem: the average ( arithmetic mean ) of 5 numbers is 5 . if 2 is subtracted from each of 4 of the numbers , what is the new average ?
Options: a ) 3.4 , b ) 4.5 , c ) 6.2 , d ) 5.7 , e ) 6.9
Rationale: let the numbers be a , b , c , d , e , f so , total of these 5 numbers must be 25 or , a + b + c + d + e = 25 so , 12 must be subtracted from the total sum i . e a + b + c + d + e - 8 or , 25 - 8 = 17 hence average of the 5 numbers now is 17 / 5 = > 3.4 so , answer will be a
Answer: a
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many q grams ?
Options: a ) q = 16
b ) q = 32
c ) 64
d ) 128
e ) 512
Rationale: weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )
Answer: b
Problem: a man can row upstream at 34 kmph and downstream at 48 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 41 , d ) 32 , e ) 23
Rationale: "us = 34 ds = 48 m = ( 48 + 34 ) / 2 = 41 answer : c"
Answer: c
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 6 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 12 , b ) 18 , c ) 14 , d ) 20 , e ) 22
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 6 ) = ( 7 / 16 ) * v 1 ( v 1 - 6 ) / v 1 = 3 / 4 6 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 6 = 24 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 24 = 14 litres . answer : c"
Answer: c
Problem: one ton has 2300 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1840 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2300 pound = 13 * 2300 * 16 ounces . hence the answer is ( 13 * 2300 * 16 ) / 260 = 1840 . answer : a ."
Answer: a
Problem: a man can row 2 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 1.8 , b ) 1.9 , c ) 1.2 , d ) 1.7 , e ) 1.3
Rationale: "m = 2 s = 1.2 ds = 2.4 us = 0.8 x / 1.2 + x / 0.8 = 1 x = 0.6 d = 0.6 * 2 = 1.2 answer : c"
Answer: c