regisss/math_qa huggingface dataset:
Problem: what quantity of water should taken out to concentrate 12 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 4 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 12 ( 60 - 40 ) / 60 = 4 liters answer is a"
Answer: a
Problem: john had a stock of 700 books in his bookshop . he sold 50 on monday , 82 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 26.5 % , b ) 50 % , c ) 46.5 % , d ) 56.5 % , e ) 60 %
Rationale: "let n be the total number of books sold . hence n = 50 + 82 + 64 + 78 + 135 = 280 let m be the books not sold m = 700 - n = 700 - 280 = 420 percentage books not sold / total number of books = 420 / 700 = 0.60 = 60 % correct answer e"
Answer: e
Problem: if it takes a tub 4 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 36 seconds , d ) 2 minutes , 14 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 4 minutes to drain 5 / 7 th of tub it takes 4 * ( 7 / 5 ) minutes to drain the entire tub and 4 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 8 / 5 minutes or 1 3 / 5 minutes or 1 minute 36 seconds so answer is c"
Answer: c
Problem: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this ordert ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . t = 12.5 * 6 = 75 . e
Answer: e
Problem: when a merchant imported a certain item , he paid a 9 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 85.50 , what was the total value of the item ?
Options: a ) $ 1,150 , b ) $ 1,350 , c ) $ 1,550 , d ) $ 1,750 , e ) $ 1,950
Rationale: "let x be the value in excess of $ 1,000 . 0.09 x = 85.5 x = $ 950 the total value was $ 950 + $ 1,000 = $ 1,950 . the answer is e ."
Answer: e
Problem: how many different 3 - digit multiples of 5 can be composed of digits 2 , 7 , 4 , and 5 if none of the digits is repeated ?
Options: a ) 3 , b ) 6 , c ) 10 , d ) 12 , e ) 18
Rationale: = 3 c 2 x 2 = 6 can you explain your method . i solved it differently xyz , where z must be 5 . therefore 1 variation of digit in z . y can be any of the 3 possible choices . x can be any of the 2 possible choices . 2 + 3 + 1 = 6 b
Answer: b
Problem: in a class of 38 children , 19 play tennis , 21 play squash and 10 play neither sport . ( 1 ) how many children play both sports ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 19
Rationale: 28 play some sport 19 + 21 - both = 28 both = 12 answer is b
Answer: b
Problem: a train 440 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 ) 72 sec , b ) 24 sec , c ) 44 sec , d ) 62 sec , e ) 21 sec
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 = [ 440 * 3 / 55 ] sec = 8 sec answer : b"
Answer: b
Problem: firm a ' s revenues are described by the equation ra = 17.12 x and its costs by ca = 12.87 x + 2400 . firm b ' s revenues are described by the equation rb = 13.27 x and its costs by cb = 8.77 x + 1500 . ( x denotes the quantity of sales ) . if a ' s volume of sales increases from 1000 to 3000 over the same period that b ' s volume increases from 2000 to 3000 , the percent increase in profits for the firm with the biggest dollar increase in profits is
Options: a ) 20 % , b ) 30 % , c ) 60 % , d ) 50 % , e ) 33 %
Rationale: ok , i do not know whether it is exactly what you want to hear but i did it that way : first look at difference between revenue and variable cost = > take the bigger one ( b ) which gives you : 4.5 x - 1500 just plug in 2000 and 3000 . you get 7500 and 12000 ( difference 4500 ) . 4500 > 0.5 * 7500 so 30 % b
Answer: b
Problem: how many seconds will a 500 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 33 , b ) 87 , c ) 30 , d ) 88 , e ) 77
Rationale: "explanation : distance = 500 m speed of the train relative to man = ( 63 - 3 ) km / hr = 60 km / hr = m / s = m / s time taken to pass the man = distance / speed = sec = 30 sec answer : c ) 30"
Answer: c
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 9 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 18 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 9 work in 1 day b alone can do ( 1 / 6 - 1 / 9 ) = 1 / 18 work in 1 day = > complete work can be done in 18 days by b answer : option c"
Answer: c
Problem: √ 6 percent of 6 √ 6 =
Options: a ) 0.3 , b ) 0.25 , c ) 0.1 , d ) 0.95 , e ) 0.35
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 √ 3 ≈ 1.7 √ 5 ≈ 2.2 √ 6 ≈ 2.4 so , √ 6 percent of 6 √ 6 ≈ 2.4 percent of ( 6 ) ( 2.4 ) ≈ ( 2.4 / 100 ) ( 14.4 ) ≈ 34.56 / 100 ≈ 0.34 check the answer choices to see that e is the only answer that ' s close . answer : e"
Answer: e
Problem: 20 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 24 , b ) 18 , c ) 17 , d ) 16 , e ) 10
Rationale: "binders books days 20 1400 21 x 1600 20 x / 20 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 24 answer : a"
Answer: a
Problem: a man can do a job in 20 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 20 + 1 / 20 + 1 / 25 ) = 7 / 50 so , all three together will complete the work in 300 / 47 = 7.1 days . answer : c"
Answer: c
Problem: what will be the vulgar fraction of 0.4
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.4 = 40 / 100 = 2 / 5 option b"
Answer: b
Problem: in a school 10 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 4 g 10 b / 100 = g / 4 b = 5 g / 2 b / g = 5 / 2 b : g = 5 : 2 answer is a"
Answer: a
Problem: the volume of a cistern is 840 cubic meters and water is flowing into the cistern . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate , in cubic meters per minutes , at which the water is flowing into the cistern ?
Options: a ) 0.125
b ) 0.25
c ) 0.5
d ) 0.75
e ) not enough information to determine the rate
Rationale: 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 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 . the correct answer is e .
Answer: e
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 6 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 31 : 1 , b ) 31 : 4 , c ) 31 : 8 , d ) 31 : 9 , e ) 31 : 2
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 2 + 21 / 4 = 31 / 4 = 7.75 litres as 10 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 7.75 : 2.25 = 31 : 9 . answer : d"
Answer: d
Problem: a number whose fifth part increased by 2 is equal to its fourth part diminished by 2 is ?
Options: a ) 160 , b ) 80 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 2 = ( n / 4 ) - 2 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 4 â ‡ ’ ( 5 n - 4 n ) / 20 = 4 â ˆ ´ n = 80 option : b"
Answer: b
Problem: if an object travels at four feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 14400 , e ) 18000
Rationale: "speed = 4 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 4 = 1800 x 10 = 14400 answer d"
Answer: d
Problem: a 230 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 270 m
Rationale: "speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 230 + x therefore , d = speed * time thus 230 + x = 500 / 9 * 9 x = 500 - 230 = 270 m answer : e"
Answer: e
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 90 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 90 , c ) 100 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 180 - - 2 subtracting 1 from 2 we have c - a = 90 ; answer : b"
Answer: b
Problem: the diagonals of a rhombus are 17 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 186 , c ) 150 , d ) 170 , e ) 172
Rationale: "1 / 2 * 17 * 20 = 170 answer : d"
Answer: d
Problem: ? x 240 = 173 x 240
Options: a ) 173 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 240 = 173 x 240 then y = ( 173 x 240 ) / 240 = 173 answer : a"
Answer: a
Problem: at a summer camp with 900 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 900 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 64 % , b ) 66 2 / 3 % , c ) 62 % , d ) 60 % , e ) 56 %
Rationale: "total - 900 participants campers are aged 8 to 12 = ( 1 / 2 ) * 900 = 450 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 450 = 600 percentage = ( 600 / 900 ) * 100 = 66 2 / 3 % answer : option b"
Answer: b
Problem: a rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles , all of the same size . the minimum number of such tiles is :
Options: a ) 425
b ) 430
c ) 440
d ) 450
e ) 460
Rationale: l = 378 cm and b = 525 cm maximum length of a square tile = hcf of ( 378,525 ) = 21 cm number of tiles = ( 378 × 525 ) / ( 21 × 21 ) = ( 18 × 25 ) = 450 answer is d .
Answer: d
Problem: 12 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) a ) 35 , b ) b ) 34 , c ) c ) 42 , d ) d ) 25 , e ) e ) 26
Rationale: explanation : let the present age of p and q be 3 x and 4 x respectively . twelve years ago , p was half of q in age = > 2 ( 3 x – 12 ) = ( 4 x – 12 ) = > 6 x – 24 = 4 x – 12 = > 2 x = 12 = > x = 6 7 x = 7 * 6 = 42 answer : option c
Answer: c
Problem: a can do a piece of work in 6 days and b can do it in 6 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 1 / 2 , c ) 3 / 4 , d ) 9 / 11 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 6 ( a + b ) ’ s one day work = 1 / 6 + 1 / 6 = 2 / 3 = = > time = 3 / 2 = 1 1 / 2 days answer : option b"
Answer: b
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 20 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 20 = 6 k + 4 k k = 2 total red ' s in bag a will be 2 k = 4 c"
Answer: c
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number n is
Options: a ) 74 , b ) n = 75 , c ) n = 175 , d ) n = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 190 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.2
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 190 / 45 = $ 4.2 answer : e ."
Answer: e
Problem: a train is travelling at 48 kmph . it crosses another train having half of its length , travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . what is the length of the platform ?
Options: a ) 400 m , b ) 500 m , c ) 600 m , d ) 550 m , e ) 700 m
Rationale: speed of i train = 48 kmph length of i train = 2 x m speed of sec train = 42 kmph length of seconf train = x m dist = ( 2 x + x ) = 3 x m time = 12 sec = 90 * 5 / 18 = 25 m / s x = 100 length of first train = 2 x = 200 m time taken = 45 sec speed of first train = 48 kmph = 48 * 5 / 18 = 40 / 3 m / s length of the platform = y metre 200 + y = 45 * 45 / 3 = 600 y = 400 answer a
Answer: a
Problem: if 3 / p = 6 and 3 / q = 15 then p – q = ?
Options: a ) 3 / 19 , b ) 3 / 11 , c ) 3 / 17 , d ) 3 / 10 , e ) 3 / 13
Rationale: explanation : 3 p 3 p = 6 , p = 3636 = 1212 and 3 q 3 q = 15 , q = 315315 = 1515 then p – q = 1 / 2 – 1 / 5 = 3 / 10 answer : d
Answer: d
Problem: light glows for every 13 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 13 ) = 382 times . answer : c"
Answer: c
Problem: in an election , candidate a got 80 % 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 favor of candidate ?
Options: a ) 355600 , b ) 380800 , c ) 356500 , d ) 356800 , e ) 357000
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 = 80 % therefore , the number of valid votes polled in favour of candidate a = 80 % of 476000 = 80 / 100 × 476000 = 38080000 / 100 = 380800 b )"
Answer: b
Problem: what is the square root of 239,121 ?
Options: a ) 476 , b ) 489 , c ) 497 , d ) 511 , e ) 524
Rationale: "according to divisibility rules , 239,121 is divisible by 9 . 2 + 3 + 9 + 1 + 2 + 1 = 18 this means , that the answer choice must be divisible by 3 a ) 4 + 7 + 6 = 17 no b ) 4 + 8 + 9 = 21 yes c ) 4 + 9 + 7 = 20 no d ) 5 + 1 + 1 = 7 no e ) 5 + 2 + 4 = 11 no b is the only answer"
Answer: b
Problem: if n = 2 ^ 0.1 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3
Rationale: 10 / 100 = 1 / 10 n = 2 ^ 1 / 10 n ^ b = 2 ^ 4 ( 2 ^ 1 / 10 ) ^ b = 2 ^ 4 b = 40 answer : c
Answer: c
Problem: find the perimeter and area of the rectangle of length 11 cm and breadth 7 cm .
Options: a ) 77 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 171 cm 2 , e ) 221 cm 2
Rationale: "length = 11 cm , breadth = 7 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 11 + 7 ) cm = 2 × 16 cm = 32 cm we know that the area of rectangle = length × breadth = ( 11 × 7 ) cm 22 = 77 cm 2 answer : a"
Answer: a
Problem: the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 37 , c ) 99 , d ) 277 , e ) 19
Rationale: explanation : required number of students = h . c . f of 1001 and 910 = 9 answer : a ) 91
Answer: a
Problem: a will states that the estate would be divided among 6 sons with the remainder donated to charity . one stipulation in the will is that no one among the sons can receive an amount within 12 % of another ' s amount . if one of the beneficiaries received $ 30000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 6 sons ?
Options: a ) $ 4096 , b ) $ 14043 , c ) $ 7892 , d ) $ 17736 , e ) $ 15336
Rationale: 1 st - 30000 . 2 nd - 0.88 * 30000 = 26400 3 rd - 0.88 * 26400 = 23232 4 th - 0.88 * 23232 = 20 , 444.16 5 th - 0.88 * 20 , 444.16 = ~ 17 , 990.86 6 th - 0.88 * 17 , 990.86 = ~ 15 , 831.96 range = 30000 - 15831 = 14168 answer : b .
Answer: b
Problem: calculate 469111 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4690640889
Rationale: answer 469111 x 9999 = 469111 x ( 10000 - 1 ) = 4691110000 - 469111 = 4690640889 . option : e
Answer: e
Problem: simple interest on a certain sum at a certain annual rate of interest is 1 / 25 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 5 % , b ) 2 % , c ) 6 % , d ) 8 % , e ) 3 %
Rationale: "explanation : let sum = x . then , s . i . = x / 25 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 25 ? r ^ 2 = 100 / 25 = 4 r = 2 hence , rate of interest = 2 % . answer : b"
Answer: b
Problem: two numbers are in the ratio of 1 : 2 . if 9 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 9 ) / ( y + 9 ) = 3 / 5 = > x = 18 and y = 36 answer : e"
Answer: e
Problem: bookman purchased 60 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 660 , how many paperback copies were sold ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "the bookman had 10 hardback ad 60 - 10 = 50 paperback copies ; 14 copies were sold , hence 60 - 14 = 46 copies were left . let # of paperback copies left be p then 10 p + 20 ( 46 - p ) = 660 - - > 10 p = 260 - - > p = 26 # of paperback copies sold is 50 - 26 = 24 answer : b"
Answer: b
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 760 ; each of his remaining paychecks was $ 30 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 783 , e ) $ 775
Rationale: "= ( 760 * 6 + 790 * 20 ) / 26 = 783 answer is d . posted from my mobile device"
Answer: d
Problem: two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 30 km apart , if they walk in the same direction ?
Options: a ) 15 hours , b ) 6 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 30 = 15 hours answer is a"
Answer: a
Problem: if a ' s salary is 20 % less than b ' s salary , by how much percentage is b ' s salary more than a ' s ?
Options: a ) 25 % , b ) 15 % , c ) 30 % , d ) 32 % , e ) 40 %
Rationale: "required percentage = [ 100 * 20 / ( 100 - 20 ) ] % = 25 % answer is a"
Answer: a
Problem: the area of a square is equal to three times the area of a rectangle of dimensions 15 cm * 5 cm . what is the perimeter of the square ?
Options: a ) 30 , b ) 80 , c ) 50 , d ) 60 , e ) 70
Rationale: "area of the square = s * s = 3 ( 15 * 5 ) = > s = 15 cm perimeter of the square = 4 * 15 = 60 cm . answer : option d"
Answer: d
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 5 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6 , b ) 1 , c ) 5 , d ) 4 , e ) 7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 5 ? - - - 1 = > rs . 4 100 - - - 80 ? - - - 4 = > rs . 5 answer : c"
Answer: c
Problem: find 103 × × 10
Options: a ) 106 / 19 , b ) 108 / 12 , c ) 108 / 19 , d ) 108 / 15 , e ) 108 / 11
Rationale: "by taking 100 as a base we can easily get the answer for the above question within seconds . 103 is 3 more than 100 and 105 is 5 more than 100 so we will write add the excess of the second number to first number or excess of first number to second number as show below to get left most digits and multiply the excesses to get the right most two digits . note : always remember if you get a single digit number put zero in the left two make it a two digit number to get the right most two digits . answer : d"
Answer: d
Problem: a worker is paid a regular rate of rs . 10 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 30 % higher than her regular rate . if she completed 60 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 180 , b ) 1180 , c ) 280 , d ) 580 , e ) 2080
Rationale: "amount earned using her cell phone = 60 * 13 = 780 earned for remaining surveys = 40 * 10 = 400 total earning = 1180 answer : b"
Answer: b
Problem: if the price of sugar rises from rs . 2 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 60 %
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 2 = x × 5 = x = 40 kg . ∴ reduction in consumption = 60 % . answer e"
Answer: e
Problem: what is the 124 th digit to the right of the decimal point in the decimal form of 24 / 44 ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 4 , e ) 2
Rationale: "to solve this question , we first have to use some long division . this long division allows us to get 24 / 44 in decimal form , which is 0.545454 … where “ 54 ” is repeating . we can see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 5 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 4 . in other words , each odd - positioned digit is a 5 , and each even - positioned digit is a 4 . then the 124 digit to the right of the decimal point and we see that 124 is even , we know that the 124 th digit is a 4 . answer d ."
Answer: d
Problem: a palindrome is a number that reads the same forward and backward , such as 145 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 80 , d ) 90 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 16 = 80 ways c"
Answer: c
Problem: when n is divided by 25 , the remainder is 4 . what is the remainder when n + 15 is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 29 remainder ( n / 24 ) = 4 n + 15 = 44 remainder ( 44 / 5 ) = 4 option c"
Answer: c
Problem: find the 25 % of rs . 500 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 125 , e ) s . 60
Rationale: "explanation : 25 % of 500 = > 25 / 100 * 500 = rs . 125 answer : d"
Answer: d
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 200 inclusive ?
Options: a ) 190 , b ) 105 , c ) 200 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 200 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 20 ( 10 ) = 200 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 200 = 210 20 + 190 = 210 30 + 180 = 210 etc . since there are 20 total terms , this pattern will create 10 ' pairs ' of 210 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 10 ) ( 210 ) / ( 20 ) = 105 answer : b"
Answer: b
Problem: the ages of two persons differ by 12 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,8 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 12 ) years . 5 ( x - 5 ) = ( x + 12 - 5 ) or 4 x = 32 or x = 8 . their present ages are 20 years and 8 years option b"
Answer: b
Problem: if n is the smallest integer such that 54 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 1 , c ) 6 , d ) 12 , e ) 24
Rationale: "54 can written as = 2 * 3 * 3 * 3 - - > 2 ^ 1 * 3 ^ 3 - - - ( 1 ) so for 54 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 1 in ( 1 ) even option b is correct"
Answer: b
Problem: two trains a and b are 150 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 150 + 150 = 300 m . time taken = 300 / 25 = 12 s . correct answer e ."
Answer: e
Problem: if 4 a = 5 b = 30 , then 40 ab =
Options: a ) 900 , b ) 1800 , c ) 2250 , d ) 1650 , e ) 1250
Rationale: "4 a * 5 b = 30 * 30 = 900 20 ab = 900 i . e . 30 ab = 1800 answer : option b"
Answer: b
Problem: if a train , travelling at a speed of 18 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 281 m , b ) 25 m , c ) 50 m , d ) 125 m , e ) 75 m
Rationale: "b b = 18 * 5 / 18 * 5 = 25 m"
Answer: b
Problem: a train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds . what is the length of the train ?
Options: a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) 165 m
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 110 = 25 * ( x / 15 ) 10 x = 1650 x = 165 meters the answer is e ."
Answer: e
Problem: a train covers a distance at a speed of 150 kmph in 3 hours . to cover the same distance in 1 hours , it must travel at a speed of ?
Options: a ) 320 , b ) 250 , c ) 560 , d ) 400 , e ) 450
Rationale: distance = 150 * 3 = 450 km required speed = 450 / 1 = 450 km / hr answer is e
Answer: e
Problem: find the quotient : 0.63 / 9
Options: a ) 0.5 , b ) 0.3 , c ) 0.9 , d ) 0.1 , e ) 0.7
Rationale: "63 / 9 = 7 . dividend contains 2 places decimal . 0.63 / 9 = 0.7 answer is e ."
Answer: e
Problem: the ratio of boys to girls in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the boys and two - third of the girls in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 272 degree
e ) e ) 192 degree
Rationale: let the common ratio be x . . so b = 2 x and g = 3 x and total = 5 x 1 / 3 of m = 2 x / 3 and 2 / 3 of f = 2 x . . total preferring that carrer = 2 x / 3 + 2 x = 8 x / 3 . . now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 ans 192 e
Answer: e
Problem: x , y , and z are different prime numbers . the product x ^ 2 * y * z is divisible by how many different positive numbers ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: the exponents of x ^ 2 * y * z are 2 , 1 , and 1 . the number of factors is ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 the answer is e .
Answer: e
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 13.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 25 = 10 * 12 / 5 = 24 time difference = 13.1 ans : b"
Answer: b
Problem: a 120 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 72 , e ) 112
Rationale: "s = 120 / 6 * 18 / 5 = 72 kmph answer : d"
Answer: d
Problem: peter takes a loan of $ 100000 with 12 % annual interest : the interest is paid once , at the end of the year . martha takes a loan of $ 100000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to peter ' s loan interest , approximately how much more does martha have to repay ?
Options: a ) $ 68.25 , b ) zero , c ) $ 6825.00 , d ) $ 6.82 , e ) $ 682.50
Rationale: peters interest = $ 100000 * 0.12 = $ 12000 or $ 1000 each month . martha ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 100000 * 0.01 = $ 1000 ; for the 2 nd month = $ 1000 + 1 % of 1000 = $ 1010 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1010 + 1 % of 1010 = ~ $ 1020 ; for the 4 th month = $ 1020 + 1 % of 1020 = ~ $ 1030 ; . . . for the 12 th month = $ 1100 + 1 % of 1100 = ~ $ 1110 . the difference between peters interest and martha ’ s interest = ~ ( 10 + 20 + . . . + 110 ) = $ 660 . answer : e .
Answer: e
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 15 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48 , d ) 56.8 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 63.75 . 4 ) now 63.75 has to be added byx % in order to equal the original price . 63.75 + ( x % ) 63.75 = 100 . solving this eq for x , we get x = 56.8 ans is d ."
Answer: d
Problem: 3 numbers are randomly selected , with replacement , from the set of integers { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . if the first number selected is w , the second number selected is x , and the third number is y , what is the probability that w < x < y ?
Options: a ) 3 / 40 , b ) 28 / 243 , c ) 3 / 25 , d ) 33 / 100 , e ) 64 / 125
Rationale: solution : total possible ways = 10 * 10 * 10 = 1000 case 1 : w = 0 . if x = 1 , then y can have 8 ways . if x = 2 , then y can have 7 ways and so on . so , no . of ways = 8 + 7 + . . + 1 case 2 : w = 1 . if x = 2 , then y can have 7 ways . if x = 3 , then y can have 6 ways and so on . so , no . of ways = 7 + 6 + . . + 1 there will be 8 cases in this way and they will follow a pattern which looks like this : no . of ways for case 1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 no . of ways for case 2 : 1 + 2 + 3 + 4 + 5 + 6 + 7 no . of ways for case 3 : 1 + 2 + 3 + 4 + 5 + 6 no . of ways for case 4 : 1 + 2 + 3 + 4 + 5 no . of ways for case 5 : 1 + 2 + 3 + 4 no . of ways for case 6 : 1 + 2 + 3 no . of ways for case 7 : 1 + 2 no . of ways for case 8 : 1 ____________________________________________________________ total number of ways : 8 ( 1 ) + 7 ( 2 ) + 6 ( 3 ) + 5 ( 4 ) + 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) = 2 ( 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) ) = 2 ( 60 ) = 120 therefore , ans is 120 / 1000 = 3 / 25 . option c .
Answer: c
Problem: two trains a and b are 200 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 14 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 200 + 150 = 350 m . time taken = 350 / 25 = 14 s . correct answer c ."
Answer: c
Problem: if 20 % of a class averages 80 % on a test , 50 % of the class averages 60 % on the test , and the remainder of the class averages 40 % on the test , what is the overall class average ?
Options: a ) 80 % , b ) 74 % , c ) 58 % , d ) 56 % , e ) 50 %
Rationale: 2 students scored 80 % 5 students scored 60 % 3 students scored 40 % ( 2 ) ( 80 ) + 5 ( 60 ) + 3 ( 40 ) = 160 + 300 + 120 = 580 580 / 10 students = 58 - - > 58 % average answer : c
Answer: c
Problem: a man whose bowling average is 12.4 , takes 6 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 113 , b ) 114 , c ) 115 , d ) 116 , e ) 117
Rationale: "12.4 * x + 26 = ( 6 + x ) 12 solve equation x = 115 answer : c"
Answer: c
Problem: of the 200 stamps in a collection , 90 are foreign and 70 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 150
Rationale: 20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 50 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 50 ) = 60 the answer is a .
Answer: a
Problem: the average age of 20 students in a class is 5 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 28 , b ) 24 , c ) 20 , d ) 22 , e ) 18
Rationale: "total age of 50 students = 20 * 5 = 100 total age of 51 persons = 20 * 6 = 120 age of teacher = 120 - 100 = 20 years answer is c"
Answer: c
Problem: how many zeroes are there at the end of the number n , if n = 80 ! + 160 ! ?
Options: a ) 15 , b ) 19 , c ) 23 , d ) 27 , e ) 31
Rationale: "the number of zeroes at the end of 80 ! will be less than the number of zeroes at the end of 160 ! hence it is sufficient to calculate the number of zeroes at the end of 80 ! the number of zeroes = [ 80 / 5 ] + [ 80 / 25 ] + [ 80 / 125 ] = 16 + 3 + 0 = 19 the answer is b ."
Answer: b
Problem: the principal that amounts to rs . 4913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) 288 , b ) 267 , c ) 200 , d ) 4096 , e ) 2771
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4096 . answer : d"
Answer: d
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by c are ?
Options: a ) 11 , b ) 18 , c ) 45 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 75 = 45 answer : c"
Answer: c
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 9 , what is the least possible value of n ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 12 , e ) 7
Rationale: we need at least 2 factors of three , which means n must be at least 6 , so b is the correct answer .
Answer: b
Problem: √ 289 - √ 625 ÷ √ 25 is equal to ?
Options: a ) 17 , b ) 15 , c ) 12 , d ) - 8 / 5 , e ) none
Rationale: answer √ 289 - √ 625 ÷ √ 25 = √ 17 x 17 - √ 25 x 25 ÷ √ 5 x 5 = 17 - 25 ÷ 5 = 17 - 5 = 12 correct option : c
Answer: c
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 83 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 28
Rationale: total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 83 thus m = 664 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 664 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 28 ans : e
Answer: e
Problem: what is the compound interest on rs . 9500 at 6 % p . a . compounded half - yearly for 1 1 / 2 years .
Options: a ) 810.91 , b ) 840.91 , c ) 880.91 , d ) 887.91 , e ) 980.91
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 10 , 380.91 c . i . > > 10 , 380.91 - 9500 > > rs . 880.91 answer : c"
Answer: c
Problem: a and b ’ s salaries together amount to rs . 4,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 2777 , b ) 1000 , c ) 2789 , d ) 2776 , e ) 2881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 1000 4 b = 1000 = > b = 1000 answer b"
Answer: b
Problem: the population of a bacteria culture doubles every 6 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 54 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 6 minutes so answer is 9 * 6 = 54 minutes answer ( d )"
Answer: d
Problem: can you solve it ? 2 + 3 = 8 , 3 + 7 = 27 , 4 + 5 = 32 , 5 + 8 = 60 , 6 + 7 = 72 , 7 + 8 = ? ?
Options: a ) 68 , b ) 78 , c ) 88 , d ) 98 , e ) 56
Rationale: 2 + 3 = 2 * [ 3 + ( 2 - 1 ) ] = 8 3 + 7 = 3 * [ 7 + ( 3 - 1 ) ] = 27 4 + 5 = 4 * [ 5 + ( 4 - 1 ) ] = 32 5 + 8 = 5 * [ 8 + ( 5 - 1 ) ] = 60 6 + 7 = 6 * [ 7 + ( 6 - 1 ) ] = 72 therefore 7 + 8 = 7 * [ 8 + ( 7 - 1 ) ] = 98 x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x correct answer is d ) 98
Answer: d
Problem: if the remainder is 10 when positive integer n is divided by 14 , what is the remainder when n is divided by 7 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "assume x is quotient here , n = 14 x + 7 - - - - - - - - - - ( 1 ) and n = 7 x + ? we can also write equation ( 1 ) as : n = ( 14 x + 7 ) + 3 . ie 7 ( 2 x + 1 ) + 3 ie the first term is perfectly divisible by 7 . so , the remainder left is 3 . so , answer ( d ) is right choice ."
Answer: d
Problem: if x ^ 2 + 1 / x ^ 2 = 2 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 2 , c ) 4 , d ) 16 , e ) 18
Rationale: important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 2 andsquareboth sides : ( x ² + 1 / x ² ) ² = 4 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 4 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 4 simplify : x ⁴ + 1 / x ⁴ = 2 answer : b
Answer: b
Problem: a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 12 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 12 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 443 , b ) 450 , c ) 460 , d ) 468 , e ) 475
Rationale: "total number of installments = 52 payment per installment for the first 12 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 12 * 410 + 40 * 475 ) / 52 = 460 answer c"
Answer: c
Problem: at what rate percent of simple interest will a sum of money double itself in 22 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 22 ) = 100 / 22 = 4.54 % answer : b"
Answer: b
Problem: consider a square of diagonal length d . let another square be formed with d as its side . find the ratio of the area of the bigger square to that of the smaller square .
Options: a ) 2
b ) 3
c ) 4
d ) 16
e ) 41
Rationale: d ^ 2 / ( 1 / 2 ) * d ^ 2 = 2 answer : a
Answer: a
Problem: find the missing value : ? - 1936248 = 1635773
Options: a ) 3572021 , b ) 3570221 , c ) 3572012 , d ) 3752012 , e ) none of them
Rationale: "let x - 1936248 = 1635773 . then , x = 1635773 + 1936248 = 3572021 answer is a ."
Answer: a
Problem: the tax on a commodity is diminished by 14 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2.1 % , b ) 8.1 % , c ) 5.1 % , d ) 6.1 % , e ) 1.1 %
Rationale: "100 * 100 = 10000 86 * 115 = 9890 - - - - - - - - - - - 10000 - - - - - - - - - - - 110 100 - - - - - - - - - - - ? = > 1.1 % decrease answer : e"
Answer: e
Problem: the sum of the ages of 4 children born at the intervals of 5 years each is 58 years . what is the age of the youngest child ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) none of these , e ) can not be determined
Rationale: "explanation : let x = the youngest child . each of the other four children will then be x + 5 , x + 10 , x + 15 we know that the sum of their ages is 58 . so , x + ( x + 5 ) + ( x + 10 ) + ( x + 15 ) = 58 x = 7 the youngest child is 4 years old . answer : a"
Answer: a
Problem: in a party every person shakes hands with every other person . if there were a total of 136 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 136 n ( n - 1 ) / 2 = 136 â ˆ ´ n = 17 answer : c"
Answer: c
Problem: set a consists of all the prime numbers between 12 and 32 . what is the range of set a ?
Options: a ) 12 , b ) 18 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 31 lowest number = 13 range = highest - lowest = 31 - 13 = 18 option b"
Answer: b
Problem: caleb spends $ 74.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 10 , c ) 20 , d ) 40 , e ) 49
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 74.50 . by solving the equations y = 49 . ans e ."
Answer: e
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 40 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 16
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 40 = 160 m = 42 tu + w + th = 192 - 42 = 150 f = 160 – 150 = 10 answer : c"
Answer: c
Problem: if eight 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 ) 45 , b ) 60 , c ) 75 , d ) 96 , 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 8 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 16 / 3 = 10 / 3 * x x = 8 / 5 hour so 96 minutes answer : d"
Answer: d
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 8 , what is the sum of the first 15 terms of the progression ?
Options: a ) 60 , b ) 120 , c ) 160 , d ) 240 , e ) 840
Rationale: "let a = first term , d = common difference . 4 th term = a + 3 d 12 th term = a + 11 d a + 3 d + a + 11 d = 8 2 a + 14 d = 8 a + 7 d = 4 . sum of the first 15 terms = 15 / 2 ( 2 a + 14 d ) = 15 ( a + 7 d ) = 15 ( 4 ) = 60 . ans ( a )"
Answer: a
Problem: niki covers a distance in 45 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 50 % .
Options: a ) 101.02 kmph , b ) 121.62 kmph , c ) 100.62 kmph , d ) 111.00 kmph , e ) 121.00 kmph
Rationale: given speed = 60 kmph . it means niki covered 60 km in 60 min ( 1 hour ) . so , in 45 min he will cover 45 km . 50 % time reduced = 45 - 50 % of 45 = 22.5 min . thus , niki needs to cover 45 km in 22.5 min ( 0.37 hour ) . speed * time = distance . speed * 0.37 = 45 speed = 121.62 kmph . answer : option b
Answer: b
Problem: a man complete a journey in 20 hours . he travels first half of the journey at the rate of 10 km / hr and second half at the rate of 15 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 240 km , c ) 230 km , d ) 232 km , e ) 234 km
Rationale: "0.5 x / 10 + 0.5 x / 15 = 20 - - > x / 10 + x / 15 = 40 - - > 5 x = 30 x 40 - - > x = ( 30 x 40 ) / 5 = 240 km . answer : b ."
Answer: b
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 4 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 4 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 4 ) = 6 x . the fraction of sensors which have been upgraded is x / ( x + 6 x ) = x / 7 x = 1 / 7 the answer is d ."
Answer: d
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many b hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) b = 5 . , d ) b = 6 . , e ) b = 8 .
Rationale: "c . 5 hrs if there were 10 beavers it could have taken double b = 6 hrs . . so closest to that option is 5 . c"
Answer: c