regisss/math_qa huggingface dataset:
Problem: the present worth of a certain bill due sometime hence is rs . 800 and the true discount is rs . 36 . the banker ’ s discount is
Options: a ) rs . 34.38 , b ) rs . 38.98 , c ) rs . 37 , d ) rs . 37.62 , e ) none
Rationale: "solution b . g = [ ( t . d ) ² / p . w ] = rs . ( 36 x 36 / 800 ) = rs . 1.62 b . d given , t . d = 36 = ( t . d + b . g ) = rs . ( 36 + 1.62 ) = rs . 37.62 . answer d"
Answer: d
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 81 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 81 , e ) 40
Rationale: let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 81 ( x - y ) - - > x + y = 81 . answer : d .
Answer: d
Problem: how much is it cost $ 0.50 each tire for 8 tires ?
Options: a ) $ 3.00 , b ) $ 9.00 , c ) $ 2.00 , d ) $ 4.00 , e ) $ 7.00
Rationale: d . $ 4.00
Answer: d
Problem: it takes avery 4 hours to build a brick wall while tom can do it in 2 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 20 , b ) 40 , c ) 30 , d ) 50 , e ) 60
Rationale: "avery takes 4 hours tom takes 2 hours efficiency of avery is 1 / 4 units / hr efficiency of tom is 1 / 2 units / hr combined efficiency of tom and avery is 1 / 4 + 1 / 2 = 3 / 4 units / hr since they worked for 1 hour they completed 3 / 4 units of work and 1 / 4 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 4 / 1 / 2 hours = > 1 / 2 * 60 = 30 minutes . . . answer will be ( c )"
Answer: c
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 4 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 90 m , d ) 180 m , e ) none
Rationale: solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 4 ) m = 90 m . answer c
Answer: c
Problem: set x consists of 15 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 60 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 40 , 40 , 40 , 50 , 60 this is possible . hence it is the greatest such number . answer ( d )"
Answer: d
Problem: if x / 2 years ago roger was 18 years old and x / 2 years from now he will be 4 x years old , how old will he be 5 x years from now ?
Options: a ) 32 , b ) 35 , c ) 30 , d ) 51 , e ) 28
Rationale: "assume the current age = a a - x / 2 = 18 ( i ) a + x / 2 = 4 x or a = 7 x / 2 ( ii ) putting the value of a from ( ii ) in ( i ) 7 x / 2 - x / 2 = 18 or 6 x / 2 = 18 therefore x = 6 and a = 21 5 x years from now , age will be 21 + 5 * 6 = 51 option d"
Answer: d
Problem: a small college reduced its faculty by approximately 23 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 253 , b ) 208 , c ) 224 , d ) 254 , e ) 302
Rationale: "if x is the original number of faculty members , then after 23 % reduction in faculty members number is . 77 x but we are given . 77 x = 195 x = 253 so the original number of faculty members is 253 correct answer - a"
Answer: a
Problem: a bakery has 6 employees . it pays annual salaries of $ 15,000 to each of 2 employees , $ 17,000 to 1 employee , and $ 18,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 16,200 , b ) $ 16,500 , c ) $ 16,800 , d ) $ 17,000 , e ) $ 17,400
Rationale: "average = 2 ( 15000 ) + ( 17000 ) + 3 ( 18000 ) / 6 = $ 16,833 the answer is c ."
Answer: c
Problem: the current birth rate per certain number of people is 32 , whereas corresponding death rate is 11 per same number of people . if the net growth rate in terms of population increase is 2.1 percent , find number of persons . ( initally )
Options: a ) 1000 , b ) 10000 , c ) 100 , d ) 2000 , e ) 20000
Rationale: sol . net growth on x = ( 32 - 11 ) = 21 . net growth on 100 = ( 21 / x ã — 100 ) % = 2.1 % . then x = 1000 answer : a
Answer: a
Problem: if a lends rs . 4000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 180
Rationale: "( 4000 * 1.5 * 3 ) / 100 = > 180 answer : e"
Answer: e
Problem: if x is less than y by 35 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 53.85 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 35 % ) = > 35 / ( 100 - 35 ) * 100 = 53.85 % answer : d"
Answer: d
Problem: two numbers are in the ratio of 3 : 8 . if 24 be subtracted from each , they are in the ratio of 4 : 9 . find the numbers ?
Options: a ) 60,89 , b ) 60,88 , c ) - 27 , - 128 , d ) 60,84 , e ) - 72 , - 192
Rationale: "( 3 x - 24 ) : ( 8 x - 24 ) = 4 : 9 x = - 24 = > - 72 , - 192 answer : e"
Answer: e
Problem: if 3 tic equals 6 tacs and 2 tacs equal 7 tocs , what is the ratio of one tic to one toc ?
Options: a ) 7 / 1 , b ) 6 / 5 , c ) 5 / 6 , d ) 3 / 10 , e ) 1 / 15
Rationale: "3 tic = 6 * tac and 2 * tac = 7 * toc ; 6 * tic = 12 * tac and 12 * tac = 42 * toc - - > 6 * tic = 42 * toc - - > tic / toc = 42 / 6 = 7 / 1 . answer : a ."
Answer: a
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 60 % of the total ?
Options: a ) 858 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is a : 858 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 60 % of total is 515 , so 100 % is approx . 858 ."
Answer: a
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.3 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 7 kg
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.3 weight of the new student = ( 30 * 27.3 – 29 * 28 ) = 819 - 812 = 7 answer : e"
Answer: e
Problem: a train 225 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 81 , b ) 90 , c ) 91 , d ) 85 , e ) 96
Rationale: "speed of the train relative to man = 225 / 10 m / sec = 45 / 2 m / sec . = 45 / 2 x 18 / 5 km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 10 = 81 = 91 km / hr . answer : c"
Answer: c
Problem: how many positive integers less than 100 are neither multiples of 4 or 5 .
Options: a ) a ) 30 , b ) b ) 60 , c ) c ) 32 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 4 till 100 = 100 / 4 = 25 2 ) multiples of 5 till 100 = 100 / 5 = 20 add the two 25 + 20 = 45 ; subtract common terms that are multiple of both 4 and 5 . . lcm of 4 and 5 = 20 multiples of 20 till 100 = 100 / 20 = 5 = so total multiples of 4 and 5 = 45 - 5 = 40 ans = 100 - 40 = 60 b"
Answer: b
Problem: the area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm . what is the perimeter of the square ?
Options: a ) 140 , b ) 240 , c ) 340 , d ) 144 , e ) 122
Rationale: "area of the square = s * s = 3 ( 27 * 16 ) = > s = 9 * 4 = 36 cm perimeter of the square = 4 * 36 = 144 cm . answer : d"
Answer: d
Problem: the present ratio of students to teachers at a certain school is 30 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "lets say t = 10 - - - > s = 300 - - - > 350 / 15 = a bit less than 25 ( a and b will only make this ratio lesser , eliminate a and b ) go for t = 12 - - > s = 30 * 12 = 360 - - - > 360 + 50 / 12 + 5 = less than 25 . either you can now go further with t = 15 or mark e as the answer . check : t = 15 - - - > s = 30 * 15 = 450 - - - > 450 + 50 / 20 = 25 . answer : e"
Answer: e
Problem: a train is 360 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 27 seconds , b ) 29 seconds , c ) 40 seconds , d ) 30 seconds , e ) 12 seconds
Rationale: "speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 3 / 50 ) = 30 seconds answer : d"
Answer: d
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 64 more for rs . 40 . what is the reduced price / dozen ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "sol . lie purchases 6 a bananas mere for 4096 of rs 40 or , rs 16 . reduced price per do 3 a"
Answer: a
Problem: a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.4 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 240 , e ) e . 200
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.4 = 240 answer : d"
Answer: d
Problem: excluding stoppages , the speed of a bus is 48 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 5 , b ) 4.15 , c ) 4.25 , d ) 5.5 , e ) none of these
Rationale: "due to stoppages , it covers 314 km less . time taken to cover 3 km = ( ( 3 / 48 ) ã — 60 ) = 4.15 min . option ( b ) is correct"
Answer: b
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 60 people were made to stand in a column , how many columns could be formed ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "16 * 30 = 60 * n n = 8 the answer is b ."
Answer: b
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 2 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 65 , b ) 63 , c ) 52 , d ) 60 , e ) 68
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 2 w = 120 = > w = 60 answer d"
Answer: d
Problem: a man took loan from a bank at the rate of 12 % p . a . s . i . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 15002 , b ) 15001 , c ) 15000 , d ) 15007 , e ) 15009
Rationale: principal = ( 100 * 5400 ) / ( 12 * 3 ) = rs . 15000 . answer : c
Answer: c
Problem: a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 8 per item . if the manufacturer ’ s selling price per item is $ 12 , how many items the manufacturer produce and sell to earn an annual profit of $ 140,000 ?
Options: a ) 2,858 , b ) 8,667 , c ) 21,429 , d ) 35,000 , e ) 67,500
Rationale: "let the items manufactured or sold bex 130000 + 8 x = 12 x - 140000 4 x = 270000 x = 67500 ans : e"
Answer: e
Problem: how many numbers between 100 and 714 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 15 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 714 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 714 : 714 / 42 = 17 hence , 42 * 14 = 714 is the last number divisible by 42 within 714 hence , total numbers divisible by 2 , 3 , 7 together are ( 17 â € “ 2 ) = 15 answer : d"
Answer: d
Problem: how many paying stones , each measuring 3 m * 2 m are required to pave a rectangular court yard 60 m long and 14 m board ?
Options: a ) 99 , b ) 140 , c ) 26 , d ) 17 , e ) 12
Rationale: "60 * 14 = 3 * 2 * x = > x = 140 answer : b"
Answer: b
Problem: if a light flashes every 6 seconds , how many times will it flash in 1 / 2 of an hour ?
Options: a ) 301 times , b ) 351 times , c ) 401 times , d ) 451 times , e ) 481 times
Rationale: "in 1 / 2 of an hour there are 30 * 60 = 1800 seconds the number of 6 - second intervals = 1800 / 6 = 300 after the first flash , there will be 300 more flashes for a total of 301 . the answer is a ."
Answer: a
Problem: the average runs scored by a batsman in 30 matches is 40 . in the next 10 matches the batsman scored an average of 13 runs . find his average in all the 30 matches ?
Options: a ) 24.3 , b ) 25.3 , c ) 26.3 , d ) 28.3 , e ) 34.5
Rationale: "total score of the batsman in 30 matches = 600 . total score of the batsman in the next 10 matches = 130 . total score of the batsman in the 30 matches = 730 . average score of the batsman = 730 / 30 = 24.3 . answer : a"
Answer: a
Problem: a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 36 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.8 x = 36 and x = 36 / 1.8 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 4 more . the answer is b .
Answer: b
Problem: in the city of san durango , 60 people own cats , dogs , or rabbits . if 30 people owned cats , 40 owned dogs , 16 owned rabbits , and 12 owned exactly two of the 3 types of pet , how many people owned all 3 ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 7 , e ) 32
Rationale: you are considering a case when cat dogs and rabbit are not exactly equal to 12 . the solution shall be 60 = 30 + 40 + 16 - 12 - 2 x and hence x shall be 7 . answer d
Answer: d
Problem: a certain company ’ s profit in 1996 was 17 percent greater than its profit in 1995 , and its profit in 1997 was 25 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 46.25 %
Rationale: "profit in 1995 - 100 profit in 1996 - 117 % increae profit in 1997 in comparison to 1995 = 17 + 117 * 25 % = 46.25 correct option : e"
Answer: e
Problem: a can give b 80 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 130.12 , b ) 130.43 , c ) 130.22 , d ) 111.0 , e ) 111.12
Rationale: a runs 1000 m while b runs 920 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 920 = 869.56 m b can give c = 1000 - 869.56 = 130.43 m . answer : b
Answer: b
Problem: what is the smallest no . that should be added to 45454 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 4 + 5 + 4 + 5 + 4 = 22 , the next multiple of 9 is 27 . 5 must be added to 45454 to make it divisible by 9 c"
Answer: c
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 58.8 sq . m . find the length of each stone slab ?
Options: a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 58.8 / 30 m 2 = 1.96 m 2 length of each slab √ 1.96 = 1.4 m = 140 cm"
Answer: a
Problem: nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days they completed 1 / 3 part of work . than how many more emploies should nhai hire to finish it in time working 10 hours a day
Options: a ) 60 , b ) 70 , c ) 80 , d ) 50 , e ) 40
Rationale: "( m 1 * d 1 * h 1 ) / w 1 = ( m 2 * d 2 * h 2 ) / w 2 ( 100 * 25 * 8 ) / ( 1 / 3 ) = ( ( 100 + a ) * 25 * 10 ) ) / ( 2 / 3 ) 160 = 100 + a a = 60 answer : a"
Answer: a
Problem: the average of first four prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "23 + 29 + 31 + 37 = 120 / 4 = 30 answer : c"
Answer: c
Problem: jar x is 1 / 4 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 4 + p / 4 = p / 2 the answer is d ."
Answer: d
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 40 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 612 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 40 + 42 + 44 + . . . . . upto 12 terms ) this is an a . p with first term , a = 40 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 40 + { 12 - 1 ) x 2 ] = 6 ( 102 ) = 612 kms . answer : c"
Answer: c
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 60 per square m ?
Options: a ) rs . 50000 , b ) rs . 52000 , c ) rs . 57000 , d ) rs . 60000 , e ) rs . 67000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 60 * 950 = rs . 57000 c"
Answer: c
Problem: in the coordinate plane , a circle centered on point ( - 3 , - 3 ) passes through point ( 1 , 1 ) . what is the area of the circle ?
Options: a ) 9 π , b ) 32 π , c ) 25 π , d ) 37 π , e ) 41 π
Rationale: "r ^ 2 = ( - 3 - 1 ) ^ 2 + ( - 3 - 1 ) ^ 2 = 16 + 16 = 32 area of circle = π r ^ 2 = 32 π answer : b"
Answer: b
Problem: a small island country of 5000 people has an emigration and immigration statistic per 500 persons of 50.4 and 15.4 respectively . how long will it take for the population to be half of its current number .
Options: a ) 6.8 , b ) 8.5 , c ) 6.1 , d ) 9.1 , e ) 7.14
Rationale: annual decrease is ( 500 + 15.4 - 50.4 ) * 10 = 4650 hence every year there is a decrease of 350 for the population to become half 2500 must emigrate therefore 2500 / 350 = 133.3 correct option is e ) 7.14
Answer: e
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.9 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 66 ) = 1178 kgs actual average weight is 1178 / 20 = 58.9 kgs c"
Answer: c
Problem: in a certain store , the profit is 320 % of the cost . if the cost increases by 40 % but the selling price remains constant , approximately what percentage of the selling price is the profit
Options: a ) 67 % , b ) 80 % , c ) 90 % , d ) 100 % , e ) none of above
Rationale: explanation : let c . p . = rs . 100 . then , profit = rs . 320 , s . p . = rs . 420 . new c . p . = 140 % of rs . 100 = rs . 140 new s . p . = rs . 420 . profit = rs . ( 420 - 140 ) = rs . 280 required percentage = ( 280 / 420 ) * 100 = 66.67 % ( approx ) = 67 % answer : a
Answer: a
Problem: if the perimeter of a rectangular garden is 480 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 140 m , c ) 200 m , d ) 167 m , e ) 128 m
Rationale: "2 ( l + 100 ) = 480 = > l = 140 m answer : b"
Answer: b
Problem: a family pays $ 800 per year for an insurance plan that pays 60 percent of the first $ 1000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,600 , e ) $ 2,000
Rationale: assuming the medical expenses are $ 1000 or more , the family pays $ 800 + $ 400 = $ 1200 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 600 when the medical expenses are $ 1600 . the answer is d .
Answer: d
Problem: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 10 and 15 . the larger of the two numbers is :
Options: a ) 350 , b ) 250 , c ) 450 , d ) 500 , e ) 620
Rationale: "explanation : clearly , the numbers are ( 30 x 10 ) and ( 30 x 15 ) . { \ color { blue } \ therefore } larger number = ( 30 x 15 ) = 450 . answer : c ) 450"
Answer: c
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 10 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 55 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 10 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 10 = 4 / 9 ( t - 10 ) 10 t = 990 - 440 = > t = 55 . answer : d"
Answer: d
Problem: in a particular state , 70 % of the counties received some rain on monday , and 50 % of the counties received some rain on tuesday . no rain fell either day in 20 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "70 + 50 + 20 = 140 % the number is 40 % above 100 % because 40 % of the counties were counted twice . the answer is b ."
Answer: b
Problem: a train passes a platform in 16 seconds . the same train passes a man standing on the platform in 10 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 40 , b ) 50 , c ) 90 , d ) 30 , e ) 20
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 10 = 150 m let the length of the platform = l time taken to cross the platform = ( 150 + l ) / 15 = > ( 150 + l ) / 15 = 16 = > 150 + l = 15 × 16 = 240 = > l = 240 - 150 = 90 meter answer is c"
Answer: c
Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 180 , e ) 315
Rationale: "1 of 7 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more thn one deparments . we can choose any of the 4 candidates for the math dep . , which gives as 4 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 4 * 45 = 180 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans d"
Answer: d
Problem: sum of two numbers is 25 . first exceeds by 5 from the other . then the numbers will be ?
Options: a ) 20 , 5 , b ) 10 , 15 , c ) 15 , 10 , d ) 5 , 20 , e ) 12 , 13
Rationale: "explanation : x + y = 25 x - y = 5 x = 15 y = 10 answer : c"
Answer: c
Problem: if 35 % of the 840 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 546 , b ) 550 , c ) 555 , d ) 532 , e ) 515
Rationale: "we know 35 % people study biology , therefore the no of people not studying = 100 - 35 = 65 % > therefore the people not studying biology out of a total 840 people are = 65 % of 840 > ( 65 / 100 ) * 840 = 546 people a"
Answer: a
Problem: a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 44 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 410 + 140 = 550 meter time = distance / speed = 550 * ( 2 / 25 ) = 44 seconds answer : e"
Answer: e
Problem: if a is thrice as fast as b and together can do a work in 30 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 54 , e ) 40
Rationale: a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 30 = 3 + 1 / 3 x = 4 / 3 x = 1 / 30 x = 30 * 4 / 3 = 40 answer : e
Answer: e
Problem: angelina walked 200 meters from her home to the grocery at a constant speed . she then walked 300 meters to the gym at double the speed . she spent 50 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 200 / x . . the speed to gym = 2 x . . so time taken = 300 / 2 x = 150 / x . . its given 200 / x - 150 / x = 50 . . 50 / x = 50 . . x = 1 m / secs . . so grocery to gym = 2 * 1 = 2 m / s . . . answer : a"
Answer: a
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 40 year . what is the age of the eldest child ?
Options: a ) 14 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 40 â ‡ ” 5 x = 10 â ‡ ” x = 2 . â ˆ ´ age of the youngest child = x + 12 = 2 + 12 = 14 years . answer a"
Answer: a
Problem: how many positive integers less than 5,000 are evenly divisible by neither 17 nor 21 ?
Options: a ) 4,514 , b ) 4,480 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 17 5000 / 17 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 17 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 17 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4480 answer b ."
Answer: b
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 2 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 40 , d ) 60 , e ) 90
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 2 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 2 * ( 2 / 3 ) ) days = > 90 days answer : e"
Answer: e
Problem: if x and y are positive integers and 42 x = 56 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 63 , d ) 196 , e ) 252
Rationale: "42 x = 56 y = > x / y = 4 / 3 = > 3 x = 4 y 3 ( 14 ) = 4 ( 14 ) = > x * y = 196 e"
Answer: e
Problem: a train 150 m long is running with a speed of 98 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going
Options: a ) 5 sec , b ) 6 sec , c ) 7 sec , d ) 8 sec , e ) 9 sec
Rationale: "explanation : speed of the train relative to man = ( 98 - 8 ) kmph = ( 90 × 5 / 18 ) m / sec = 25 m / sec time taken by the train to cross the man i = time taken by it to cover 150 m at 25 m / sec = 150 × 1 / 25 sec = 6 sec answer : option b"
Answer: b
Problem: what is the sum of the greatest common factor and the lowest common multiple of 36 and 56 ?
Options: a ) 512 , b ) 508 , c ) 451 , d ) 516 , e ) 451
Rationale: "prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 56 = 2 x 2 x 2 x 7 gcf = 4 lcm = 504 sum = 508 ans : b"
Answer: b
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 7225 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2500 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 7225 = x = 7225 / 2.89 = 2500 therefore , amount invested by raghu is rs . 2500 . answer : c"
Answer: c
Problem: the difference between two parallel sides of a trapezium is 4 cm . perpendicular distance between them is 10 cm . if the area of the trapezium is 250 cm 2 find the lengths of the parallel side
Options: a ) 27 , 23
b ) 25 , 25
c ) 24 , 26
d ) 23 , 29
e ) 24 , 45
Rationale: explanation : let the two parallel sides of the trapezium be a cm and b cm . then , a - b = 4 - - - - - - ( 1 ) and , ( 1 / 2 ) x ( a + b ) x 10 = 475 = > ( a + b ) = ( ( 250 x 2 ) / 10 ) = > a + b = 50 - - - - - - - ( 2 ) solving 1 and 2 , we get : a = 27 , b = 23 so , the two parallel sides are 27 cm and 23 cm . answer : option a
Answer: a
Problem: in a box of 8 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 12 , b ) 5 / 14 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: "first , there are 6 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 8 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 6 c 3 / 8 c 3 = 20 / 56 = 5 / 14 answer is b"
Answer: b
Problem: what is the area of square field whose side of length 17 m ?
Options: a ) 225 , b ) 777 , c ) 266 , d ) 289 , e ) 261
Rationale: "17 * 17 = 289 sq m answer : d"
Answer: d
Problem: a sum is divided between a and b in the ratio of 1 : 2 . a purchased a car from his part , which depreciates 14 2 / 7 % per annum and b deposited his amount in a bank , which pays him 20 % interest per annum compounded annually . by what percentage will the total sum of money increase after two years due to this investment pattern ( approximately ) .
Options: a ) 22.48 % , b ) 20.48 % , c ) 24.48 % , d ) 25.48 % , e ) 26.48 %
Rationale: let the total money = 300 a ' s part = 100 b ' s part = 200 after 2 years a ' s part = 73.46 ( as it depreciates by 14.29 % per annum ) after 2 years b ' s part = 288 ( using the compound interest formula , a = p ( 1 + r / n ) ^ nt ) , where p = 200 , r = 0.2 , n = 1 , t = 2 ) so , after 2 years total amount = 361.46 therefore % increase in money = ( 361.46 - 300 ) * 100 / 300 = 20.48 % answer : b
Answer: b
Problem: how many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph ?
Options: a ) 54 sec , b ) 35 sec , c ) 25 sec , d ) 45 sec , e ) 24 sec
Rationale: "d = 100 + 250 = 350 s = 36 * 5 / 18 = 10 mps t = 350 / 10 = 35 sec answer : b"
Answer: b
Problem: two trains of length 100 m and 160 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 ) 18 sec , b ) 70 sec , c ) 13 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 160 = 260 m . the time required = d / s = 260 / 20 = 13 sec . answer : c"
Answer: c
Problem: pipe a fills a tank in 30 minutes . pipe b can fill the same tank 5 times as fast as pipe a . if both the pipes were kept open when the tank is empty , how much time will it take for the tank to overflow ?
Options: a ) 4 mins , b ) 6 mins , c ) 5 mins , d ) 3 mins , e ) 7 mins
Rationale: "let the total capacity of tank be 90 liters . capacity of tank filled in 1 minute by a = 3 liters . capacity of tank filled in 1 minute by b = 15 liters . therefore , capacity of the tank filled by both a and b in 1 minute = 18 liters . hence , time taken by both the pipes to overflow the tank = 90 / 18 = 5 minutes . answer : c"
Answer: c
Problem: the average age of a class of 15 students is 10 years . if the age of the teacher be included , then the average increased by 1 year . find the age of the teacher ?
Options: a ) 22 , b ) 23 , c ) 26 , d ) 29 , e ) 31
Rationale: "total age of 15 persons = 15 * 10 = 150 years average age of 16 persons = 11 years total age of 16 persons = 16 * 11 = 176 years age of the teacher = 176 - 150 = 26 years answer is c"
Answer: c
Problem: the sum of digits of a two digit number is 12 , the difference between the digits is 4 . find the number
Options: a ) 84 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 12 , x - y = 4 adding these 2 x = 16 = > x = 8 , y = 4 . thus the number is 84 answer a"
Answer: a
Problem: find number which is 80 % less than 80 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 26 , e ) 16
Rationale: "explanation : 80 % less is 20 % of the given number therefore , 20 % of 80 is 16 . answer : e"
Answer: e
Problem: there are some birds in cage , 1 / 3 rd fly away . then 2 / 5 th of the remaining left the cage , then 2 / 3 rd of the remaining left the cage . at last 8 were remaining . how many birds were in total ?
Options: a ) 60 , b ) 27 , c ) 28 , d ) 26 , e ) 91
Rationale: sol : if x birds were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 8 x × 2 / 3 × 3 / 5 × 1 / 3 = 8 x = 60 answer : a
Answer: a
Problem: x is 3 times as fast as y and working together , they can complete a work in 20 days . in how many days can y alone complete the work ?
Options: a ) 11 days , b ) 80 days , c ) 13 days , d ) 15 days , e ) 19 days
Rationale: x = 3 y x + y = 3 y + y = 4 y these 4 y people together can do the work in 20 days , which means y can alone do the work in 4 * 20 = 80 days . answer : b
Answer: b
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 9 m wide at the top and 7 m wide at the bottom and the area of cross - section is 560 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 70 , d ) 80 , e ) 71
Rationale: "1 / 2 * d ( 9 + 7 ) = 560 d = 70 answer : c"
Answer: c
Problem: on dividing 199 by a number , the quotient is 11 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 199 - 1 ) / 11 = 198 / 11 = 18 d )"
Answer: d
Problem: of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak hindi and 20 % of the diplomats spoke neither french nor hindi . if 10 % of the diplomats spoke both french and hindi , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer"
Answer: d
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 59 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.20 $ , b ) 380.20 $ , c ) 421.20 $ , d ) 451.20 $ , e ) 481.20 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 59 ) = 481.20 hence answer will be ( e )"
Answer: e
Problem: what is the nearest no . to 2304 which is divisible by 21 ?
Options: a ) 2289 , b ) 2310 , c ) 2333 , d ) 2456 , e ) 2309
Rationale: remainder when 2304 is divided by 21 = 15 so , no . should added to make 15 to 21 = 6 no . = 2304 + 6 = 2310 answer b
Answer: b
Problem: the population of a town is 10000 . it increases annually at the rate of 25 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 14500 , d ) 15625 , e ) 14700
Rationale: formula : 10000 × 125 / 100 × 125 / 100 = 15625 answer : d
Answer: d
Problem: when asked what the time is , a person answered that the amount of time left is 4 / 8 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 4 pm , d ) 8 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 4 / 8 x ⇒ x = 20 time is 4 pm answer : c"
Answer: c
Problem: if x and y are integers , what is the least positive number of 24 x + 20 y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: 24 x + 20 y = 4 ( 6 x + 5 y ) which will be a minimum positive number when 6 x + 5 y = 1 . 6 ( 1 ) + 5 ( - 1 ) = 1 then 4 ( 6 x + 5 y ) can have a minimum positive value of 4 . the answer is c .
Answer: c
Problem: of 25 applicants for a job , 14 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 25 - 3 = 22 aub = a + b - aib aib = 18 + 14 - 22 = 10 answer b"
Answer: b
Problem: the sector of a circle has radius of 28 cm and central angle 90 o . find its perimeter ?
Options: a ) 100 cm , b ) 85 cm , c ) 75 cm , d ) 95 cm , e ) 110 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 90 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 28 ) = 44 + 56 = 100 cm answer : a"
Answer: a
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . [ ( 2 - 1 ) / 1 ] * 100 % = 100 % answer : c"
Answer: c
Problem: 3 * 11 + 3 * 12 + 3 * 15 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 148 , e ) 151
Rationale: "we have : 3 * 11 = 33 3 * 12 = 36 3 * 15 = 45 all of this is : ( 33 + 36 + 45 ) + 11 = 114 + 11 = 125 correct answer a"
Answer: a
Problem: one pump drains one - half of a pond in 8 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: first pump drains 1 / 2 of the tank in 8 hours so 16 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 16 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 16 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 16 + 1 / a ) = 1 / 2 solving u get a = 16 / 15 = 1.1 hence answer is b
Answer: b
Problem: there are 2 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 100
Rationale: "using anagram method : 4 _ 3 _ 2 _ 1 r _ r _ b _ b so . . 4 ! / number of repeated letters ( 2 ! ) ( 2 ! ) = 6 ans : d"
Answer: d
Problem: the speed of a car is 50 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 85 kmph , c ) 55 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 55 + 60 ) / 2 = 55 kmph answer : c"
Answer: c
Problem: the top and bottom of a tower were seen to be at angles of depression 30 ° and 60 ° from the top of a hill of height 100 m . find the height of the tower
Options: a ) 64.67 m , b ) 66.67 m , c ) 68.67 m , d ) 56.67 m , e ) 46.67 m
Rationale: by making a diagram ac represents the hill and de represents the pole given that ac = 100 m anglexad = angleadb = 30 ° ( ∵ ax | | bd ) anglexae = angleaec = 60 ° ( ∵ ax | | ce ) let de = h then , bc = de = h , ab = ( 100 - h ) ( ∵ ac = 100 and bc = h ) , bd = ce tan 60 ° = acce = > 3 √ = 100 ce = > ce = 1003 √ - - - ( 1 ) tan 30 ° = abbd = > 13 √ = 100 − hbd = > 13 √ = 100 − h ( 1003 √ ) ( ∵ bd = ce and substituted the value of ce from equation 1 ) = > ( 100 − h ) = 13 √ × 1003 √ = 1003 = 33.33 = > h = 100 − 33.33 = 66.67 m i . e . , the height of the pole = 66.67 m answer : b
Answer: b
Problem: the age of the daughter is same as the digit in the mother ' s age , but in reverse order . in thirteen years mother will be twice as old as daughter will be then . what is the difference in their current age ?
Options: a ) 15 , b ) 23 , c ) 27 , d ) 46 , e ) 32
Rationale: daughter ' s age = 10 x + y so mother ' s age = 10 y + x . . after 13 years , 10 x + y + 13 = 2 * ( 10 y + x + 13 ) . . . . so 13 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 4 . . . so ages are 41 and 14 and ans as found correctly by u is c . . 27
Answer: c
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel four times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 9 , e ) 12
Rationale: "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 4 and w = 4 s then we have 1 / ( 4 * s ) + 1 / s = 1 / 4 < = > 5 / ( 4 * s ) = 1 / 4 < = > s = 5 ans : c"
Answer: c
Problem: a larger cube has 125 cubic inch as a volume and in the cube there are 125 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 125 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 600 , c ) 81 , d ) 108 , e ) 120
Rationale: "volume of larger cube = 125 = 5 ^ 3 side of larger cube = 5 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 5 ^ 2 = 150 surface area of 27 smaller cubes = 125 * 6 * 1 = 750 difference = 750 - 150 = 600 answer : b"
Answer: b
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 12 , find the other ?
Options: a ) 100 , b ) 600 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 12 = 600 answer is b"
Answer: b
Problem: if below equation are true 24 $ 6 = 64 35 $ 5 = 87 63 $ 7 = 99 by using same logic what is the value of the below question 88 $ 8 = ?
Options: a ) 1621 , b ) 1711 , c ) 1611 , d ) 1511 , e ) 1311
Rationale: correct answer : c the number on the right side is formed as ( sum of digits of the 1 st number ) no 1 / no 2 ex : 35 $ 5 = 87 ( 3 + 5 = 8 ) ( 35 / 5 = 7 ) 63 $ 7 = 99 ( 6 + 3 = 9 ) ( 63 / 7 = 9 )
Answer: c
Problem: the average weight of 10 persons increases by 3.2 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 ) 76 kg , b ) 80 kg , c ) 85 kg , d ) 97 kg , e ) none
Rationale: "solution total weight increased = ( 10 x 3.2 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer d"
Answer: d
Problem: the average of runs of a cricket player of 10 innings was 37 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 81 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 37 so , total = average x no . of innings = 37 x 10 = 370 . now increase in avg = 4 runs . so , new avg = 37 + 4 = 41 runs total runs = new avg x new no . of innings = 41 x 11 = 451 runs made in the 11 th inning = 451 - 370 = 81 answer : b"
Answer: b
Problem: a , b , and c started a partnership business by investing $ 45,000 , $ 63,000 , and $ 72,000 respectively . at the end of the year , the profit was distributed among them . if c ' s share of profit is $ 24,000 , what is the total profit ?
Options: a ) $ 48,000 , b ) $ 52,000 , c ) $ 56,000 , d ) $ 60,000 , e ) $ 64,000
Rationale: a : b : c = 45000 : 63000 : 72000 which is a ratio of 5 : 7 : 8 . let the total profit be x . x * 8 / 20 = 24000 x = 24000 * 20 / 8 = 60,000 . the answer is d .
Answer: d
Problem: what will be the vulgar fraction of 0.75
Options: a ) 3 / 5 , b ) 3 / 4 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.75 = 75 / 100 = 3 / 4 option b"
Answer: b
Problem: a company decreased the price of its main product by 75 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 1.33 , b ) 2.33 , c ) 3.33 , d ) 4.33 , e ) 1.45
Rationale: "for the total revenue to remain the same when the price is 3 / 4 , the number of products sold must 3 / 4 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 75 % = 1.33 answer : a"
Answer: a
Problem: a ' s speed is 15 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?
Options: a ) 35 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %
Rationale: first calculate the distance , b has covered with his speed in the time , in which a reached 80 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.75 ) = 0.65 % ( which means b would have covered 0.65 of the race length during the time in which a has covered 0.75 of the race length . therefore to win , b needs a headstart of ( 1 - 0.65 = ) 0.35 of the race length . so the answer is a
Answer: a
Problem: company c sells a line of 20 products with an average retail price of $ 1200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000
Rationale: the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b .
Answer: b