regisss/math_qa huggingface dataset:
Problem: n and m are each 3 - digit integers . each of the numbers 3,4 , 5 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: "you have 6 digits : 3 , 4 , 5 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 3 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . 487 and 536 ( difference is 49 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 685 and 734 ( difference is 49 ) b"
Answer: b
Problem: a jogger running at 9 km / hr along side a railway track is 190 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 88 , b ) 27 , c ) 36 , d ) 31 , e ) 12
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 190 + 120 = 310 m . time taken = 310 / 10 = 31 sec . answer : d"
Answer: d
Problem: a fruit seller sells mangoes at the rate of rs . 11 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 10 % ?
Options: a ) rs . 13.44 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 90 : 11 = 110 : x x = ( 11 ã — 110 / 90 ) = rs . 13.44 hence , s . p per kg = rs . 13.44 answer a"
Answer: a
Problem: when 1 / 20 % of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 598 , e ) 400
Rationale: "1 / 20 % of 6000 = 3 1 / 10 of 6000 = 600 600 - 3 = 598 ans : d"
Answer: d
Problem: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 620 in all . for how many days was he absent ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 7 , e ) 4
Rationale: "30 * 25 = 750 620 - - - - - - - - - - - 130 25 + 7.50 = 32.5 130 / 32.5 = 4 e"
Answer: e
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 13.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 46 1 / 6 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 13 = 2.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 2.6 ) / 2.6 * 100 % = 46 1 / 6 % answer b"
Answer: b
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 80 respectively . the sum is :
Options: a ) rs . 1800 , b ) rs . 1450 , c ) rs . 1360 , d ) rs . 6800 , e ) none
Rationale: "solution sum = s . i xt . d / ( s . i ) - ( t . d ) = 85 x 80 / 85 - 80 = rs . 1360 . answer c"
Answer: c
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 75 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 69.55 $ , b ) 50.63 $ , c ) 60.95 $ , d ) 52.15 $ , e ) 53.15 $
Rationale: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 75 x = 60.95 hence , the correct option is c"
Answer: c
Problem: the age of father 5 years ago was 4 times the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
Options: a ) 5 : 4 , b ) 7 : 4 , c ) 5 : 2 , d ) 5 : 3 , e ) 7 : 5
Rationale: let the ages of father and son 5 years ago be 4 x and x years respectively . then , ( 4 x + 5 ) + 5 = 2 [ ( x + 5 ) + 5 ] 4 x + 10 = 2 x + 20 x = 5 . required ratio = ( 4 x + 5 ) : ( x + 5 ) = 25 : 10 = 5 : 2 . answer : option c
Answer: c
Problem: the average of 11 numbers is 50 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) a ) 188 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 50 = 188 answer is a"
Answer: a
Problem: in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 15 %
Rationale: "d 10 % 100 - [ ( 100 - 85 ) + ( 100 - 80 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 15 + 20 + 25 + 30 ) = 100 - 90"
Answer: d
Problem: the population of a town is 20000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 12800
Rationale: "20000 × 80 / 100 × 80 / 100 = 12800 answer : e"
Answer: e
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 8 cm above the ground , what is the radius of the other ball ?
Options: a ) 12 cm , b ) 16 cm , c ) 18 cm , d ) 20 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 6 = 6 / r - 6 giving r = 12 . answer : a"
Answer: a
Problem: the population of a village is 15540 . it increases annually at the rate of 28 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 25460 , c ) 26709 , d ) 14000 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 15540 × 128 / 100 × 128 / 100 = 25460 b"
Answer: b
Problem: if x / 4 + 24 / x = 5 , what are the values of 2 x - 7 ?
Options: a ) 8 and 9 , b ) 8 and 24 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 9
Rationale: i got the same thing e is the answer 9 or 17
Answer: e
Problem: which greatest possible length can be used to measure exactly 12 meter 15 cm , 10 meter 15 cm and 10 meter 65 cm
Options: a ) 45 cm , b ) 25 cm , c ) 4 cm , d ) 5 cm , e ) 50 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1215 cm , 1015 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option d"
Answer: d
Problem: the sum of money will be double itself in 10 years and simple interest find rate of interest ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: t = 10 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 10 x = 10 % answer is a
Answer: a
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 11 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 14 , b ) 15 , c ) 18 , d ) 22 , e ) 33
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 11 t 1 = 11 and so t 2 = 22 . the answer is d ."
Answer: d
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 6 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 36 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 6 = x 5 x + 36 = 6 x x = 36 km answer : option e"
Answer: e
Problem: the cost price of a radio is rs . 4500 and it was sold for rs . 3200 , find the loss % ?
Options: a ) 28.9 % , b ) 22 % , c ) 28 % , d ) 45 % , e ) 32 %
Rationale: "4500 - - - - 1300 100 - - - - ? = > 28.9 % answer : a"
Answer: a
Problem: the ratio of three numbers is 4 : 2 : 5 and their sum is 121 . the second number of the three numbers is ?
Options: a ) 22 , b ) 26 , c ) 27 , d ) 29 , e ) 30
Rationale: "4 : 2 : 5 total parts = 11 11 parts - - > 121 1 part - - - - > 11 the second number of the three numbers is = 2 * 11 = 22 answer : a"
Answer: a
Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 197 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 9801 , b ) 10,000 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus it will be ( 99 + 98 ) * ( 99 - 98 ) . thus x = 99 and y = 98 x ^ 2 = 99 ^ 2 = 9801 the answer is a ."
Answer: a
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company ’ s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 300,000 , e ) $ 2 , 200,000
Rationale: answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000
Answer: d
Problem: when positive integer n is divided by positive integer p , the quotient is 20 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 2 . what is the value of n ?
Options: a ) 107 , b ) 331 , c ) 511 , d ) 691 , e ) 871
Rationale: "n / p = 10 7 / p = 20 p + 7 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 2 solving these two equations we get p = 5 n = 107 answer is a ."
Answer: a
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 4 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 600 , c ) 200 , d ) 800 , e ) 700
Rationale: explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 4 = > x = 800 answer : d ) rs 800
Answer: d
Problem: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 40 people were made to stand in a column , how many columns could be formed ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "16 * 30 = 40 * n n = 12 the answer is a ."
Answer: a
Problem: find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 5 as quotient and the 4 as remainder
Options: a ) 1234 , b ) 1345 , c ) 1456 , d ) 1567 , e ) 1499
Rationale: "let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e"
Answer: e
Problem: the area of a rectangular field is equal to 50 square meters . its perimeter is equal to 30 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 50 : area , l is the length and w is the width . 2 l + 2 w = 30 : perimeter l = 15 - w : solve for l ( 15 - w ) * w = 30 : substitute in the area equation w = 5 and l = 10 correct answer a"
Answer: a
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 35 % ?
Options: a ) 600 , b ) 887 , c ) 256 , d ) 654 , e ) 675
Rationale: "cost price = rs . 500 profit = 35 % of 500 = rs . 175 selling price = cost price + profit = 500 + 175 = 675 answer : e"
Answer: e
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 3000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 13,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 3000 ) solving for x , we get the shares as 13000 . ans : ( option a )"
Answer: a
Problem: 65 boys can complete a work in 30 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 170 , c ) 180 , d ) 195 , e ) 200
Rationale: "one man can complete the work in 30 * 65 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : d"
Answer: d
Problem: in a recent election , james received 0.5 percent of the 2000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001
Rationale: james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d
Answer: d
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 12000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 403200 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b"
Answer: b
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) 50 , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 42.5 ) / ( 100 â ˆ ’ 5 ) = 150 hence , required % profit = 150 â € “ 100 = 50 % answer d"
Answer: d
Problem: pants , shorts and shirts in a dresser are in the ratio of 7 : 7 : 10 . if there are 14 pants , the number of shirts in the dresser is :
Options: a ) 14 , b ) 7 , c ) 20 , d ) 70 , e ) 35
Rationale: explanation : let pants = 7 x , shorts = 7 x & shirts = 10 x . now , 7 x = 14 hence x = 2 . number of apples = 10 x = 20 . answer : c
Answer: c
Problem: if x / ( 11 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c"
Answer: c
Problem: list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median r of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals
Options: a ) 5 , b ) 7 , c ) 8 , d ) r = 9 , e ) 10
Rationale: mode of list ii = 3 median r of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d )
Answer: d
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 194
Rationale: "by the question , the equation would be 150 p - 84 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 194 . answer e for me ."
Answer: e
Problem: at a special sale , 9 tickets can be purchased for the price of 6 tickets . if 9 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 9 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 9 tickets cost 900 9 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 300 , % of 9 tickets = ( 300 / 900 ) * 100 = 33.3 % answer : b"
Answer: b
Problem: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.35 * 8 = 0.2 ( x + 8 ) - - > x = 12 . answer : b ."
Answer: b
Problem: a students was asked to find the arithmetic mean of the numbers 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x . he found the mean to be 12 . what should be the number in place of x ?
Options: a ) 3 , b ) 7 , c ) 17 , d ) 31 , e ) 38
Rationale: adding all the numbers we get 137 + x given - ( 137 + x ) / 12 = 12 137 + x = 12 * 12 x = 144 - 137 x = 7 answer : b
Answer: b
Problem: harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1190 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 10 kg grapes = 70 × 10 = 700 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 700 + 490 = 1190 a"
Answer: a
Problem: a chemical supply company has 60 liters of a 40 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 40 % hno 3 solution means hno 3 = 24 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 24 + x = 50 % of ( 60 + x ) or x = 12 . hence , a"
Answer: a
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 36 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 24 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) solve the equation . 262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) 9 , 462.6 + 3 , 104.35 x = 50 , 380.2 + 1 , 399.45 x 9 , 462.6 + 1 , 704.9 x = 50 , 380.2 1 , 704.9 x = 40 , 917.6 x = 24 answer is b ."
Answer: b
Problem: a man spends 35 % of his income on food , 25 % on children education and 80 % of the remaining on house rent . what percent of his income he is left with ?
Options: a ) 1 % , b ) 8 % , c ) 12 % , d ) 5 % , e ) 4 %
Rationale: let the total income be x then , income left = ( 100 - 80 ) % of x - [ 100 - ( 35 + 25 ) ] % of x = 20 % of 40 % of x = 8 % of x answer is b
Answer: b
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 261 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 408 , b ) 475 , c ) 550 , d ) 625 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 261 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 561 a + b + c = 51 per hour so for eight hrs = 51 * 8 = 408 = answer = a"
Answer: a
Problem: a container contains 20 liters of milk , from this container 2 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?
Options: a ) 14.58 liters , b ) 20.16 liters , c ) 22.45 liters , d ) 26.95 liters , e ) 31.45 liters
Rationale: "amount of milk left after 3 operations = 20 ( 1 - 2 / 20 ) ^ 3 = 20 * 9 / 10 * 9 / 10 * 9 / 10 = 14.58 liters answer is a"
Answer: a
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "given that the area of the square = 2025 sq . units = > side of square = √ 2025 = 45 units the radius of the circle = side of the square = 45 units length of the rectangle = 2 / 5 * 45 = 18 units given that breadth = 10 units area of the rectangle = lb = 18 * 10 = 180 sq . units answer : option e"
Answer: e
Problem: a train of length 250 m crosses a bridge of length 150 m in 25 seconds . what is the speed of train ?
Options: a ) 57.6 , b ) 27 , c ) 25 , d ) 22 , e ) 72
Rationale: sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 25 x speed speed = 400 / 25 = 16 m / s = 57.6 km / h answer = a
Answer: a
Problem: indu gave bindu rs . 500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 0.2 , b ) 1.2 , c ) 3 , d ) 4 , e ) 0.8
Rationale: "500 = d ( 100 / 4 ) 2 d = 0.8 answer : e"
Answer: e
Problem: the product of the squares of two positive integers is 9 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : b - 1 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 9 [ square root both sides ] xy = 3 3 = 1 x 3 , 3 x 1 cancel the repeats this leaves us with exactly 1 options . hence , b"
Answer: b
Problem: with both inlets open , a water tank will be filled with water in 52 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 10,500 , c ) 11,750 , d ) 17,500 , e ) 19,500
Rationale: "the work done by inlet a and b together in 1 min = 1 / 52 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 52 ) - ( 1 / 120 ) = 1 / 92 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 92 ) - ( 1 / 120 ) = 50 cubic meter = 19,500 cubic meter answer : option e"
Answer: e
Problem: if each edge of a cube is increased by 50 % , find the percentage increase in its surface area
Options: a ) 125 %
b ) 129 %
c ) 185 %
d ) 725 %
e ) 145 %
Rationale: let the edge = a cm so increase by 50 % = = total surface area of original cube = tsa of new cube = = = increase in area = = increase % = = 125 % answer : a
Answer: a
Problem: 12 : 8 seconds : : ? : 4 minutes
Options: a ) 10 , b ) 15 , c ) 6 , d ) 8 , e ) 7
Rationale: "12 * 4 = 8 * x x = 6 answer : c"
Answer: c
Problem: in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 0 ) lies inside the circle and the point ( 2 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 2 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 2 , - 3 ) - - - > lesser than 5 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,0 ) - - - - > greater than 3 units . thus the radius is > 3 but < 5 and as it is an integer , the only possible value of radius = 4 units . c is the correct answer ."
Answer: c
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 4 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 2700 , c ) 18 , d ) 18000 , e ) 1.8
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 40 * 50 ) therefore , number of stones = ( 3600 * 1500 / 40 * 50 ) = 2700 answer : b"
Answer: b
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 r ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "c . 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 ] ) . r = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c"
Answer: c
Problem: the cost to park a car in a certain parking garage is $ 15.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 3.03
Rationale: total cost of parking for 9 hours = 15 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 15 + 7 * 1.75 = 27.25 thus the average parking price = 27.25 / 9 = 3.03 $ e is the correct answer .
Answer: e
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 2 ) / ( 10 - 4 ) = 2 / 6 = 1 / 3 so they should be mixed in the ratio 1 : 3 answer - e"
Answer: e
Problem: a trader sells 75 meters of cloth for rs . 4950 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 51 , b ) 88 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 4950 / 75 = rs . 66 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 66 - rs . 15 = rs . 51 answer : a"
Answer: a
Problem: 587 x 999 = ?
Options: a ) 586413 , b ) 587523 , c ) 614823 , d ) 615173 , e ) none of them
Rationale: "= 587 x 999 = 587 x ( 1000 - 1 ) = 587 x 1000 - 587 - 1 = 587000 - 587 = 586413 answer is a"
Answer: a
Problem: the contents of a certain box consist of 14 apples and 12 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 12 oranges , so to get to 6 oranges , we should remove 12 - 6 = 6 oranges . answer b"
Answer: b
Problem: he total marks obtained by a student in physics , chemistry and mathematics is 110 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 110 + p c + m = 110 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 110 / 2 = 55 . answer : a"
Answer: a
Problem: the diagonal of a square is 4 ? 2 cm . what will be the diameter of another square if their area is double that of the first square ?
Options: a ) 8 cm
b ) 9 cm
c ) 10 cm
d ) 11 cm
e ) 12 cm
Rationale: d 1 = 4 ? 2 = > area = 1 / 2 d 12 = 1 / 2 * ( 4 ? 2 ) 2 = 16 cm 2 area of new square = ( 2 * 16 ) cm 2 = 32 cm 2 therefore 1 / 2 * d 22 = 32 = > d 22 = 64 = > d 2 = 8 cm answer a
Answer: a
Problem: the sale price sarees listed for rs . 400 after successive discount is 10 % and 5 % is ?
Options: a ) 166 , b ) 178 , c ) 342 , d ) 199 , e ) 112
Rationale: "400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 answer : c"
Answer: c
Problem: a volume of 10936 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812
b ) 8231
c ) 2734
d ) 4222
e ) 4254
Rationale: a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10936 l can be kept in ( 10936 / 4 ) hemispheres ans . 2734 answer : c
Answer: c
Problem: the average age of 31 students in a group is 16 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 31 , b ) 36 , c ) 48 , d ) 45 , e ) 57
Rationale: "age of the teacher = ( 32 * 17 - 31 * 16 ) = 48 years . answer : c"
Answer: c
Problem: venki takes a trip and drives 5 hours from town x to town z at a rate of 80 miles per hour . on her way back , venki drives 45 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take venki to drive from town z to town y ?
Options: a ) 1.01 , b ) 4.44 , c ) 11.5 , d ) 1.75 , e ) 2.14
Rationale: distance from x to z = 5 hr * 80 mph = 400 miles hence distance from y to z = 1 / 2 * 400 = 200 time = 200 / 45 = 4.44 hrs imo : b
Answer: b
Problem: if a rectangle have length 16 cm and diagonal 20 cm . calculate its area .
Options: a ) 185
b ) 132
c ) 165
d ) 192
e ) 212
Rationale: breadth = √ 20 ^ 2 - 16 ^ 2 = √ 144 = 12 cm area = 16 * 12 = 192 sq . cm answer d
Answer: d
Problem: a qualified worker digs a well in 5 hours . he invites 2 apprentices , both capable of working 3 / 5 as fast and 2 trainees both working 1 / 5 as fast as he . if the 5 - person team digs the same well , how much time does the team need to finish the job ?
Options: a ) 1 : 42 , b ) 1 : 34 , c ) 1 : 44 , d ) 1 : 54 , e ) 2 : 14
Rationale: and answer is correct as you have calculated : 100 / 59 hrs that is 1.71 hrs - 1 hr and 42 minutes , so 1 : 42 , hence , a .
Answer: a
Problem: find the cost of fencing around a circular field of diameter 28 m at the rate of rs . 1.50 a meter ?
Options: a ) rs . 150
b ) rs . 132
c ) rs . 100
d ) rs . 125
e ) rs . 225
Rationale: 2 * 22 / 7 * 14 = 88 88 * 1 1 / 2 = rs . 132 answer : b
Answer: b
Problem: truck x is 14 miles ahead of truck y , which is traveling the same direction along the same route as truck x . if truck x is traveling at an average speed of 57 miles per hour and truck y is traveling at an average speed of 63 miles per hour , how long will it take truck y to overtake and drive 4 miles ahead of truck x ?
Options: a ) 5 hours , b ) 3 hours 20 minutes , c ) 3 hours , d ) 2 hours 45 minutes , e ) 8 hours
Rationale: "relative speed = 63 - 57 = 6 miles per hour dist required = 14 + 4 = 18 miles time taken to overtake = 18 / 6 = 3 hours . c is the answer ."
Answer: c
Problem: a and b ’ s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a ’ s salary ?
Options: a ) rs . 500 , b ) rs . 750 , c ) rs . 1250 , d ) rs . 1500 , e ) rs . 1520
Rationale: "explanation : ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 a = 1500 answer is d"
Answer: d
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 80 vehicles were involved in accidents . if 4 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 1600 , b ) 3200 , c ) 800 , d ) 400 , e ) 200
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 4,000 million rather than 4 billion . creating a proportion we have : 100 / 80 = 4,000 / x cross multiplying gives us : 100 x = 4,000 * 80 x = 40 * 80 = 3200 answer : b"
Answer: b
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 20 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 20 . . 4 x + 12 = 20 . . x = 2 . . ans = x + 4 = 2 + 4 = 6 answer b
Answer: b
Problem: log root ( 8 ) / log 8 is equal to
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: = > log ( 8 ) ^ 1 / 2 / log 8 = 1 / 2 log 8 / log 8 = 1 / 2 answer a
Answer: a
Problem: one - third less than 40 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 48
Rationale: "lots of ways to tackle this . 40 % of 180 = 72 1 / 3 of 72 = 24 so , 1 / 3 less than 72 is equal to 72 - 24 = 48 answer : e"
Answer: e
Problem: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 4,600 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,700 , d ) 2,550 , e ) 2,300
Rationale: "assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 4600 therefore x = 3400 / 4 = 850 price of 28 inch + 30 inch = 1050 + 1250 = 2300 option e"
Answer: e
Problem: a can finish a piece of work in 4 days . b can do it in 12 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "2 / 4 + ( 2 + x ) / 12 = 1 = > x = 4 days answer : a"
Answer: a
Problem: when positive integer x is divided by 9 , the quotient is y and the remainder is 4 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 1 . what is the value of 5 y – x ?
Options: a ) - 3 , b ) 3 , c ) - 4 , d ) 4 , e ) - 5
Rationale: "( 1 ) x = 9 y + 4 ( 2 ) 2 x = 14 y + 1 ( 2 ) - ( 1 ) : x = 5 y - 3 5 y - x = 3 the answer is b ."
Answer: b
Problem: a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "total subjects = 4 + 3 + 3 = 10 max subjects by 1 teacher = 2 so , min of teachers required = 10 / 2 = 5 answer : b"
Answer: b
Problem: two stations a and b are 245 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 1
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 245 45 x = 270 x = 6 . so , they meet at 1 p . m . answer : option e"
Answer: e
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 6 + 3 and * 6 + 6 , inclusive ?
Options: a ) one , b ) none , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 6 would be divisible by all numbers from 1 to 6 . = > * 6 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 6 is divisible by 3 ) in fact adding anyprimenumber between 1 to 6 to * 6 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 6 + 3 and * 6 + 11 then the answer would be 1 . for * 6 + 3 and * 6 + 13 , it is 2 and so on . . . b"
Answer: b
Problem: the tax on a commodity is diminished by 35 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 32 % , d ) 25.25 % , e ) 52.25 %
Rationale: "100 * 100 = 10000 65 * 115 = 7475 10000 - - - - - - - 2525 100 - - - - - - - ? = 25.25 % answer : d"
Answer: d
Problem: a university cafeteria offers 4 flavors of pizza - pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 32
Rationale: there are 4 flavors of pizza and each can be : 1 . without cheese and mushrooms ; 2 . with cheese ; 3 . with mushrooms ; 4 . with cheese and mushrooms . so , the total number of pizza varieties is 4 * 4 = 16 . answer : d .
Answer: d
Problem: find the least number of five digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) 1080 , b ) 10080 , c ) 10025 , d ) 11080 , e ) 12080
Rationale: "lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b"
Answer: b
Problem: a tank can be filled by pipe a in 5 hours and by pipe b in 8 hours , each pump working on its own . when the tank is full and a drainage hole is open , the water is drained in 20 hours . if initially the tank was empty and someone started the two pumps together but left the drainage hole open , how long does it take for the tank to be filled ?
Options: a ) 2.6 hours , b ) 3.6 hours , c ) 4.6 hours , d ) 5.6 hours , e ) none of these
Rationale: let ' s first find the rates of the pumps and the drainage hole pump a : 1 / 5 , pump b : 1 / 8 , drainage hole : 1 / 20 let t be the time for the pumps to fill the tank . the pumps , add water into the tank however the drainage hole drains water out of the tank , hence t ( 1 / 5 + 1 / 8 - 1 / 20 ) = 1 solve for t t = 3.6 hours answer b
Answer: b
Problem: a and b invests rs . 3000 and rs . 5000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 8 : 8 , b ) 9 : 8 , c ) 9 : 7 , d ) 9 : 5 , e ) 9 : 10
Rationale: ( 3 * 6 + 6 * 6 ) : ( 5 * 12 ) 54 : 60 = > 9 : 10 answer : e
Answer: e
Problem: express a speed of 720 kmph in meters per second ?
Options: a ) 120 mps , b ) 200 mps , c ) 181 mps , d ) 190 mps , e ) 125 mps
Rationale: "720 * 5 / 18 = 200 mps answer : b"
Answer: b
Problem: 84 / 12 / 0.8 = ?
Options: a ) 8.17 , b ) 7.14 , c ) 6.23 , d ) 4.35 , e ) 8.75
Rationale: "e 8.75 ? = 84 / ( 12 * 0.8 ) = 8.75"
Answer: e
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king ?
Options: a ) 2 / 13 , b ) 1 / 26 , c ) 5 / 26 , d ) 1 / 52 , e ) 17 / 52
Rationale: "p ( club ) = 1 / 4 p ( king ) = 1 / 13 p ( club then a king ) = 1 / 4 * 1 / 13 = 1 / 52 the answer is d ."
Answer: d
Problem: the length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencingthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 50 m
b ) 60 m
c ) 65 m
d ) 75 m
e ) 80 m
Rationale: let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b
Answer: b
Problem: define r * by the equation r * = π - r . then ( ( − π ) * ) * =
Options: a ) − 2 π , b ) - 1 , c ) − π , d ) 2 π , e ) 4 π
Rationale: for r * f ( f ( − π ) ) = f ( π − ( − π ) ) = f ( π + π ) = f ( 2 π ) = π − 2 π = − π = c
Answer: c
Problem: how many multiples of 5 are there between 5 to 100 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) none of these , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 . answer : b"
Answer: b
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase r in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase r = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c .
Answer: c
Problem: a person travels equal distances with speeds of 3 km / hr , 6 km / hr , 9 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 900 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 6 ) + ( x / 9 ) = 11 / 60 x = 0.3 total distance = 3 * 0.3 = 0.9 km = 900 meters correct option is c"
Answer: c
Problem: a bag of potatoes weighs 28 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 14 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 28 ÷ 2 = 14 . answer : b"
Answer: b
Problem: pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 4 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 4 , e ) 1
Rationale: "let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 4 = > 1 / x = 1 / 2 - 1 / 4 = 1 / 4 = > x = 4 . answer : d"
Answer: d
Problem: the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 15 + b + c = > a ? c = 15 + b ? b = 15 = > c is younger than a by 15 years answer : option e"
Answer: e
Problem: 306 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 34 , d ) 39 , e ) 43
Rationale: explanation : 306 ã · ? ã — 15 = 405 - 270 = 135 ( 306 ã — 15 ) / ? = 135 ? = ( 306 ã — 15 ) / 135 = 34 answer : option c
Answer: c
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 11 sec , c ) 77 sec , d ) 99 sec , e ) 67 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2500 / 9 * 18 / 500 = 10 sec answer : a"
Answer: a
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 540 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 12 / 5 , e ) 5 / 3
Rationale: "distance traveled by eddy = 540 km time taken by eddy = 3 hours average speed of eddy = 540 / 3 = 180 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 180 / 75 = 12 / 5 answer d"
Answer: d
Problem: in the first 10 overs of a cricket game , the run rate was only 3.4 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 4.25 , b ) 5 , c ) 6.2 , d ) 7 , e ) 7.5
Rationale: "required run rate = 282 - ( 3.4 x 10 ) = 248 248 / 40 = 6.2 c )"
Answer: c
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 32 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 11 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 32 kg joins the group , total weight of boys = 20 x + 32 so 20 x + 32 = 21 ( x + 1 ) = > x = 11 . answer : b"
Answer: b
Problem: a football team lost 5 yards and then gained 11 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 11 = 6 yards d"
Answer: d
Problem: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 160 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 160 + 160 ) / 20 = 16 sec . answer : c"
Answer: c
Problem: last year a worker saved 10 % of her annual salary . this year , she made 10 % more money than last year and she saved 12 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 126 % , b ) 128 % , c ) 130 % , d ) 132 % , e ) 134 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.1 x . this year , she saved 0.12 ( 1.1 x ) = 0.132 x 0.132 x / 0.1 x = 132 % the answer is d ."
Answer: d
Problem: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120 ?
Options: a ) 60 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 120 / 2 = 60 answer is a"
Answer: a
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 14 ?
Options: a ) 15 , b ) 12 , c ) 17 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 4 < = 14 or in - 3 i < = 10 so n can have - 7 to 13 = 12 true values . . . . b"
Answer: b