regisss/math_qa huggingface dataset:
Problem: a man speaks truth 3 out of 4 times . he throws a die and reports it to be a 6 . what is the probability of it being a 6 ?
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 4 , d ) 3 / 8 , e ) 3 / 6
Rationale: explanation : there are two cases 1 ) he is telling truth that the die reports 6 , its probability = 3 / 4 * 1 / 6 = 1 / 8 2 ) he is telling lie that the die reports 6 , its probability = 1 / 4 * 5 / 6 = 5 / 24 so required probability = ( 1 / 8 ) / ( 1 / 8 ) + ( 5 / 24 ) = ( 1 / 8 ) / ( 1 / 3 ) = 3 / 8 hencer ( d ) is the correct answer answer : d
Answer: d
Problem: a fair coin is tossed 11 times . what is the probability of getting more heads than tails in 11 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Problem: on a sum of money , simple interest for 2 years is rs 660 and compound interest is rs 696.30 , the rate of interest being the same in both cases .
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) none of these
Rationale: explanation : difference between c . i and s . i for 2 years = 36.30 s . i . for one year = 330 . s . i . on rs 330 for one year = 36.30 so r % = \ frac { 100 * 36.30 } { 330 * 1 } = 11 % answer : d
Answer: d
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 19404 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 10 % , e ) 12 %
Rationale: explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 19404 / - - 17640 / - = rs . 1764 / - rate of interest = ( 1764 / 17640 ) × ( 100 / 1 ) = > 10 % answer : option d
Answer: d
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 30 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 41
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 30 % discount then the original price of it was x * 0.7 = $ 14 - - > x = $ 20 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 20 + 21 = $ 41 . answer : e ."
Answer: e
Problem: a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 x = 20 . answer : c"
Answer: c
Problem: a is twice as good a work man as b and together they finish the work in 10 days . in how many days a alone can finish the work ?
Options: a ) 23 , b ) 15 , c ) 77 , d ) 92 , e ) 61
Rationale: "wc = 2 : 1 2 x + x = 1 / 10 = > x = 1 / 30 2 x = 1 / 15 a can do the work in 15 days . answer : b"
Answer: b
Problem: pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 1 / 2 hours ; pumps a and c , operating simultaneously , can fill the tank in 1 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 2 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6
Rationale: "a + b = 1 / 2 ; a + c = 1 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 3 a + b + c = 3 / 2 hrs e"
Answer: e
Problem: if y > 0 , ( 10 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to y / 2 + 3 y / 10 = 4 y / 5 = 80 % e"
Answer: e
Problem: the ages of two persons differ by 16 years . if 6 years ago , the elder one be 3 times as old as the younger one , find their present ages .
Options: a ) 10 years and 18 years , b ) 18 years and 26 years , c ) 20 years and 28 years , d ) 14 years and 30 years , e ) 16 years and 25 years
Rationale: "explanation : sol . let the age of the younger person be xx years then , age of the elder person = ( x + 16 ) ( x + 16 ) years â ˆ ´ â ˆ ´ 3 ( x â ˆ ’ 6 ) = ( x + 16 â ˆ ’ 6 ) 3 ( x - 6 ) = ( x + 16 - 6 ) â ‡ ” 3 x â ˆ ’ 18 = x + 10 â ‡ ” 3 x - 18 = x + 10 â ‡ ” 2 x = 28 â ‡ ” 2 x = 28 â ‡ ” x = 14 â ‡ ” x = 14 hence , their present age are 14 years and 30 years . answer is d"
Answer: d
Problem: let the number which when multiplied by 11 is increased by 300 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: solution let the number be x . then , 11 x - x = 300 ‹ = › 10 x = 300 x ‹ = › 30 . answer e
Answer: e
Problem: in a division , a student took 78 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 52 , e ) 38
Rationale: "x / 78 = 24 . x = 24 * 78 . so correct answer would be , ( 24 * 78 ) / 36 = 52 . answer : d"
Answer: d
Problem: an athlete takes 10 seconds to run 100 m . what is his avg . speed in miles per hour ?
Options: a ) 22.37 , b ) 26.66 , c ) 24.35 , d ) 36.0 , e ) 42.44
Rationale: his average speed is 10 m / s . which is 36 km / hr . but 36 km = 22.37 miles . the average speed of the athlete is 22.37 mph answer : a
Answer: a
Problem: chris age after 13 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 12
Rationale: "chris present age = x after 13 years = x + 13 5 years back = x - 5 x + 13 = 5 ( x - 5 ) x = 12 answer is e"
Answer: e
Problem: a pair of articles was bought for $ 50 at a discount of 50 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 12.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 50 % of x = 25 x = 25 * . 5 = $ 12.50 answer is b"
Answer: b
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 40 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 24 % , e ) 26 %
Rationale: the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.4 ( 6 ) = 2.4 gallons at the start , the amount of water is 0.6 ( 6 ) = 3.6 gallons after 6 hours , the amount of water is 3.6 - 0.5 ( 6 ) = 0.6 gallons the concentration of water is 0.6 / ( 2.4 + 0.6 ) = 2 / 10 = 20 % the answer is b .
Answer: b
Problem: in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.75 per kg , so that the mixture be worth rs 3.25 a kg ?
Options: a ) 7 / 3 , b ) 5 / 3 , c ) 10 / 3 , d ) 3 / 7 , e ) 11 / 5
Rationale: c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.75 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.75 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.50 ) / ( 0.15 ) = 10 / 3 c
Answer: c
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 12 p . m . and travels towards b at 100 km / hr . another starts from b at 1 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 5 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 12 p . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 10 + 5 = 5 p . m . answer is c"
Answer: c
Problem: in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 300 points , how many points is the third question worth ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 300 10 x = 120 x = 12 3 rd question = x + 8 = 12 + 8 = 20 answer d"
Answer: d
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 256 sq . feet , how many feet of fencing will be required ?
Options: a ) 45.6 , b ) 40 , c ) 68 , d ) 88 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 256 breadth = 12.8 feet area to be fenced = 2 b + l = 2 ( 12.8 ) + 20 = 45.6 feet answer : a"
Answer: a
Problem: there are 180 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?
Options: a ) 100 , b ) 104 , c ) 108 , d ) 112 , e ) 116
Rationale: "the number of nurses at the hospital is ( 3 / 5 ) * 180 = 108 . the answer is c ."
Answer: c
Problem: a reduction of 40 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 80 , b ) 72 , c ) 64 , d ) 56 , e ) 48
Rationale: "800 * ( 40 / 100 ) = 320 - - - - 5 ? - - - - 1 = > rs . 64 answer : c"
Answer: c
Problem: a tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.12 % , b ) 6.12 % , c ) 7.12 % , d ) 8.12 % , e ) 9.12 %
Rationale: "we start with 6,500 gallons of a solution that is 5 % sodium chloride by volume . this means that there are 0.05 x 6,500 = 325 gallons of sodium chloride . when 2,500 gallons of water evaporate we are left with 4,000 gallons of solution . from here we can determine what percent of the 4,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 325 / 4,000 ) x 100 = ? 0.0812 x 100 = ? = 8.12 % answer is d ."
Answer: d
Problem: the l . c . m . of 2 numbers is 72 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 48 , d ) 60 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 72 x = 12 the numbers are = 24 and 36 required sum = 24 + 36 = 60 answer is d"
Answer: d
Problem: if a farmer sells 15 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 25 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 55 , e ) 49
Rationale: "say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 15 ) * d + 4 = ( n + 25 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 25 d - 3 n = 75 4 n - 15 d = 60 = > n ~ 49 ans e it is !"
Answer: e
Problem: what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ?
Options: a ) 36
b ) 14
c ) 12
d ) 15
e ) 11
Rationale: the 4 inch side should be aligned to the 16 inch side ( 4 layer ) 6 inch side should be aligned to the 18 inch side . ( 3 layer ) and 10 inch side should be aligned to the 30 inch side . ( 3 layer ) maximum number of rectangles = 4 * 3 * 3 = 36 answer is a
Answer: a
Problem: after decreasing 80 % in the price of an article costs rs . 320 . find the actual cost of an article ?
Options: a ) 2777 , b ) 2987 , c ) 1200 , d ) 9977 , e ) 1600
Rationale: "cp * ( 20 / 100 ) = 320 cp = 16 * 100 = > cp = 1600 answer : e"
Answer: e
Problem: how many seconds will a 500 m long train take to cros a man walking with a speed of 3 kmph in the direction of the moving train if the speed of the train is 63 kmph
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: time = distance ( here length of the train ) / relative speed ( 63 - 3 ) thus time = 500 / 60 * 5 / 18 = 500 * 18 / 60 * 5 = 30 seconds answer : b
Answer: b
Problem: a batsman had a certain average of runs for 16 innings . in the 17 th innings , he made a score of 87 runs thereby increasing his average by 3 . what is his average after 17 innings ?
Options: a ) 39 , b ) 88 , c ) 266 , d ) 278 , e ) 221
Rationale: explanation : assume his initial average = xx his total runs after 16 innings = 16 xx after scoring 87 runs his average got increased by 3 to xx + 3 so his total runs after 17 innings = 17 × ( xx + 3 ) but it was given that the difference in the total scores after 16 innings and 17 innings = 87 therefore 17 × ( x + 3 ) − 16 x = 87 ⇒ x = 3617 × ( x + 3 ) − 16 x = 87 ⇒ x = 36 his new average = 36 + 3 = 39 answer : a
Answer: a
Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - .
Options: a ) 2 / 10 , b ) 4 / 13 , c ) 3 / 5 , d ) 9 / 7 , e ) 1 / 4
Rationale: "explanation : p ( s ᴜ k ) = p ( s ) + p ( k ) - p ( s ∩ k ) , where s denotes spade and k denotes king . p ( s ᴜ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : b"
Answer: b
Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 3 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24
Rationale: "probability of first member an english teacher = 3 / 10 probability of second member an english teacher = 2 / 10 probability of both being english teacher = 3 / 9 x 2 / 8 = 3 / 5 ( d )"
Answer: d
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 5 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 22.378 , b ) 37.78 , c ) 76.88 , d ) 27.888 , e ) 12.771
Rationale: explanation : capital = rs . x , then 4 / 5 x = 61.5 x = 76.88 answer : c ) rs . 76.88
Answer: c
Problem: thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 19 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 70 , c ) 100 , d ) 120 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 19 = 49 members have not passed the test , thus 0.7 * total = 49 - - > total = 70 . answer : b ."
Answer: b
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 3 ?
Options: a ) 10 , b ) 10 ^ 2 , c ) 10 ^ 5 , d ) 10 ^ 8 , e ) 10 ^ 10
Rationale: 0.1 = 10 ^ - 1 ( 0.01 ) ^ 3 = ( 10 ^ - 2 ) ^ 3 = 10 ^ - 6 10 ^ 5 * 10 ^ - 6 = 10 ^ - 1 the answer is c .
Answer: c
Problem: the current in a river is 5 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 93,75 miles , d ) 100 miles , e ) 112 miles
Rationale: "upstream speed = 20 - 5 = 15 mph downstream speed = 20 + 5 = 25 mph d / 15 + d / 25 = 10 hours solving for d we get d = 93,75 answer : c"
Answer: c
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 16 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the question is finding y such that ( 16 - y ) ! is a multiple of 16 . that means we need to have 2 ^ 4 in ( 16 - y ) ! 6 ! is the smallest factorial number with 2 ^ 4 as a factor . 16 - y = 6 y = 10 the answer is b ."
Answer: b
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 249 marks in the second test and failed by 66 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 280 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 66 marks in the second test . pass mark in the second test = 249 + 66 = 315 45 / 100 m = 315 pass mark in the first test = 40 / 100 m = 40 / 45 * 315 = 280 . answer : d"
Answer: d
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 14 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 14 = 406 hence , new average = 406 ⁄ 10 = 40.6 answer c"
Answer: c
Problem: in 1990 the budgets for projects q and v were $ 500,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1997
Rationale: "let the no of years it takes is x . 500 + 30 x = 780 - 10 x - - > 40 x = 280 and x = 7 . thus , it happens in 1997 . e ."
Answer: e
Problem: how many numbers between 100 and 798 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 17 , 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 798 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 798 : 798 / 42 = 19 hence , 42 * 19 = 798 is the last number divisible by 42 within 798 hence , total numbers divisible by 2 , 3 , 7 together are ( 19 â € “ 2 ) = 17 answer : d
Answer: d
Problem: a car traveled 340 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 504 , b ) 416 , c ) 321 , d ) 220 , e ) 170
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 340 miles will be covered in 340 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 340 / h = > 336 / c = 340 / ( c + 6 ) = > 336 c + 336 * 6 = 340 c = > c = 336 * 6 / 4 = 504 answer a ."
Answer: a
Problem: 1850 men have provisions for 15 days . if 150 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 13.9 , d ) 13.5 , e ) 12.1
Rationale: "1850 * 15 = 2000 * x x = 13.9 answer : c"
Answer: c
Problem: the product of the squares of two positive integers is 100 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : c - 2 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 100 [ square root both sides ] xy = 10 10 = 1 x 10 , 10 x 1 , 2 x 5 , 5 x 2 cancel the repeats this leaves us with exactly 2 options . hence , c"
Answer: c
Problem: a number increased by 30 % gives 780 . the number is
Options: a ) 250 , b ) 400 , c ) 450 , d ) 600 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 780 ( 130 × 6 = 780 ) 100 % - - - - - - - > 600 ( 100 × 6 = 600 ) d )"
Answer: d
Problem: if a > x > y > z on the number line , y is halfway between x and z , and x is halfway between w and z , then ( y - x ) / ( y - a ) =
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 1
Rationale: let y - z = t - - - > since y is halfway between x and z and x > y we have x - y = t . moreover x - z = ( x - y ) + ( y - z ) = 2 t . similarly since x is halfway between w and z , we have a - x = 2 t . so y - x = - t , y - a = - 3 t . - - - > ( y - x ) / ( y - a ) = 1 / 3 . the answer is ( b ) .
Answer: b
Problem: 3 friends james , david and charlie divide $ 1230 amongs them in such a way that if $ 5 , $ 10 and $ 15 are removed from the sums that james , david and charlie received respectively , then the share of the sums that they got will be in the ratio of 9 : 10 : 11 . how much did charlie receive ?
Options: a ) $ 600 , b ) $ 575 , c ) $ 550 , d ) $ 580 , e ) $ 615
Rationale: a + b + c = 1230 given ratio 9 : 10 : 11 let us say the shares of a , b , c deducting 5 , 1015 be a , b , c a + b + c = 1230 - 30 = 1200 = 30 k c share = ( 1200 x 30 ) / 60 = 600 c = charlie share = 600 + 15 = 615 option e
Answer: e
Problem: if 2 + 3 = 31 ; 3 + 5 = 134 ; 5 + 7 = 368 then 7 + 11 = ?
Options: a ) 1250 , b ) 1360 , c ) 1270 , d ) 1380 , e ) 1290
Rationale: "2 ^ 2 + 3 ^ 3 = 4 + 27 = 31 3 ^ 2 + 5 ^ 3 = 9 + 125 = 134 5 ^ 2 + 7 ^ 3 = 25 + 343 = 368 and 7 ^ 2 + 11 ^ 3 = 49 + 1331 = 1380 answer : d"
Answer: d
Problem: a rectangular grass field is 70 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1300 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927
Rationale: "area = ( l + b + 2 d ) 2 d = ( 70 + 55 + 2.5 * 2 ) 2 * 2.5 = > 650 650 * 2 = rs . 1300 answer : b"
Answer: b
Problem: calculate the area of a triangle , if the sides of are 39 cm , 36 cm and 15 cm , what is its area ?
Options: a ) 570 cm 2 , b ) 370 cm 2 , c ) 170 cm 2 , d ) 271 cm 2 , e ) 270 cm 2
Rationale: "the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e"
Answer: e
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 20 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 6 , e ) 16
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 20 hours . he would have saved 20 â € “ 4 = 16 hours . answer : e"
Answer: e
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 144 min , b ) 250 min , c ) 196 min , d ) 100 min , e ) 112 min
Rationale: "let the slower pipe alone fill the tank in x minutes then , faster pipe will fill it in x / 3 minutes 1 / x + 3 / x = 1 / 36 4 / x = 1 / 36 x = 144 min answer is a"
Answer: a
Problem: a man can do a job in 15 days . his father takes 20 days and his son finishes it in 15 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 5.5 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 15 ) = 11 / 60 so , all three together will complete the work in 300 / 47 = 5.5 days . answer : c"
Answer: c
Problem: how long does a train 250 meters long running at the rate of 72 km / hr take to cross a bridge 150 meters in length ?
Options: a ) 10 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 35 sec
Rationale: "distance = length of train + length of bridge = 250 + 150 = 400 speed = 72 km / hr = 72 * 5 / 18 = 20 m / s required time = 400 / 20 = 20 seconds answer is b"
Answer: b
Problem: the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 10 cents less than the price of commodity y ?
Options: a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) 2012
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 10 cents less than commodity y . $ 2.00 / 25 cents = 8 years the answer is 2001 + 8 years = 2009 . the answer is b ."
Answer: b
Problem: if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 , then find the total number of items the wholesaler distributes ?
Options: a ) 567 , b ) 167 , c ) 267 , d ) 467 , e ) 667
Rationale: here , a : b : c : d = 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 1 ) l . c . m of 12 : 13 : 15 : 2 is 780 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 12 ) x 780 = 65 b = ( 1 / 13 ) x 780 = 60 c = ( 1 / 15 ) x 780 = 52 d = ( 1 / 2 ) x 780 = 390 3 ) total number of toys = ( 65 x + 60 x + 52 x + 390 x ) = 567 x minimum number of pens ( x ) = 1 therefore , total number of items = 567 items . correct option : a
Answer: a
Problem: john makes $ 50 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 20 %
Rationale: "increase = ( 10 / 50 ) * 100 = ( 1 / 5 ) * 100 = 20 % . e"
Answer: e
Problem: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 83 . , c ) 81 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 90 % of 250 = 225 are boys who play soccer . girls who play soccer = 25 . total girls who do not play soccer = 108 - 25 = 83 . correct option : b"
Answer: b
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 14 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 34.31 , c ) $ 24.88 , d ) $ 67.54 , e ) $ 65.23
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 14 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 14 solve for x x = $ 24.88 correct answer c"
Answer: c
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1690 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 190 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1650 x = 60 required perimeter = 2 ( 60 + 70 ) = 260 e"
Answer: e
Problem: the average weight of 4 person ' s increases by 1.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?
Options: a ) 101 kg , b ) 103.4 kg , c ) 105 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 4 x 1.5 ) kg = 6 kg . weight of new person = ( 95 + 6 ) kg = 101 kg . answer : option a"
Answer: a
Problem: each of the three people individually can complete a certain job in 3 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 4 / 15 , b ) 7 / 30 , c ) 11 / 30 , d ) 7 / 18 , e ) 5 / 18
Rationale: "the two slowest people work at rates of 1 / 5 and 1 / 6 of the job per hour . the sum of these rates is 1 / 5 + 1 / 6 = 11 / 30 of the job per hour . the answer is c ."
Answer: c
Problem: the average of 5 consecutive odd numbers a , b , c , d and e is 33 . what percent of a is d ?
Options: a ) 86.8 , b ) 88.6 , c ) 89.2 , d ) 90.1 , e ) 92.2
Rationale: explanation : in such a case the middle number ( c ) is the average ∴ c = 33 and a = 31 and d = 35 required percentage = 31 / 35 x 100 = 88.6 answer : option b
Answer: b
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 30 cm ?
Options: a ) 827 cm 2 , b ) 570 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 176 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 30 ) = 570 cm 2 answer : b"
Answer: b
Problem: daniel went to a shop and bought things worth rs . 25 , out of which 60 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) a ) 14.4 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.5 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 60 paise = rs . 60 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 60 / 100 − x ) 6 / 100 = 60 / 100 ⇒ 6 ( 25 − 0.6 − x ) = 60 ⇒ ( 25 − 0.6 − x ) = 10 ⇒ x = 25 − 0.6 − 10 = 14.4 a"
Answer: a
Problem: the volumes of two cubes are in the ratio 27 : 125 , what shall be the ratio of their surface areas ?
Options: a ) 6 : 25
b ) 3 : 5
c ) 9 : 25
d ) 16 : 25
e ) 19 : 25
Rationale: a 13 : a 23 = 27 : 125 a 1 : a 2 = 3 : 5 6 a 12 : 6 a 22 a 12 : a 22 = 9 : 25 answer : c
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 15 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 187.5
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 15 so , 134.08 = 134 + 15 / j so , j = 187.5 ans e"
Answer: e
Problem: bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .
Options: a ) 7 / 15 , b ) 2 / 8 , c ) 7 / 11 , d ) 13 / 5 , e ) 87
Rationale: explanation : drawing two balls of same color from seven green balls can be done in â  · c â ‚ ‚ ways . similarly from eight white balls two can be drawn in â  ¸ c â ‚ ‚ ways . p = â  · c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ + â  ¸ c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ = 7 / 15 a
Answer: a
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 75 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 ) 15 sec , b ) 16 sec , c ) 14 sec , d ) 67 sec , e ) 13 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 75 d = 75 * 100 / 18 = 1250 / 3 rs = 60 + 50 = 100 * 5 / 18 t = 1250 / 3 * 18 / 500 = 15 sec answer : a"
Answer: a
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,900 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2100 , c ) 3400 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 11900 = > 7 x = 11900 = > x = 1700 total number of motorcycles = 2 x = 2 * 1700 = 3400 answer c"
Answer: c
Problem: how many figures are required to number the pages the pages of a book containing 223 pages ?
Options: a ) 372 , b ) 661 , c ) 561 , d ) 467 , e ) 761
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 223 = 124 * 3 = 372 - - - - - - - - - - - 561 answer : c"
Answer: c
Problem: if 40 % of a certain number is 160 , then what is 90 % of that number ?
Options: a ) 270 , b ) 380 , c ) 260 , d ) 360 , e ) 290
Rationale: "explanation : 40 % = 40 * 4 = 160 90 % = 90 * 4 = 360 answer : option d"
Answer: d
Problem: if x / y = 8 / 7 , then ( 7 x + 6 y ) / ( 7 x â € “ 6 y ) = ?
Options: a ) 11 , b ) 8 , c ) 9 , d ) 7 , e ) 6
Rationale: "answer dividing numerator as well as denominator by y , we get given exp . = ( 7 x + 6 y ) / ( 7 x â € “ 6 y ) = ( 7 x / y + 6 ) / ( 7 x / y â € “ 6 ) since x / y = 8 / 7 this implies that = [ ( 7 * 8 ) / 7 + 6 ] / [ ( 7 * 8 ) / 7 - 6 ) ] = ( 8 + 6 ) / ( 8 - 6 ) = 7 option : d"
Answer: d
Problem: subtracting 30 from a number , the remainder is one fourth of the number . find the number ?
Options: a ) 29 , b ) 88 , c ) 40 , d ) 28 , e ) 27
Rationale: explanation : 3 / 4 x = 30 = > x = 40 answer : c
Answer: c
Problem: the sum of three consecutive multiples of 3 is 108 . what is the largest number ?
Options: a ) 36 , b ) 39 , c ) 33 , d ) 30 , e ) 42
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 108 9 x = 99 x = 11 largest number = 3 x + 6 = 39 answer : b"
Answer: b
Problem: the sum of four consecutive even integers is 1284 . the greatest of them is :
Options: a ) 324 , b ) 342 , c ) 364 , d ) 382 , e ) none
Rationale: "sol . let the four integers be x , x + 2 , x + 4 and x + 6 then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 1284 ⇔ 4 x = 1272 ⇔ x = 318 ∴ greatest integer = x + 6 = 324 . answer a"
Answer: a
Problem: the area of a square field is 24200 sq m . how long will a lady take to cross the field diagonally at the rate of 6.6 km / hr ?
Options: a ) 3 minutes , b ) 0.04 hours , c ) 2 minutes , d ) 2.4 minutes , e ) 2 minutes 40 seconds
Rationale: "explanatory answer step 1 : compute the length of the diagonal of the square let ' a ' meters be the length of a side of the square field . therefore , its area = a 2 square meters . - - - ( 1 ) the length of the diagonal ' d ' of a square whose side is ' a ' meters = √ 2 a - - - ( 2 ) from ( 1 ) and ( 2 ) , we can deduce that the square of the diagonal = d 2 = 2 a 2 = 2 ( area of the square ) or d = √ 2 * area meters . d = √ 2 ∗ 24200 = 48400 = 220 m . step 2 : compute the time taken to cross the field the time taken to cross a distance of 220 meters while traveling at 6.6 kmph = 220 m / 6.6 kmph convert unit of speed from kmph to m / min 1 km = 1000 meters and 1 hour = 60 minutes . so , 6.6 kmph = 6.6 ∗ 1000 / 60 m / min = 110 m / min ∴ time taken = 220 / 110 = 2 minutes choice c"
Answer: c
Problem: anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 26 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 12 + 6 + 8 = 26 . answer is b ."
Answer: b
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 90 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 4 sec , d ) 2.8 , e ) 2.1
Rationale: "speed = 90 * 5 / 18 = 25 m / sec time taken = 100 / 25 = 4 sec . answer : c"
Answer: c
Problem: if the number is divided by 3 , it reduced by 34 . the number is
Options: a ) 51 , b ) 50 , c ) 45 , d ) 40 , e ) 36
Rationale: explanation : let the number be x . then , x - ( x / 3 ) = 34 = > 2 x / 3 = 34 = > x = 51 answer : option a
Answer: a
Problem: if a train runs at 40 kmph , it reach its destination late by 11 minutes but if it runs at 50 kmph it is late by 5 minutes only . the correct time for a train to complete its journey is ? let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min
Options: a ) 19 min , b ) 19 hrs , c ) 52 min , d ) 126 min , e ) 52 min
Rationale: let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )
Answer: a
Problem: how many cubes of 8 cm edge can be cut out of a cube of 16 cm edge
Options: a ) 36 , b ) 2 , c ) 8 , d ) 48 , e ) none of these
Rationale: "explanation : number of cubes = ( 16 x 16 x 16 ) / ( 8 x 8 x 8 ) = 8 answer : c"
Answer: c
Problem: share rs . 5400 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 1800 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400
Rationale: "amount received by sanjay . 4 / 12 x 5400 = 1800 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1800 . a"
Answer: a
Problem: a room is a square of side 50 feet . a second room is of area 100 square yards . a third room is of area 200 square feet . which of these can seat maximum people ? ( hint : 1 yard = 3 feet )
Options: a ) 200 sq feet , b ) 300 sq feet , c ) 400 sq feet , d ) 500 sq feet , e ) 600 sq feet
Rationale: first room because area 50 * 50 = 2500 sq feet second room area 100 sq yard in feet 300 sq feet third room area 200 sq feet answer : a
Answer: a
Problem: alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ?
Options: a ) 5 : 4 , b ) 4 : 3 , c ) 18 : 11 , d ) 3 : 2 , e ) 18 : 13
Rationale: alex invests rs . 7000 for 18 months , but brian invests rs . 7000 for the first 8 months and then withdraws rs . 3500 . so , the investment of brian for remaining 10 months is rs . 3500 only . alex : brian 7000 * 18 : ( 7000 * 8 ) + ( 3500 * 10 ) 126000 : 91000 alex : brian = 18 : 13 answer : e
Answer: e
Problem: of the people who responded to a market survey , 240 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 6 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 280 , d ) 360 , e ) 480
Rationale: "ratio = 6 : 1 = > 6 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 240 = > 6 x = 240 = > x = 40 hence total no . of respondents = 240 + 40 = 280 hence c is the answer ."
Answer: c
Problem: a block of wood has dimensions 10 cm x 10 cm x 40 cm . the block is painted red and then cut evenly at the 20 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "the area of each half is 100 + 4 ( 200 ) + 100 = 1000 the area that is not painted is 100 . the fraction that is not painted is 100 / 1000 = 1 / 10 = 10 % the answer is b ."
Answer: b
Problem: two trains 119 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.17 , c ) 7.2 , d ) 7.15 , e ) 7.05
Rationale: "t = ( 119 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.05 answer : e"
Answer: e
Problem: if an integer e is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that e ( e + 1 ) ( e + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: for e total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d
Answer: d
Problem: if 20 men can build a wall 66 metres long in 10 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 227.04 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 10 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 10 * 20 ) = 227.04 mtrs answer : a"
Answer: a
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 9 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 9 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 9 hence x = 11 . answer is b"
Answer: b
Problem: by travelling at 60 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 30 kmph , b ) 28 kmph , c ) 26 kmph , d ) 24 kmph , e ) 22 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 60 * 3 x = 180 x km he covered 2 / 3 * 180 x = 120 x km in 1 / 3 * 3 x = x hours so , the remaining 60 x km , he has to cover in 2 x hours . required speed = 60 x / 2 x = 30 kmph . answer : a"
Answer: a
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2430 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 8100 , d ) 2888 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2430 100 % - - - - - - - - - ? = > 8100 answer : c"
Answer: c
Problem: if the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 52 , c ) 59 , d ) 68 , e ) 73
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 65 = 325 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 325 i . e . 5 a = 315 i . e . a = 63 i . e . largest e = 63 + 10 = 73 answer : option e"
Answer: e
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 20 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 22 , c ) 25 , d ) 27 , e ) 40
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 20 work done by p , q and r in 1 day = 1 / 10 + 1 / 20 = 3 / 20 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 3 / 20 = > work done by p in 1 day = 3 / 40 = > work done by q and r in 1 day = 3 / 40 hence work done by q in 1 day = 3 / 40 â € “ 1 / 20 = 1 / 40 so q alone can do the work in 40 days answer is e ."
Answer: e
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6500 ?
Options: a ) 4966 , b ) 2477 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4966 answer : a
Answer: a
Problem: find the area of a parallelogram with base 15 cm and height 40 cm ?
Options: a ) 200 cm 2 , b ) 100 cm 2 , c ) 42 cm 2 , d ) 600 cm 2 , e ) 230 cm 2
Rationale: "area of a parallelogram = base * height = 15 * 40 = 600 cm 2 answer : d"
Answer: d
Problem: the number 70 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 70 : 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 . now , 70 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 70 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 60 equals to 9 + 25 + 36 = 3 ^ 2 + 5 ^ 2 + 6 ^ 2 = 70 - - > 3 + 5 + 6 = 14 . answer : d ."
Answer: d
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 25 to produce 100 units ?
Options: a ) 5 , b ) 9 , c ) 6 , d ) 10 , e ) 2
Rationale: "5 machines would produce 100 units in 50 hours . increasing the amount of machines by 5 would mean dividing 50 hours by 5 . 50 / 5 = 10 answer : d"
Answer: d
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 1034355 , b ) 1035677 , c ) 1045778 , d ) 1067675 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1083875 e"
Answer: e
Problem: a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?
Options: a ) $ 450 , b ) $ 500 , c ) $ 750 , d ) $ 800 , e ) $ 840
Rationale: let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c
Answer: c
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 507 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 13 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 507 3 b 2 = 507 b 2 = 169 b = 13 m . answer : option c"
Answer: c
Problem: the number 341 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 21 , d ) 30 , e ) 39
Rationale: 5 ^ 3 + 6 ^ 3 = 341 number is 5 * 6 = 30 d
Answer: d
Problem: what is the sum of the multiples of 7 from 77 to 91 , inclusive ?
Options: a ) 260 , b ) 452 , c ) 352 , d ) 260 , e ) 252
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 91 / 7 ) - ( 77 / 7 ) + 1 = 3 multiply these together so what we show average * total numbers = sum ( 91 + 77 ) / 2 * 3 = sum 84 * 3 = 252 e"
Answer: e
Problem: 45 x ? = 25 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) none
Rationale: "answer let 45 x a = ( 25 x 900 ) / 100 ∴ a = ( 25 x 9 ) / 45 = 5 correct option : c"
Answer: c
Problem: if there are thrice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ?
Options: a ) 3 ⁄ 20 , b ) 11 ⁄ 60 , c ) 9 ⁄ 40 , d ) 1 ⁄ 10 , e ) 11 ⁄ 20
Rationale: consider a group of 100 men and 300 women , a total of 400 people . 30 % of them , which is 120 , form a group of people who do n ' t own a car . half of them are men , and the other half are women , more precisely 60 . it means that there are 100 - 60 = 40 men who own a car , and this represents 40 / 400 = 1 / 10 of the total . answer d
Answer: d