regisss/math_qa huggingface dataset:
Problem: in township k , 1 / 4 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: "1 / 4 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 4 ) = 1 / 12 therefore only video cassette recorder = 1 / 10 - 1 / 12 = 1 / 60 total = 1 / 4 + 1 / 60 + neither cable tv nor videocassette recorders 1 = 4 / 15 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 4 / 15 = 11 / 15 hence b ."
Answer: b
Problem: if both 5 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 80 , b ) 120 , c ) 150 , d ) 225 , e ) 300
Rationale: "the number a must include at least 3 ^ 2 * 5 ^ 2 = 225 the answer is d ."
Answer: d
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe oundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 7889890 m , b ) 2334356 m , c ) 1536001 m , d ) 1232431 m , e ) 2435467 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Problem: what will be the result of 12 ^ 4 + 3 + 2 ^ 9 + 3 - 8 / 2 ?
Options: a ) 58 , b ) 14 , c ) 145 , d ) 69 , e ) 74
Rationale: "the multiplication ( e . g . 12 ^ 4 ) and division ( e . g . 8 / 2 ) is done first and then the sum ( e . g . 48 + 3 ) and subtraction ( e . g . 4 - 4 ) , and the answer is 69 , option d ."
Answer: d
Problem: in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 21 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42
Rationale: toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and jim will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d
Answer: d
Problem: how many times will the digit 6 be written when listing the integers from 1 to 1000 ?
Options: a ) 150 , b ) 280 , c ) 310 , d ) 420 , e ) 300
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 6 ) 3000 / 10 = 300 times . answer : e ."
Answer: e
Problem: an assembly line produces 20 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "the time to produce the first 60 cogs is 60 / 20 = 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 4 hours = 30 cogs per hour . the answer is b ."
Answer: b
Problem: what is 120 % of 13 / 24 of 960 ?
Options: a ) 420 , b ) 484 , c ) 526 , d ) 578 , e ) 624
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 40 = 624 the answer is e ."
Answer: e
Problem: 3 candidates in an election and received 1136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 56 % , c ) 57 % , d ) 70 % , e ) 72 %
Rationale: "total number of votes polled = ( 1136 + 7636 + 11628 ) = 20400 so , required percentage = 11628 / 20400 * 100 = 57 % c"
Answer: c
Problem: the average of first 80 non - zero positive numbers is :
Options: a ) 22.25 , b ) 31.25 , c ) 35 , d ) 40.5 , e ) none of these
Rationale: "explanation : sum of first n natural numbers = n ( n + 1 ) / 2 so , average of first n natural numbers = n ( n + 1 ) / 2 n = ( n + 1 ) / 2 required average = ( 80 + 1 ) / 2 = 81 / 2 = 40.5 . answer : d"
Answer: d
Problem: yesterday it took robert 4 hours to drive from city a to city b . today it took robert 3.5 hours to drive back from city в to city a along the same route . if he had saved 15 minutes in both trips , the speed for the round trip would be 60 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 210 , e ) 300
Rationale: "2 d / 60 = 7 ( because time = 4 + 3.5 - 0.5 hrs ) = > d = 210 answer - d"
Answer: d
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 153 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 147 , b ) s . 248 , c ) s . 244 , d ) s . 229 , e ) s . 216
Rationale: given that sp = rs . 153 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 153 ) / 85 = rs . 180 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 180 * 120 ) / 100 = rs . 216 answer : e
Answer: e
Problem: the sum of two numbers is 45 . sum of their quotient and reciprocal is 2.05 , find the product of the numbers .
Options: a ) 339 , b ) 500 , c ) 288 , d ) 277 , e ) 112
Rationale: sol : let a , b be the numbers . a + b = 45 ab + baab + ba = 2.05 ⇒ a 2 + b 2 ab ⇒ a 2 + b 2 ab = 2.05 ⇒ ( a + b ) 2 − 2 abab = 2.05 ⇒ ( a + b ) 2 − 2 abab = 2.05 ⇒ ( a + b ) 2 ⇒ ( a + b ) 2 = 2.05 ab + 2 ab = 4.05 ab ⇒ ⇒ ab = 4524 . 054524.05 = 500 answer : b
Answer: b
Problem: in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what q percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people q = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Problem: company p had 15 percent more employees in december than it had in january . if company p had 500 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 435 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 500 j = 500 / 1.15 j = 50,000 / 115 = 435 thus b is the correct answer ."
Answer: b
Problem: at a certain fruit stand , the price of each apple is 50 cents and the price of each orange is 60 cents . mary selects a total of 10 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 56 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 52 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let number of apples = a number of oranges = b a + b = 10 - - - 1 . 56 = ( . 5 a + . 6 b ) / 10 = > 56 = 5 a + 6 b - - - - 2 solving 1 and 2 , we get a = 4 b = 6 let the number of oranges put back = c 52 * ( 10 - c ) = 50 * 4 + 60 ( 6 - c ) = > c = 5 answer e"
Answer: e
Problem: mary can do a piece of work in 28 days . rosy is 40 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 22 , b ) 24 , c ) 20 , d ) 25 , e ) 27
Rationale: "ratio of times taken by mary and rosy = 140 : 100 = 14 : 10 suppose rosy takes x days to do the work . 14 : 10 : : 28 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : c"
Answer: c
Problem: company x provides bottled water to its employees in 5 liter bottles , $ 5 each . at least how many 5 l bottles must company x buy monthly , so that new contract with $ 40 fixed monthly rate and $ 2 for 20 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 4 , b ) 9 , c ) 12 , d ) 20 , e ) 25
Rationale: let the no . of 5 liter bottles be x , so the no . of 20 l bottles will be x / 4 ( to equate the vol . ) since the total cost will be equal , 5 x = 40 + 2 * x / 4 so x = 8.88 or 9 . answer is ( b ) .
Answer: b
Problem: a reduction of 15 % 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 ) 12 , b ) 16 , c ) 24 , d ) 28 , e ) 32
Rationale: "800 * ( 15 / 100 ) = 120 - - - - 5 ? - - - - 1 = > rs . 24 answer : c"
Answer: c
Problem: a certain number when divided by 39 leaves a remainder 18 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: "explanation : 39 + 18 = 57 / 13 = 5 ( remainder ) answer : e"
Answer: e
Problem: the membership of a committee consists of 4 english teachers , 2 mathematics teachers , and 2 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 ) 3 / 28
Rationale: "probability of first member an english teacher = 3 / 8 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 8 x 2 / 7 = 3 / 28 ( e )"
Answer: e
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 215 m long ?
Options: a ) 40 , b ) 46 , c ) 88 , d ) 77 , e ) 21
Rationale: ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 215 = 575 m required time = 575 * 2 / 25 = 46 sec answer : b"
Answer: b
Problem: a and b complete a work in 5 days . a alone can do it in 10 days . if both together can do the work in how many days ?
Options: a ) 3.33 days , b ) 3.99 days , c ) 2.99 days , d ) 2.98 days , e ) 2.44 days
Rationale: "1 / 5 + 1 / 10 = 3 / 10 10 / 3 = 3.33 days answer : a"
Answer: a
Problem: when tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tom is what percent lesser than the quantifying chopped by tammy ? .
Options: a ) 44 % , b ) 100 % , c ) 105 % , d ) 225 % , e ) 125 %
Rationale: "tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tom chops 125 % less than tammy , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : e"
Answer: e
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 35 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 14 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 35 = 14 hours answer c"
Answer: c
Problem: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 9 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 12 , b ) 25 , c ) 60 , d ) 30 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 9 days whole work will be done by a in 9 * 4 / 3 = 12 days answer is a"
Answer: a
Problem: two trains of length 90 m and 95 m are 250 m apart . they start moving towards each other on parallel tracks , at speeds 64 kmph and 92 kmph . after how much time will the trains meet ?
Options: a ) 53 / 10 , b ) 55 / 10 , c ) 56 / 10 , d ) 57 / 10 , e ) 58 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 64 + 92 ) * 5 / 18 = 43.3 mps . the time required = d / s = 250 / 43.3 = 58 / 10 sec . answer : e"
Answer: e
Problem: what is the greatest 6 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 4 , 5 , 6 , 7 , and 8 respectively ?
Options: a ) 456780 , b ) 678910 , c ) 997479 , d ) 997918 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so d is the only possible answer .
Answer: d
Problem: in one alloy there is 12 % chromium while in another alloy it is 10 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 10.6 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.12 * 15 + 0.10 * 35 = 5.3 kg , so the percentage is 5.3 / 50 * 100 = 10.6 % . answer : e ."
Answer: e
Problem: a baseball card decreased in value 10 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 19 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.9 = 90 after second year price = 90 * 0.9 = 81 final decrease = [ ( 100 - 81 ) / 100 ] * 100 = 19 % correct answer - a"
Answer: a
Problem: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 80 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?
Options: a ) 2 , b ) 3 , c ) 9 , d ) 15 , e ) 30
Rationale: "withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 80 customers per day . 30 / 10 = 3 days . choice ( a ) . withthe formula , we can set up the following : 90 = ( 80 x + 120 ) / ( x + 1 ) 90 x + 90 = 80 x + 120 10 x = 30 x = 3 answer choice ( b )"
Answer: b
Problem: bhanu spends 30 % of his income on petrol on scooter 10 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 70 , c ) 128 , d ) 797 , e ) 120
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 10 % ( 700 ) = rs . 70 answer : b"
Answer: b
Problem: how many 4 digit numbers are there , if it is known that the first digit is odd , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 1 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 384 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 1 , 3 , 5 , 7 , 9 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 5 * 5 * 4 * 4 = 400 numbers with one 1 - s , 1 x 1 x 1 * 1 * 4 * 4 = 16 . thus there are 400 - 16 = 384 such numbers . answer : c ."
Answer: c
Problem: if the length of the sides of two cubes are in the ratio 5 : 1 , what is the ratio of their total surface area ?
Options: a ) 5 : 1 , b ) 10 : 1 , c ) 25 : 1 , d ) 50 : 1 , e ) 150 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 5 x ) ^ 2 = 150 x ^ 2 . the ratio of surface areas is 25 : 1 . the answer is c ."
Answer: c
Problem: the average monthly salary of 24 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 400 . what is the manager ' s monthly salary ?
Options: a ) rs . 11,300 , b ) rs . 11,500 , c ) rs . 11,302 , d ) rs . 11,301 , e ) rs . 11,303
Rationale: explanation : manager ' s monthly salary = rs . ( 1900 x 25 - 1500 x 24 ) = rs . 11,500 answer : b
Answer: b
Problem: the triplicate ratio of 1 : 4 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 64 , e ) 1 : 2
Rationale: "1 ^ 3 : 4 ^ 3 = 1 : 64 answer : d"
Answer: d
Problem: in an election , candidate a got 70 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 347000 , d ) 333200 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 70 % therefore , the number of valid votes polled in favour of candidate a = 70 % of 476000 = 70 / 100 × 476000 = 33320000 / 100 = 333200 d )"
Answer: d
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 400 m ?
Options: a ) 122.9 m , b ) 127.5 m . , c ) 122.2 m , d ) 85 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 400 m , the number of meters by which a beats c = ( 400 * 212.5 ) / 1000 = 85 m . answer : d"
Answer: d
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 3 days . b can do the work alone in ?
Options: a ) 18 , b ) 12 , c ) 11 , d ) 19 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 3 6 / x = 1 / 3 = > x = 18 so , b takes 9 hours to finish the work . answer : a"
Answer: a
Problem: paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , quentin ' s new income would be what fraction of paul ' s new income ?
Options: a ) 11 / 12 , b ) 13 / 17 , c ) 22 / 30 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get p = 12 and q 8.8 so 8.8 / 12 = = 2.2 / 3 ans : c"
Answer: c
Problem: if the length of the side of a square is doubled , what is the ratio of the areas of the original square to the area of the new square ?
Options: a ) 1 : 4
b ) 2 : 4
c ) 3 : 4
d ) 4 : 4
e ) 5 : 4
Rationale: solution if x be the side of the original square , then its area is equal to x 2 if x is doubled to 2 x , then the new area is equal to ( 2 x ) 2 = 4 x 2 the ratio of the areas of the original square to the area of the new square x 2 / ( 4 x 2 ) = 1 / 4 or 1 : 4 answer is a
Answer: a
Problem: in country x a returning tourist may import goods with a total value of $ 500 or less tax free , but must pay an 8 percent tax on the portion of the total value in excess of $ 500 . what tax must be paid by a returning tourist who imports goods with a total value of $ 730 ?
Options: a ) $ 58.40 , b ) $ 40 . 00 , c ) $ 24.60 , d ) $ 18.40 , e ) $ 16.00
Rationale: the tourist must pay tax on $ 730 - $ 500 = $ 230 . thus the amount to be paid is 0.08 * $ 230 = $ 18.40 . answer : d .
Answer: d
Problem: total 45 cows 15 cow gives each 2 liter milk 15 cow gives each 3 / 4 liter milk 15 cow gives each 1 / 4 liter milk this is split into 3 son per each 15 cows & 15 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "15 cow 2 liter each = 30 liter 15 cow 3 / 4 liter each = 3 / 4 = 0.75 * 15 = 11.25 15 cow 1 / 4 liter each = 1 / 4 = 0.25 * 15 = 3.75 add 30 + 11.25 + 3.75 = 45 milk split into 3 son each 15 liter then 45 / 3 = 15 answer : c"
Answer: c
Problem: if both 2 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "the number a must include at least 3 ^ 2 = 9 the answer is b ."
Answer: b
Problem: an outlet pipe can empty 3 / 4 of a cistern in 12 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "4 / 12 * 3 / 4 = 1 / 4 the answer is c ."
Answer: c
Problem: a couple decides to have 6 children . if they succeed in having 6 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 3 girls and 3 boys ?
Options: a ) 1 , b ) 9 / 64 , c ) 1 / 8 , d ) 3 / 16 , e ) 9 / 32
Rationale: "sample space = 2 ^ 6 = 64 . favourable events = { bbbggg } , { bgbgbg } , { bgbggb } , { bggbbg } { gggbbb } , { gbgbgb } , { gbbggb } . { gbgbbg } { gbbgbg } probability = 9 / 64 = 9 / 64 ans ( b ) ."
Answer: b
Problem: how long does a train 110 meters long running at the speed of 72 km / hour take to cross a bridge 132 meters in length ?
Options: a ) 15 seconds , b ) 12.1 seconds , c ) 10 seconds , d ) 8.1 seconds , e ) none of these
Rationale: "explanation : speed = 72 km / hour = 72 * ( 5 / 18 ) m / sec = 20 m / sec total distance to be covered = 110 + 132 = 142 meters time = distance / speed = 242 / 20 = 12.1 seconds option b"
Answer: b
Problem: the averageincome of m and n is rs . 5050 . the average monthly income of n and o is rs . 6250 and the average monthly income of m and ois rs . 5200 . the income of m is ?
Options: a ) rs . 2000 , b ) rs . 3000 , c ) rs . 4000 , d ) rs . 4500 , e ) rs . 5000
Rationale: let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) m + o = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( m + n + o ) = 33000 or m + n + o = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get m = 4000 . m ' s monthly income = rs . 4000 c
Answer: c
Problem: a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 1 a rupee . find his net profit or loss percent ?
Options: a ) 330 % , b ) 390 % , c ) 200 % , d ) 250 % , e ) 300 %
Rationale: "the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 1 he selling at 3 a rupee , his sp = 4 profit = sp - cp = 4 - 1 = 3 profit percent = 3 / 1 * 100 = 300 % answer : e"
Answer: e
Problem: a can do a job in 5 days and b can do it in 15 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 22 ½ days , c ) 23 ½ days , d ) 12 ½ days , e ) 7 ½ days
Rationale: "explanation : 1 / 5 + 1 / 15 = 4 / 15 = 4 / 15 15 / 4 = 15 / 4 * 2 = 7 ½ days answer : e"
Answer: e
Problem: a tank contains 10,000 gallons of a solution that is 3 percent sodium chloride by volume . if 4,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 5 % , c ) 6.25 % , d ) 6.67 % , e ) 11.7 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 4,000 = 6,000 gallons and sodium chloride is 300 gallons ( 3 % of initial solution of 10,000 gallons ) then sodium chloride is 300 / 6,000 * 100 = 5 % of the remaining solution of 6,000 gallons . answer : b ."
Answer: b
Problem: in a simultaneous throw of a pair of dice , find the probability of getting a total more than 8
Options: a ) 1 / 2 , b ) 7 / 12 , c ) 3 / 7 , d ) 5 / 12 , e ) 6 / 17
Rationale: "total number of cases = 7 * 7 = 49 favourable cases = [ ( 2,7 ) , ( 3,6 ) , ( 3,7 ) , ( 4,5 ) , ( 4,6 ) , ( 4,7 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 5,7 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) , ( 6,7 ) , ( 7,2 ) , ( 7,3 ) , ( 7,4 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) ] = 21 so probability = 21 / 49 = 3 / 7 answer is c"
Answer: c
Problem: what is the value of â ˆ š 81 % ?
Options: a ) 25 % , b ) 36 % , c ) 42 % , d ) 60 % , e ) 90 %
Rationale: "explanation : br > â ˆ š 81 % = â ˆ š 81 / â ˆ š 100 = 9 / 10 = 90 / 100 = 90 % correct answer is e ) 90 %"
Answer: e
Problem: if x is 20 percent more than y and y is 50 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 125 % , e ) 60 %
Rationale: "let ' s take values of x , y , z which can satisfy given equations . let z = 200 , so y becomes 100 ( since y is 50 % less than z ) , x becomes 120 ( since 20 % more than y ) now req is ( x / z ) * 100 = ( 120 / 200 ) * 100 = 60 % answer : e"
Answer: e
Problem: a sum of money at simple interest amounts to rs . 1072 in 2 years and to rs . 1144 in 4 years . the sum is :
Options: a ) rs . 1000 , b ) rs . 850 , c ) rs . 500 , d ) rs . 1200 , e ) rs . 900
Rationale: "s . i . for 2 years = rs . ( 1144 - 1072 ) = rs . 72 . s . i . for 1 year = rs . 72 / 2 = rs . 36 . principal = rs . ( 1072 - 72 ) = rs . 1000 . answer : option a"
Answer: a
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 12 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 80.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 20 % , thus he must pay slightly more than $ 80 . only answer choice d fits . answer : d ."
Answer: d
Problem: a , b and c can do a work in 15 , 20,45 days respectively . in how many days they can complete the work together .
Options: a ) 5.2 days , b ) 9.2 days , c ) 8.2 days , d ) 6.2 days , e ) 7.2 days
Rationale: lcm = 180 no of days = [ 180 / ( 180 / 15 + 180 / 20 + 180 / 45 ) = [ 180 / ( 12 + 9 + 4 ) ] = [ 180 / 25 ] = 7.2 days answer : e
Answer: e
Problem: the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is :
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) none
Rationale: "solution let the numbers be x and ( x + 1365 ) . then , x + 1365 = 6 x + 15 ⇔ 5 x = 1350 ⇔ x = 270 . answer b"
Answer: b
Problem: how long does a train 100 m long running at the speed of 65 km / hr takes to cross a bridge 145 m length ?
Options: a ) 13.6 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 65 * 5 / 18 = 18 m / sec total distance covered = 100 + 145 = 245 m . required time = 245 / 18 = 13.6 sec . answer : a"
Answer: a
Problem: lilly has 10 fish and rosy has 11 fish . in total , how many fish do they have in all ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "10 + 11 = 21 the answer is c ."
Answer: c
Problem: what percent is 4 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.4 % , c ) 2.5 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 4 / 1000 × 100 = 400 / 1000 = 2 / 5 = 0.4 % b )"
Answer: b
Problem: the curved surface of a right circular cone of height 15 cm and base diameter 16 cm is
Options: a ) 40 ∏ cm ³
b ) 60 ∏ cm ³
c ) 136 ∏ cm ³
d ) 138 ∏ cm ³
e ) none
Rationale: sol . h = 14 cm , r = 7 cm . so , l = √ r ² + h ² = √ 8 ² + ( 15 ) ² = 17 cm . ∴ curved surface area = ∏ rl = ( ∏ * 8 * 17 ) cm ² = 136 ∏ cm ² answer c
Answer: c
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 11 per day , and a kayak rental costs $ 16 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 460 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: "let x be the number of canoes . then 3 x / 4 is the number of kayaks . 11 x + ( 3 x / 4 ) * 16 = 460 11 x + 12 x = 460 23 x = 460 x = 20 ( canoes ) 3 x / 4 = 15 ( kayaks ) there were 20 - 15 = 5 more canoes rented out . the answer is d ."
Answer: d
Problem: set w consists of all the prime numbers between 10 and 25 . what is the range of set w ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: answer of set w is 12 .
Answer: a
Problem: at 15 : 15 pm railway time , what will be the angle between minute and hour hand ?
Options: a ) 238 , b ) 360 , c ) 377 , d ) 277 , e ) 291
Rationale: at 15 : 15 both minute and hour hands will be in same position . hence the angle between them will be zero degrees . however 360 degree also means both minute and hour hands are in same position . hence correct answers are both zero and 360 degrees answer : b
Answer: b
Problem: x and y start a business with rs . 2000 and rs . 12000 respectively . hoe should they share their profits at the end of one year ?
Options: a ) 1 : 6 , b ) 6 : 1 , c ) 1 : 5 , d ) 5 : 1 , e ) 1 : 4
Rationale: "they should share the profits in the ratio of their investments . the ratio of the investments made by x and y = 2000 : 12000 = > 1 : 6 . answer : a"
Answer: a
Problem: a train 130 m long crosses a platform with a speed of 70 kmph in 20 sec ; find the length of the platform ?
Options: a ) 150 , b ) 145 , c ) 165 , d ) 162 , e ) 152
Rationale: "d = 130 + x t = 20 s = 130 + x / 15 * 18 / 5 = 70 kmph . = > ( 130 + x ) * 18 = 5250 = > 130 + x = 292 = > x = 162 m answer : d"
Answer: d
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 288 meters , what is the width of the field ?
Options: a ) 50
b ) 60
c ) 70
d ) 80
e ) 90
Rationale: let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 288 , 2 ( 7 / 5 ) w + 2 w = 288 solve the above equation to find : w = 60 m and l = 84 m . correct answer b ) 60
Answer: b
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 9 percent . overall he make a .
Options: a ) 228 , b ) 288 , c ) 27 , d ) 120 , e ) 881
Rationale: let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 9 / 100 ) = 8000 + 720 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 720 = rs . 120 as this is positive , an overall profit of rs . 200 was made . answer : d
Answer: d
Problem: sheela deposits rs . 3800 in bank savings account . if this is 32 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 11875 , d ) 12340 , e ) none of these
Rationale: "explanation : 32 % of income = rs . 3800 100 % of income = 3800 x 100 / 32 = rs . 11875 answer : c"
Answer: c
Problem: there are 11 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
Options: a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75
Rationale: 11 c 2 = 55 the answer is c .
Answer: c
Problem: if greg buys 6 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 4 shirts , 2 trousers and 2 ties , the total cost is $ 140 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 60 , b ) $ 64 , c ) $ 75 , d ) $ 110 , e ) can not be determined
Rationale: solution : 6 x + 4 y + 2 z = 80 4 x + 2 y + 2 z = 140 adding both the equations = 10 x + 6 y + 4 z = 220 5 x + 3 y + 2 z = 110 ans d
Answer: d
Problem: three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 138 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters , b ) 19 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 138 = 200 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : b ."
Answer: b
Problem: if jenee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 3 / 50 , e ) 1 / 20
Rationale: perhaps it is also easy to just translate the % into fractions : 6 % : 6 / 100 = 3 / 50 7 % : 7 / 100 8 % : 8 / 100 = 4 / 50 = 2 / 25 9 % : 9 / 100 only 3 / 50 exists in the answer choices , so ans d
Answer: d
Problem: length of a rectangular plot is 28 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 54 m , b ) 64 m , c ) 74 m , d ) 84 m , e ) 94 m
Rationale: "let breadth = x metres . then , length = ( x + 28 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 28 ) + x ] = 200 2 x + 28 = 100 2 x = 72 x = 36 . hence , length = x + 28 = 64 m b"
Answer: b
Problem: if x = 3 y , where y is a prime number greater than 2 , how many different positive even divisors does x have , including x ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) it can not be determined from the information given
Rationale: for x to have even divisors , xx has to be an even number . we know that x = 3 y , where yy is a prime number greater than 2 . as 2 is the only even prime number , y has to be an odd prime number . this means that x must also be an odd number , since odd x odd = odd . as x is odd , it can not have any even divisors . therefore , a is the correct answer .
Answer: a
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a sixth of a circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 360 , d ) 6000 , e ) 36000
Rationale: 1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 60 degrees = 6000 anglets answer - d
Answer: d
Problem: ratio of girl and boys in class is 5 : 6 . if 20 girl leave the class and ratio become 2 : 3 . calculate the no . of boys ?
Options: a ) 100 , b ) 120 , c ) 80 , d ) 90 , e ) none of the above
Rationale: girl 5 x and boys 6 x 5 x - 20 / 6 x = 2 / 3,15 x - 60 = 12 x , 3 x = 60 , x = 20 boys = 6 x = 120 answer b
Answer: b
Problem: if 30 % of a number exceeds 20 % of it by 18 , then find the number ?
Options: a ) 120 , b ) 200 , c ) 180 , d ) 150 , e ) none of these
Rationale: "let the number be x . 30 % of x = 30 / 100 * x = 3 x / 10 20 % of x = 20 / 100 * x = x / 5 = 2 x / 10 . given that 3 x / 10 - 2 x / 10 = 18 = > x = 180 . required number is 180 . answer : c"
Answer: c
Problem: what is the sum of the numbers between 1 and 20 , inclusive ?
Options: a ) 310 , b ) 200 , c ) 215 , d ) 285 , e ) 210
Rationale: "sol . 1 + 2 + 3 . . . 17 + 18 + 19 + 20 answer . e"
Answer: e
Problem: a company recently conducted a survey and found that 30,000 of its customers live in rural areas . if the number of customers who live in urban areas is 130 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 65,000 , b ) 67,000 , c ) 69,000 , d ) 71,000 , e ) 73,000
Rationale: "the number of customers in urban areas is 30,000 + 1.3 * 30,000 = 69,000 . the answer is c ."
Answer: c
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 3 / 4 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 6 / 22 , b ) 5 / 22 , c ) 7 / 22 , d ) 4 / 22 , e ) 3 / 22
Rationale: "# of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 c"
Answer: c
Problem: what is ( 24 ^ 7 + 24 ) / 24 ?
Options: a ) 159202573 , b ) 160902641 , c ) 172502765 , d ) 182302834 , e ) 191102977
Rationale: "( 24 ^ 7 + 24 ) / 24 = 24 * ( 24 ^ 6 + 1 ) / 24 = 24 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is e ."
Answer: e
Problem: 3 consecutive even numbers are such that thrice the first number exceeds double the third number by 7 . what is the third number ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: let the three numbers be x , x + 2 , and x + 4 . 3 x = 2 ( x + 4 ) + 7 x = 15 and then the third number is x + 4 = 19 . the answer is a .
Answer: a
Problem: what is the units digit of ( 22 ^ 4 ) ( 16 ^ 3 ) ( 41 ^ 8 ) ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the units digit of 22 ^ 4 is the units digit of 2 ^ 4 which is 6 . the units digit of 16 ^ 3 is the units digit of 6 ^ 3 which is 6 . the units digit of 41 ^ 8 is the units digit of 1 ^ 8 which is 1 . the units digit of 6 * 6 * 1 is 6 . the answer is e ."
Answer: e
Problem: in a factory , each day the expected number of accidents is related to the number of overtime hour by linear equation . suppose that on one day there were 1000 overtime hours logged and 8 accidents reported and on another day there were 400 overtime hours logged and 5 accidents . what is the expected number of accidents when no overtime hours are logged ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : let , the number of over time hours be x and expected number of accidents be y . we will use the equation y = mx + c , where m and c are constant . now , according to the question , if x = 1000 , then y = 8 i . e 8 = 1000 x + c - - - - ( i ) and , if x = 400 , then y = 5 i . e 5 = 400 x + c . - - - - ( ii ) on solving these equations , we get m = 1 / 200 and c = 3 . hence , in case , no overtime is there i . e x = 0 , then the number of expected accident will be 3 . answer : b
Answer: b
Problem: last week vartan spent 20 percent of his wages on recreation . this week , his wages are 20 percent less than last week ʼ s wages and he spent 40 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?
Options: a ) 150 % , b ) 170 % , c ) 175 % , d ) 160 % , e ) 180 %
Rationale: "say vartan ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.8 * 100 = $ 80 , so he spends 0.4 * 80 = $ 32 on recreation ; 32 / 20 = 1.6 , hence the amount he spends on recreation this week is 160 % of the amount he spent on recreation last week : 20 * 1.6 = 32 answer : d"
Answer: d
Problem: 4 , 12 , 48 , 240 , ( . . . )
Options: a ) 1440 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , answer : option a"
Answer: a
Problem: rs 3200 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 400 , b ) s 200 , c ) s 800 , d ) s 500 , e ) s 100
Rationale: "explanation : average rate = ( 144 / 3200 ) * 100 = 4.5 ratio = 5 : 15 so , first part = ( 5 / 20 ) * 3200 = rs 800 . answer : c"
Answer: c
Problem: if you add all the numbers on your mobile phone except 8 and 2 , what is the answer ?
Options: a ) 55 , b ) 25 , c ) 85 , d ) 45 , e ) 35
Rationale: "we have to add 0 , 1,3 , 4,5 , 6,7 & 9 to find the answer . therefore 0 + 1 + 3 + 4 + 5 + 6 + 7 + 9 = 35 answer is e"
Answer: e
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 6 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 72 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 360 x = 72 min answer : c"
Answer: c
Problem: evaluate : 40 - 10 ÷ 2 × 2 =
Options: a ) 20 , b ) 25 , c ) 10 , d ) 16 , e ) 30
Rationale: "according to order of operations , 10 ÷ 2 × 2 ( division and multiplication ) is done first from left to right 10 ÷ 2 × 2 = 5 × 2 = 10 hence 40 - 10 ÷ 2 × 2 = 40 - 10 = 30 correct answer e ) 30"
Answer: e
Problem: the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 10 of her stamps , the ration of the number of kaye had to the number of alberto had was 6 : 4 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 80 , b ) 85 , c ) 65 , d ) 55 , e ) 50
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 10 a 2 = 3 x + 10 k 2 / a 2 = 6 / 4 ( 5 x - 10 ) / ( 3 x + 10 ) = 6 / 4 4 * ( 5 x - 10 ) = 6 * ( 3 x + 10 ) 20 x - 40 = 18 x + 60 2 x = 100 x = 50 k 2 = 5 * 50 - 10 = 240 a 2 = 3 * 50 + 10 = 160 k 2 - a 2 = 80 answer : a"
Answer: a
Problem: the speed at which a man can row a boat in still water is 18 kmph . if he rows downstream , where the speed of current is 6 kmph , what time will he take to cover 100 metres ?
Options: a ) 6.67 seconds , b ) 18 seconds , c ) 26 seconds , d ) 14.99 seconds , e ) 6 seconds
Rationale: "speed of the boat downstream = 18 + 6 = 24 kmph = 24 * 5 / 18 = 6.67 m / s hence time taken to cover 100 m = 100 / 6.67 = 14.99 seconds . answer : d"
Answer: d
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 10 kmph and the other is going towards south 25 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.42 hr , b ) 2.22 hrs , c ) 3.24 hrs , d ) 5 hrs , e ) 6.02 hrs
Rationale: "to be ( 10 + 25 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 35 * 50 = 1.42 hrs answer is a"
Answer: a
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 5000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 15,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 5000 ) solving for x , we get the shares as 15000 . ans : ( option d )"
Answer: d
Problem: the ratio of pens to pencils is 5 to 6 . there are 8 more pencils than pens . how many pencils are there ?
Options: a ) 30 , b ) 32 , c ) 48 , d ) 55 , e ) 64
Rationale: "let x equal the number of pens , and y the number of pencils . then , x = 5 / 6 y . we also know that x = y - 8 . and so , we can substitute : y - 8 = 5 / 6 y so to isolate y , we get : 1 / 6 y = 8 and therefore : y = 48 answer : c"
Answer: c
Problem: if 0.4 of a number is equal to 0.06 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.4 a = 0.06 b ⇔ a / b = 0.06 / 0.40 = 6 / 40 = 3 / 20 . ∴ a : b = 3 : 20 . answer c"
Answer: c
Problem: a 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m
Rationale: "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 260 ) / 9 = 500 / 9 x + 260 = 500 x = 240 . b"
Answer: b
Problem: a boatman can row 96 km downstream in 8 hr . if the speed of the current is 4 km / hr , then find in what time he will be able to cover 8 km upstream ?
Options: a ) 3 hrs , b ) 7 hrs , c ) 9 hrs , d ) 2 hrs , e ) 6 hrs
Rationale: explanation : speed in downstream = 96 / 8 = 12 kmph speed of current = 4 km / hr speed of the boatman in still water = 12 â € “ 4 = 8 kmph speed in upstream = 8 â € “ 4 = 4 kmph time taken to cover 8 km upstream = 8 / 4 = 2 hours . answer : d
Answer: d
Problem: choose the number pair / group which is different from others ?
Options: a ) 8 : 39 , b ) 8 : 38 , c ) 8 : 33 , d ) 8 : 32 , e ) 8 : 31
Rationale: explanation : in all other pairs , 2 nd number = ( 1 st number × 3 ) + 1 . answer : c ) 8 : 33
Answer: c
Problem: the ratio of two numbers is 2 : 3 and the sum of their cubes is 945 . the difference of number is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 2 x 3 x 8 x cube + 27 x cube = 945 35 x cube = 945 x cube = 27 = > x = 3 . answer : a
Answer: a
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 21,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,300 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 21000 x 3 / 10 = rs . 6,300 . d"
Answer: d
Problem: the mean of 1 ^ 22 ^ 23 ^ 24 ^ 25 ^ 26 ^ 27 ^ 2 is ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 25 , e ) 30
Rationale: 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + n ^ 2 = n ( n + 1 ) ( 2 n + 1 ) / 6 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + - - - - - + 7 ^ 2 = 7 * 8 * 156 = 140 required average is = 140 / 7 = 20 answer is c
Answer: c
Problem: if 25 % of x is 20 less than 15 % of 1500 , then x is ?
Options: a ) 872 , b ) 820 , c ) 837 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 20 = > x / 4 = 205 = > x = 820 . answer : b"
Answer: b
Problem: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 15 more revolutions than gear p ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: gear q makes 30 more revolutions each 60 seconds . the time to make 15 = 30 / 2 more revolutions is 60 / 2 = 30 seconds . the answer is e .
Answer: e
Problem: ( 8956231 x 465 ) = ?
Options: a ) 4584638125 , b ) 4164647415 , c ) 4584638135 , d ) 4584638140 , e ) 4584638145
Rationale: 8956231 x 465 = 4164647415 ans b
Answer: b
Problem: population is 25000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 33275 , c ) 36625 , d ) 26625 , e ) 26825
Rationale: population after 1 st year = 25000 * 10 / 100 = 2500 = = = > 25000 + 2000 = 27500 population after 2 nd year = 27500 * 10 / 100 = 2750 = = = > 27500 + 2750 = 30250 population after 3 rd year = 30250 * 10 / 100 = 3025 = = = > 30250 + 3025 = 33275 answer : b
Answer: b
Problem: a number , x is chosen at random from the set of positive integers less than 10 . what is the probability that ( 8 / x ) > x ?
Options: a ) 1 / 5 , b ) 2 / 8 , c ) 1 / 3 , d ) 2 / 3 , e ) 7 / 9
Rationale: number x has to be chosen from numbers 1 - 9 ( 8 / x ) > x = > 8 > x ^ 2 = > x ^ 2 - 8 < 0 x can have 2 values only 1 , 2 therefore , probability = 2 / 8 answer b
Answer: b