regisss/math_qa huggingface dataset:
Problem: in a 8 x 8 chess board what is the total number of squares .
Options: a ) 238 , b ) 204 , c ) 678 , d ) 169 , e ) 161
Rationale: ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares ' ' i . e . , n ( n + 1 ) ( 2 n + 1 ) 6 n ( n + 1 ) ( 2 n + 1 ) 6 so substituting 8 in the above formula we get 204 answer : b
Answer: b
Problem: in a division , divident is 686 , divisior is 36 and quotient is 19 . find the remainder .
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6
Rationale: "explanation : 686 = 36 x 19 + r 686 = 684 + r r = 686 - 684 = 2 answer : option c"
Answer: c
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is :
Options: a ) 1 / 4 , b ) 1 / 10 , c ) 7 / 15 , d ) 8 / 15 , e ) 9 / 15
Rationale: "explanation : a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 4 day ' s work = 7 / 60 x 4 = 7 / 15 therefore , remaining work = 1 - 7 / 15 = 8 / 15 answer is d"
Answer: d
Problem: rakesh credits 15 % of his salary in his fixed deposit account and spends 30 % of the remaining amount on groceries . if the cash in hand is rs . 2380 , what is his salary ?
Options: a ) rs . 3500 , b ) rs . 4000 , c ) rs . 4500 , d ) rs . 5000 , e ) none
Rationale: explanation : let salary be rs . x . then , x - 15 % of x - 30 % of 85 % of x = 2380 or x - 15 x / 100 − 30 × 85 × x / 100 × 100 = 2380 or 200 x - 30 x - 51 x = 2380 × 2002380 × 200 or 119 x = 2380 × 2002380 × 200 or x 2380 × 200 / 119 = 4000 correct option : b
Answer: b
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth
Options: a ) 12000 , b ) 14000 , c ) 15000 , d ) 20000 , e ) 60000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer a"
Answer: a
Problem: if a light flashes every 6 seconds , how many times will it flash in ¾ of an hour ?
Options: a ) 451 times , b ) 638 times , c ) 838 times , d ) 436 times , e ) 435 times
Rationale: there are 60 minutes in an hour . in ¾ of an hour there are ( 60 * ¾ ) minutes = 45 minutes . in ¾ of an hour there are ( 60 * 45 ) seconds = 2700 seconds . light flashed for every 6 seconds . in 2700 seconds 2700 / 6 = 450 times . the count start after the first flash , the light will flashes 451 times in ¾ of an hour . answer : a
Answer: a
Problem: by selling an article at rs . 400 , a profit of 60 % is made . find its cost price ?
Options: a ) 228 , b ) 267 , c ) 287 , d ) 250 , e ) 811
Rationale: "sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 60 ) ] = 400 * [ 100 / 160 ] = rs . 250 answer : d"
Answer: d
Problem: while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 3 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 1.6 , b ) 1.8 , c ) 2 , d ) 2.2 , e ) 2.4
Rationale: "both computers together process files at a rate of 240 / 12 + 240 / 3 = 20 + 80 = 100 files per hour . the time required to process 240 files is 240 / 100 = 2.4 hours the answer is e ."
Answer: e
Problem: on dividing a number by 357 , we get 39 as remainder . on dividing the same number 17 , what will be the remainder ?
Options: a ) 10 , b ) 12 , c ) 5 , d ) 25 , e ) 85
Rationale: "explanation : let x be the number and y be the quotient . then , x = 357 x y + 39 = ( 17 x 21 x y ) + ( 17 x 2 ) + 5 = 17 x ( 21 y + 2 ) + 5 ) required remainder = 5 . c )"
Answer: c
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team r . if team a ' s average speed was 5 mph greater than team r ' s , what was team r ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team r ' s speed was s . then team r ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team r . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team r is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Problem: the average marks of a class of 24 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 53.5 , e ) 52.1
Rationale: "sum of the marks for the class of 24 students = 24 * 40 = 960 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 74 students = 960 + 3000 = 3960 average marks of all the students = 3960 / 74 = 53.5 answer : d"
Answer: d
Problem: each month a retailer sells 100 identical items . on each item he makes a profit of $ 30 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 30 sell price = $ 300 + $ 30 thus , the sell price is $ 330 for each item . selling all 100 items gives the retailer . . . 100 ( $ 30 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 330 ) = $ 16.5 discount $ 313.5 = $ 300 + $ 13.5 now , the retailer makes a profit of just $ 13.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 13.5 ( x ) = $ 2,000 x = 2,000 / 13.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 555 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 150 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 555 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 55 3.7 z = 555 , z = 150 answer : . d"
Answer: d
Problem: for integers x , y , and z , if ( 3 ^ x ) ( 4 ^ y ) ( 5 ^ z ) = 13107 , 200000 and x + y + z = 16 , what is the value of xy / z ?
Options: a ) undefined , b ) 0 , c ) 3 , d ) 5 , e ) 7
Rationale: the number 13,107 , 200,000 is not divisible by 3 . ( we can verify this by adding the digits of the number to see that the sum is not a multiple of 3 . ) thus x = 0 and xy / z = 0 . the answer is b .
Answer: b
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 972 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 972 3 b 2 = 972 b 2 = 324 b = 18 m . answer : option c"
Answer: c
Problem: the mean of 15 observations was 25 . it was found later that an observation 40 was wrongly taken as 25 . the corrected new mean is
Options: a ) 20 , b ) 30 , c ) 15 , d ) 18 , e ) 26
Rationale: "explanation : correct sum = ( 25 * 15 + 40 - 25 ) = 390 correct mean = = 390 / 15 = 26 answer : e"
Answer: e
Problem: what is the area of a square field whose diagonal of length 24 m ?
Options: a ) 240 sq m , b ) 250 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m
Rationale: "d 2 / 2 = ( 24 * 24 ) / 2 = 240 answer : a"
Answer: a
Problem: if 40 % of a number is equal to two - thirds of another number , what is the ratio of the first number to the second ?
Options: a ) 7 : 3 , b ) 3 : 7 , c ) 2 : 5 , d ) 5 : 3 , e ) none of these
Rationale: "suppose the first number is x and the second numbery . therefore , 40 % of x = 2 ⁄ 3 of y ∴ x ⁄ y = 2 ⁄ 3 × 100 ⁄ 40 = 5 ⁄ 3 answer d"
Answer: d
Problem: ( x ) + 3612 + 16125 - 6149 = 90189 . calculate the value of x
Options: a ) 76601 , b ) 76600 , c ) 76655 , d ) 76313 , e ) 76723
Rationale: "x + 3612 + 16125 - 6149 = 90189 = x + 3612 + 16125 = 90189 + 6149 = x + 19737 = 96338 = x = 96338 - 19737 = 76601 answer is a"
Answer: a
Problem: if the radius of a circle is increased by 12 % , then the area of the circle
Options: a ) decreases by 25.44 %
b ) increases by 25.44 %
c ) no change in area
d ) decreases by 12 %
e ) none
Rationale: a 1 = pi ( 100 ) ^ 2 a 2 = pi ( 112 ) ^ 2 so ( a 2 - a 1 ) / a 1 * 100 = 25.44 answer : b
Answer: b
Problem: a grocer has a sale of rs . 2500 , rs . 6500 , rs . 9855 , rs . 7230 and rs . 7000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) s . 49180 , b ) s . 49910 , c ) s . 11915 , d ) s 6997 , e ) s . 5000
Rationale: total sale for 5 months = rs . ( 2500 + 6500 + 9855 + 7230 + 7000 ) = rs . 33085 . required sale = rs . [ ( 7500 x 6 ) - 33085 ] = rs . ( 45000 - 33085 ) = rs . 11915 . c
Answer: c
Problem: a cyclist bikes x distance at 20 miles per hour and returns over the same path at 16 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 17.6 , b ) 17.3 , c ) 8.6 , d ) 17.2 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 20 miles per hour time = t 1 = distance / speed = x / 20 2 . going from b to a distance = d 2 = x miles speed = s 2 = 16 miles per hour time = t 2 = distance / speed = x / 16 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 20 + x / 16 = 9 x / 80 speed = 2 x / ( 9 x / 80 ) = 160 / 9 = 17.6 answer : a"
Answer: a
Problem: if a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29 , what is the range of a / b ?
Options: a ) 15 / 4 , b ) 13 / 2 , c ) 9 / 7 , d ) 1 / 5 , e ) 7 / 6
Rationale: "the way to approach this problem is 6 < a < 17 and 3 < b < 29 minimum possible value of a is 7 and maximum is 16 minimum possible value of b is 4 and maximum is 28 range = max a / min b - min a / max b ( highest - lowest ) 16 / 4 - 7 / 28 = 15 / 4 hence a"
Answer: a
Problem: increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 56.25
Rationale: "soln : - x * 1.25 * 1.25 = 1.5625 x so there is a net increase of 56.25 % . answer e ."
Answer: e
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 61900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 99 , e ) 12.5
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 61900 profit ( % ) = ( 61900 - 55000 ) / 55000 * 100 = 12.5 % answer : e"
Answer: e
Problem: increasing the original price of an article by 5 percent and then increasing the new price by 5 percent is equivalent to increasing the original price by
Options: a ) 10.25 % , b ) 12.5 % , c ) 14.75 % , d ) 15.15 % , e ) 16.25 %
Rationale: "1.05 * 1.05 * x = 1.1025 * x the answer is a ."
Answer: a
Problem: there are 1200 jelly beans divided between two jars , jar x and jar y . if there are 400 fewer jelly beans in jar x than 3 times the number of beans in jar y , how many beans are in jar x ?
Options: a ) 650 , b ) 700 , c ) 750 , d ) 800 , e ) 850
Rationale: x + y = 1200 so y = 1200 - x x = 3 y - 400 x = 3 ( 1200 - x ) - 400 4 x = 3200 x = 800 the answer is d .
Answer: d
Problem: if x is 20 percent more than y and y is 70 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 36 % , e ) 60 %
Rationale: z = 100 ; y = 30 so x = 36 x as % of z = 36 / 100 * 100 = > 36 % answer will be ( d )
Answer: d
Problem: how many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language ?
Options: a ) 321 , b ) 65 , c ) 120 , d ) 100 , e ) 80
Rationale: 1 million distinct 3 digit initials are needed . let the number of required alphabets in the language be ‘ n ’ . therefore , using ‘ n ’ alphabets we can form n * n * n = n 3 distinct 3 digit initials . note distinct initials is different from initials where the digits are different . for instance , aaa and bbb are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different . this n 3 different initials = 1 million i . e . n 3 = 106 ( 1 million = 106 ) = > n 3 = ( 102 ) 3 = > n = 102 = 100 hence , the language needs to have a minimum of 100 alphabets to achieve the objective . ans : d
Answer: d
Problem: a train covers a distance of 12 km in 10 min . if it takes 8 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 100 , b ) 110 , c ) 160 , d ) 130 , e ) 140
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 8 = 160 m . answer : option c"
Answer: c
Problem: at a certain restaurant , the ratio of the number of cooks to the number of waiters is 3 to 11 . when 12 more waiters are hired , the ratio of the number of cooks to the number of waiters changes to 3 to 14 . how many cooks does the restaurant have ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "originally there were 3 k cooks and 11 k waiters . 14 k = 11 k + 12 k = 4 there are 12 cooks . the answer is d ."
Answer: d
Problem: bruce purchased 8 kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1165 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 11 kg of mangoes = 55 × 11 = 605 . total cost he has to pay = 560 + 605 = 1165 b"
Answer: b
Problem: a 56 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 8 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 5.6 assume x gallons of water are added . 5.6 / 56 + x = 8 / 100 560 = 8 x + 448 8 x = 112 x = 14 correct option : d"
Answer: d
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 120 more than a :
Options: a ) 2348 , b ) 3480 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 120 total earning = \ inline \ frac { 58 xy } { 100 } = 3480 answer : b ) rs . 3480"
Answer: b
Problem: if log 2 = 0.3010 and log 3 = 0.4771 , the value of log 5 ( 512 )
Options: a ) 3.876 , b ) 2.967 , c ) 2.87 , d ) 3.912 , e ) 1.9
Rationale: "log 5 ( 512 ) = log ( 512 ) / log 5 = log 2 ^ 9 / log ( 10 / 2 ) = 9 log 2 / ( log 10 - log 2 ) = ( 9 x 0.3010 ) / ( 1 - 0.3010 ) = 2.709 / 0.699 = 2709 / 699 = 3.876 answer is a ."
Answer: a
Problem: what is the smallest positive integer x such that 507 + x is the cube of a positive integer ?
Options: a ) 15 , b ) 5 , c ) 50 , d ) 2 , e ) 4
Rationale: "given 507 + x is a perfect cube so we will take 512 = 8 * 8 * 8 507 + x = 512 x = 512 - 507 = 5 correct option is b"
Answer: b
Problem: a train which has 440 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 44 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 440 / ( ( 45 - 9 ) ( 5 / 18 ) = 440 / 36 * ( 5 / 18 ) = 440 / 10 = 44 sec answer : b"
Answer: b
Problem: two numbers have a h . c . f of 16 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 16 = 160 . answer : c"
Answer: c
Problem: what is the tens digit of 36 ^ 4 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 6 ( dont actually calculate full values ) and answer is c : 5"
Answer: c
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 38 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 38 % of 1100 ) + ( 32 % of 900 ) = 418 + 288 = 706 failed = 2000 - 706 = 1294 failed % = [ ( 1294 / 2000 ) x 100 ] % = 64.7 % . answer : b"
Answer: b
Problem: an article is bought for rs . 600 and sold for rs . 450 , find the loss percent ?
Options: a ) 16 % , b ) 18 % , c ) 19 % , d ) 20 % , e ) 25 %
Rationale: "600 - - - - 150 100 - - - - ? = > 16 2 / 3 % answer : e"
Answer: e
Problem: 0.003 * 0.5 = ?
Options: a ) 0.00015 , b ) 0.0015 , c ) 0.015 , d ) 0.15 , e ) none of these
Rationale: "explanation : 3 * 5 = 15 . sum of decimal places = 4 . 0.003 * 0.5 = 0.0015 = 0.0015 answer b"
Answer: b
Problem: a man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 8 kmph , d ) 1 kmph , e ) 2 kmph
Rationale: explanation : speed of the boat downstream = speed of the boat upstream \ small \ therefore the speed of the stream = answer : a
Answer: a
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 10 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140
Rationale: "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 10 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 10 ) = $ 60 . the answer is a ."
Answer: a
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 600 inclusive ?
Options: a ) 190 , b ) 195 , c ) 305 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 600 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 60 ( 10 ) = 600 so we know that there are 60 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 600 = 610 20 + 590 = 610 30 + 580 = 610 etc . since there are 60 total terms , this pattern will create 30 ' pairs ' of 610 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 30 ) ( 610 ) / ( 60 ) = 305 final answer : c"
Answer: c
Problem: a $ 74.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 74.95 $ discounted selling price of chair = 59.95 $ discount = 74.95 - 59.95 = 15 $ % decrease in price of chair = ( 15 / 74.95 ) * 100 % = 20 % approx answer b"
Answer: b
Problem: if rs . 595 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 420 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 595 * 2 / 17 = rs . 70 b ' s share = 595 * 3 / 17 = rs . 105 c ' s share = 595 * 12 / 17 = rs . 420 . answer : a"
Answer: a
Problem: a part - time employee ’ s hourly wage was increased by 50 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 25 % , d ) 33 % , e ) 50 %
Rationale: let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 50 % wage increase , the employee makes $ 1.50 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.50 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.50 to get : new # of hours = 100 / 1.50 ≈ 67 hours so , the number of hours decreases from 100 hours to ( approximately ) 67 hours . this represents a 33 % decrease ( approximately ) . answer : d
Answer: d
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 3 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 3 ) / ( 10 - 5 ) = 2 / 5 so they should be mixed in the ratio 2 : 5 answer - a"
Answer: a
Problem: the q train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the q train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says it q took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Problem: what is the area of a square field whose sides have a length of 12 meters ?
Options: a ) 225 sq m , b ) 126 sq m , c ) 144 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "12 * 12 = 144 sq m the answer is c ."
Answer: c
Problem: if 4 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . d"
Answer: d
Problem: a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 117 , c ) 127 , d ) 137 , e ) 147
Rationale: "let us calculate both the length and width of the room in centimeters . length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 624 and 432 = 48 thus , the number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 answer : b"
Answer: b
Problem: how many integers are between 8 and 122 / 7 , inclusive ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 16
Rationale: 122 / 7 = 17 . xx we are not concerned about the exact value of 122 / 7 as we just need the integers . the different integers between 8 and 122 / 7 would be 8 , 9 , 10 , 11 , 12,13 , 14,15 , 16,17 total number of integers = 10 option b
Answer: b
Problem: what percent of 10 is 10 percent of 1 ?
Options: a ) 0.1 % , b ) 1 % , c ) 10 % , d ) 90 % , e ) 100 %
Rationale: "10 percent of 1 is equal to 0.1 so we have to compute what percent of 10 is 0.1 . so this means we have to compute what percent of 100 is 1 . . . . so 1 % answer b ."
Answer: b
Problem: there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 37 , c ) 42 , d ) 53 , e ) 64
Rationale: "x + ( x - 14 ) = 60 - - > x = 37 . answer : b ."
Answer: b
Problem: a man sitting in a train which is traveling at 50 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 50 ) kmph = 62 kmph . answer : c .
Answer: c
Problem: the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of the remainingplayers is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 18 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"
Answer: c
Problem: the true discount on a bill of rs . 2160 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2160 td = rs . 360 pw = f - td = 2160 - 360 = rs . 1800 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1800 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 1800 × 2160 = 15 × 2160 = rs . 432 answer : option a"
Answer: a
Problem: if the cost price is 82 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 22 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 82 profit = $ 18 profit % = 18 / 82 * 100 = 25 / 6 = 22 % approximately answer is b"
Answer: b
Problem: the average of first six prime numbers which are between 50 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 64 , e ) 67
Rationale: "explanation : first six prime numbers which are between 50 and 90 = 53 , 59 , 61 , 67 , 71 , 73 average = ( 53 + 59 + 61 + 67 + 71 + 73 ) / 6 = 64 answer : d"
Answer: d
Problem: if 0.5 % of a = 85 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 85 / 100 ∴ a = rs . ( 85 / 0.5 ) = rs . 170 correct option : a"
Answer: a
Problem: suganya and suriya are partners in a business . suganya invests rs . 15,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 18,040 , d ) rs . 7015.56 , e ) none
Rationale: "solution ratio of their shares = ( 15000 ã — 8 ) : ( 42000 ã — 10 ) = 2 : 7 . suganya ' s share = rs . ( 31570 ã — 2 / 9 ) = rs . 7015.56 answer d"
Answer: d
Problem: find the compound interest on $ 1200 for 5 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 1786 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 5 = $ 2986 ci = $ 1786 answer is c"
Answer: c
Problem: a person want to give his money of $ 15800 to his 4 children a , b , c , d in the ratio 5 : 9 : 6 : 5 . what is the a + c share ?
Options: a ) $ 4000 , b ) $ 2890 , c ) $ 3005 , d ) $ 6952 , e ) $ 6003
Rationale: "a ' s share = 15800 * 5 / 25 = $ 3160 c ' s share = 15800 * 6 / 25 = $ 3792 a + c = $ 6952 answer is d"
Answer: d
Problem: a certain class of students is being divided into teams . the class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 12 24 so , lets find the least common multiple of 12 24 , ie 24 so our answer is ( a ) 24"
Answer: a
Problem: a group of 6 children and 10 adults are going to the zoo . child tickets cost $ 10 , and adult tickets cost $ 16 . how much will the zoo tickets cost in all ?
Options: a ) $ 220 , b ) $ 340 , c ) $ 150 , d ) $ 100 , e ) $ 120
Rationale: step 1 : find the cost of the children ' s tickets . 6 × $ 10 = $ 60 step 2 : find the cost of the adults ' tickets . 10 × $ 16 = $ 160 step 3 : find the total cost . $ 60 + $ 160 = $ 220 the zoo tickets will cost $ 220 . answer is a .
Answer: a
Problem: the price of rice falls by 40 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 40 % , new price for 20 kg rice , = ( 100 - 40 % of 100 ) = 60 new price of rice = 60 / 20 = rs . 3 per kg . rice can bought now at = 100 / 3 = 33.33 kg . answer : option e"
Answer: e
Problem: the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 30 , b ) 15 , c ) 40 , d ) 45 , e ) 20
Rationale: "a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 a + b + c ^ 2 = 400 root ( 400 ) = 20 answer e"
Answer: e
Problem: divide rs . 1200 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 500 , e ) s . 300
Rationale: "a + b + c = 1200 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1200 = > 300 answer : e"
Answer: e
Problem: 108 . triangle a ’ s base is 9 % greater than the base of triangle b , and a ’ s height is 9 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1.3 % more , e ) 9 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 10 / 9 * base of b height of a = 8 / 9 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 10 / 9 * 8 / 9 * area of b = 80 / 81 * area of b area of a is 1.3 % more than the area of b . answer ( d )"
Answer: d
Problem: tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 62.5 ?
Options: a ) 6 , b ) 12 , c ) 15 , d ) 20 , e ) 24
Rationale: "you could set - up a quick table and brute force the answer . a 6 * 50 300 1800 - 300 1500 24 62.50 b 16 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is a"
Answer: a
Problem: what will be the compound interest on rs . 40000 after 3 years at the rate of 12 % per annum
Options: a ) rs 16123.20 , b ) rs 16123.30 , c ) rs 16197.12 , d ) rs 16123.50 , e ) none of these
Rationale: "explanation : ( 40000 × ( 1 + 12 / 100 ) 3 ) = > 40000 × 28 / 25 × 28 / 25 × 28 / 25 = > 56197.12 so compound interest will be 56197.12 - 40000 = rs 16197.12 option c"
Answer: c
Problem: how many pieces of 75 cm can be cut from a rope 54 meters long ?
Options: a ) 30 , b ) 40 , c ) 60 , d ) 72 , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 54 meters long is = ( 54 meters ) / ( 75 cm ) = ( 54 meters ) / ( 0.75 meters ) = 72 answer : d"
Answer: d
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 7 / 4 , b ) 10 / 3 , c ) 12 / 5 , d ) 15 / 7 , e ) 18 / 11
Rationale: "the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 16 / ( 20 / 3 ) = 3 * 16 / 20 = 12 / 5 the answer is c ."
Answer: c
Problem: the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weight 53 kg is replaced by a new man . find the weight of the new man .
Options: a ) 59 kg , b ) 62 kg , c ) 74 kg , d ) 85 kg , e ) 71 kg
Rationale: "total weight increased = 1.8 * 10 = 18 kg weight of the new man = 53 + 18 = 71 kg answer is e"
Answer: e
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 7 , 0 ) , ( 0 , - 3.5 ) , ( - 7 , 0 ) ?
Options: a ) 56 , b ) 88 , c ) 112 , d ) 49 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 7 + 7 = 14 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 14 * 7 = 49 d is the answer"
Answer: d
Problem: how many multiples of 13 are less than 6000 , and also multiples of 16 ?
Options: a ) 30 , b ) 29 , c ) 34 , d ) 32 , e ) 33
Rationale: "lcm of 13 & 16 = 208 tried dividing 6000 by 208 got quotient 28.84 ' so b is answer"
Answer: b
Problem: two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of m crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of m ?
Options: a ) x / 2 , b ) x , c ) 3 m / 2 , d ) mx , e ) mx
Rationale: "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( m ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"
Answer: e
Problem: a man is walking at the rate of 7 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1750 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 7 â ˆ — 5 / 18 = 35 / 18 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 35 / 18 â ˆ — 900 = 1750 meter option d"
Answer: d
Problem: if two sides of a triangle are 6 and 13 , respectively , which of the following could not be the area of this triangle ?
Options: a ) 40
b ) 6
c ) 17
d ) 29
e ) 38
Rationale: for this question it would be helpful to know the largest area that this triangle could be , given the two sides of 6 and 12 . we know that the area of a triangle will be maximized when two sides are perpendicular to each other ( consult bunuel ' s drawing above ) . thus we have a max area being equal to one half the base times the height , either ( . 5 ) 13 * 6 - or - ( . 5 ) 6 * 13 will result in a maximum area of 39 for the triangle ; therefore , the triangle could never have an area of 40 . a
Answer: a
Problem: average expenditure of a person for the first 3 days of a week is rs . 350 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 350 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 350 + rs . 40 = rs . 390 correct option : c"
Answer: c
Problem: compound interest of rs . 1000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 157 , e ) none of the above
Rationale: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 3000 [ 1 + ( 5 / 100 ) ] ^ 3 - 1000 = 1000 [ ( 21 / 20 ) ^ 3 - 1 ] = 1000 ( 9261 - 8000 ) / 8000 = 1 * 1261 / 8 = 157 answer : d"
Answer: d
Problem: 4,25 , 49,121 , 169,289 , 361,529 ,
Options: a ) 149 , b ) 169 , c ) 841 , d ) 920 , e ) 219
Rationale: "29 ^ 2 = 841 because follow sequence of square of the prime numbers answer : c"
Answer: c
Problem: what will be the vulgar fraction of 0.70
Options: a ) 3 / 5 , b ) 7 / 10 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.70 = 70 / 100 = 7 / 10 option b"
Answer: b
Problem: susan drove an average speed of 30 miles per hour for the first 40 miles of a trip then at a average speed of 15 miles / hr for the remaining 40 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 80 miles total time = 40 / 30 + 40 / 15 = 4 avg . speed = 20 . answer - b
Answer: b
Problem: if 25 % of x is 15 less than 15 % of 1500 , then x is ?
Options: a ) 720 , b ) 750 , c ) 820 , d ) 840 , e ) 860
Rationale: "25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 15 = > x / 4 = 210 = > x = 840 . answer : d"
Answer: d
Problem: two good train each 250 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 250 + 250 ) m = 1000 m . required time = ( 500 x 6 / 125 ) sec = 24 sec . answer b"
Answer: b
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 3500 and b rs . 1500 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 7008 , e ) 7291
Rationale: "35 : 15 = > 7 : 3 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 10 = 6048 + 960 = 7008 answer : d"
Answer: d
Problem: 45 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 45 % of companies which offer wireless internet also offer snacks . the answer is c ."
Answer: c
Problem: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 4725 . what was the number of original inhabitants ?
Options: a ) 5000 , b ) 7000 , c ) 4000 , d ) 8000 , e ) 9000
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4725 ( 27 / 40 ) * x = 4725 x = 4725 * 40 / 27 = 7000 the answer is b ."
Answer: b
Problem: a and b invests rs . 3000 and rs . 6500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 8 : 8 , b ) 9 : 8 , c ) 9 : 6 , d ) 9 : 5 , e ) 9 : 13
Rationale: "( 3 * 6 + 6 * 6 ) : ( 6.5 * 12 ) 54 : 78 = > 9 : 13 answer : e"
Answer: e
Problem: if a car went the first third of the distance at 10 kmh , the second third at 24 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 19 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 10 , 24 and 48 ) so : 240 = 10 * t 1 = 24 hrs 240 = 24 * t 2 = 10 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 39 hrs d = rt ( 240 * 3 ) = r * 39 r = 19 answer : b"
Answer: b
Problem: if 70 % of an equal to 40 % of b , then ratio between a and b is ?
Options: a ) 4 : 7 , b ) 4 : 9 , c ) 4 : 2 , d ) 4 : 1 , e ) 4 : 5
Rationale: explanation : 70 a = 40 b a : b = 4 : 7 answer : a
Answer: a
Problem: a college has classes from 10 : 00 am until 1 : 40 pm . in this duration , there are 5 periods . if 5 minutes are provided between each period to leave one class and enter the next class , how many minutes long is each period ?
Options: a ) 38 min , b ) 41 min , c ) 40 min , d ) 42 min , e ) 52 min
Rationale: the total time is 220 minutes . there are four breaks of five minutes between the classes for a total of 20 minutes . the total class time is 200 minutes . 200 / 5 classes = 40 minutes per class the answer is c .
Answer: c
Problem: a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 5 points if you must draw exactly 3 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: to get a 5 , you need one high and three lows ( you could have had 2 highs and one low , but the constraint is that you must have three low cards ) hlll = 4 ! 3 ! = 4 4 ! is the number of ways you can arrange these four spaces . divide by 3 ! because you you repeat three low cards ans : d
Answer: d
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 41 , b ) 65 , c ) 70 , d ) 77 , e ) 98
Rationale: rakesh : rahul : ranjan : rohit = 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,3 and 5 is 30 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 2 x 30 ) = 15 . rahul = ( 1 / 3 x 30 ) = 10 . ranjan = ( 1 / 3 x 30 ) = 10 . rohit = ( 1 / 5 x 30 ) = 6 . step 3 : total number of pencils are ( 15 x + 10 x + 10 x + 6 x ) = 41 x . for minimum number of pencils x = 1 . the person should have at least 41 pencils . a )
Answer: a
Problem: the jogging track in a sports complex is 726 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 450 min , b ) 528 min , c ) 610 min , d ) 714 min , e ) 359 min
Rationale: "clearly , the two will meet when they are 726 m apart to be 4.5 + 3.75 = 8.25 km apart , they take 1 hour to be 726 m apart , they take 100 / 825 * 726 / 1000 = 242 / 2750 * 60 = 528 min . answer is b"
Answer: b
Problem: the marks obtained by vijay and amith are in the ratio 4 : 7 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 6 : 1 , c ) 6 : 5 , d ) 6 : 7 , e ) 6 : 3
Rationale: "4 : 7 3 : 2 - - - - - - - 12 : 21 : 14 12 : 14 6 : 7 answer : d"
Answer: d
Problem: there are , in a certain league , 10 teams , and each team face another team for a total of 10 times . how many games are played in the season ?
Options: a ) 1000 , b ) 450 , c ) 720 , d ) 180 , e ) 400
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 450 option a ."
Answer: a
Problem: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 8 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 38 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 8 ) years . ( x + 8 + 10 ) = 2 ( x — 10 ) hence x = 38 . present age of b = 38 years answer : option c"
Answer: c
Problem: an assembly line produces 36 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 ) 38 , b ) 40 , c ) 42 , d ) 45 , e ) 50
Rationale: the time to produce the first 60 cogs is 60 / 36 = 5 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 8 / 3 ) hours = 45 cogs per hour . the answer is d .
Answer: d
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 2 is subtracted and divided by 13 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 2 ) / 13 = ( 54 - 2 ) / 13 = 4 answer : option a"
Answer: a