regisss/math_qa huggingface dataset:
Problem: john makes $ 30 a week from his job . he earns a raise andnow makes $ 40 a week . what is the % increase ?
Options: a ) 16 % , b ) 33.33 % , c ) 33.69 % , d ) 33.98 % , e ) 37 %
Rationale: "increase = ( 10 / 30 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b"
Answer: b
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 6 , - 4 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) 1
Rationale: "the midpoint of ( 2,8 ) and ( 6 , - 4 ) is ( 4,2 ) . the slope of a line through ( 0 , - 2 ) and ( 4,2 ) is ( 2 - ( - 2 ) ) / ( 4 - 0 ) = 4 / 4 = 1 the answer is e ."
Answer: e
Problem: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years b in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) 25 , c ) b = 30 , d ) b = 35 , e ) b = 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Problem: if 36 men can do a piece of work in 5 hours , in how many hours will 15 men do it ?
Options: a ) 12 , b ) 38 , c ) 60 , d ) 88 , e ) 72
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 5 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 5 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 5 } { 15 } = 12 hence , 15 men can do it in 12 hours . answer : a ) 12"
Answer: a
Problem: in business , a and c invested amounts in the ratio 4 : 2 , whereas the ratio between amounts invested by a and b was 4 : 1 , if rs 20,000 was their profit , how much amount did a receive .
Options: a ) 13333 , b ) 26758 , c ) 45896 , d ) 14639 , e ) 89576
Rationale: "explanation : a : b = 4 : 1 = 4 : 1 = > a : c = 4 : 2 = 4 : 2 = > a : b : c = 4 : 1 : 2 a share = ( 4 / 6 ) * 20000 = 13333 option a"
Answer: a
Problem: if the average of 10 consecutive integers is 24.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 29 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 24 , integer 6 = 25 . counting up to the tenth integer we get 29 . answer : d"
Answer: d
Problem: the letters o , l and t are rearranged to form the word ' lot ' . find its probability .
Options: a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 6
Rationale: explanation : there are total 3 letters . the probability that o gets the first position is 1 / 3 . likewise , probability for l and t are 1 / 2 and 1 / 1 . hence , the required probability is : - = > ( 1 / 3 ) x ( 1 / 2 ) x 1 . = > 1 / 6 . answer : e
Answer: e
Problem: the product of two numbers is 168 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 168 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 168 ) = 625 x + y = 25 . option b"
Answer: b
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 64 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 88
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 64 ( subtracting twice of incorrect from correct ) 3 x = 264 x = 88 answer : e"
Answer: e
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 7 is how many times as great as the frequency corresponding to a reading of 2 ?
Options: a ) 40 , b ) 50 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 2 to 3 it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 so it will from 2 to 7 i . e 3 , 4,5 , 6,7 = 10 * 10 * 10 * 10 * 10 = 10 ^ 5 answer is d"
Answer: d
Problem: a wildlife preserve is being planned for 8000 rhinoceroses . the preserve is to contain a total of 10000 acres of watering area , plus 100 acres of grazing area for each rhinoceros . if the number of rhinoceroses is expected to increase by 10 percent , how many 1000 acres should the preserve have in order to provide for the increased population ?
Options: a ) 340 , b ) 330 , c ) 320 , d ) 310 , e ) 890
Rationale: number of rhinos = 8000 watering area = 10,000 acres number of rhino to increase by 10 percent , then number of rhino = 8800 grazing area for a rhino = 100 total grazing area for 8800 rhinos = 8800 * 100 = 8 , 80,000 total area required for the wildlife preserve = 8 , 80,000 + 10,000 = 8 , 90,000 = 890 * 1000 answer e
Answer: e
Problem: at a certain organisation , the number of male members went up by 14 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 7
Rationale: "men increase by 14 % = = > 1.14 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.14 m + 0.94 f = 1.012 * ( m + f ) 1.14 m + 0.94 f = 1.012 m + 1.012 f 1.14 m - 1.012 m = 1.012 f - 0.94 f 0.128 m = 0.072 f m / f = ( 0.072 ) / ( 0.128 ) = 72 / 128 = 4 / 7 answer = ( e )"
Answer: e
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 50 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "distance between maxwell ' s and brad ' s home = 50 km maxwell ' s speed = 4 km / h brad ' s speed = 6 km / h relative speed of approach = 10 km / h time = 50 / 10 = 5 hours distance traveled by maxwell when they meet in the middle = 4 * 5 = 20 km answer c"
Answer: c
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 10 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 112.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80
Rationale: "correct answer : a the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.1 ( $ 1120 ) = $ 112 . the correct answer is a ."
Answer: a
Problem: a man is 37 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 78 years , b ) 22 years , c ) 88 years , d ) 35 years , e ) 65 years
Rationale: "let ' s son age is x , then father age is x + 37 . = > 2 ( x + 2 ) = ( x + 37 + 2 ) = > 2 x + 4 = x + 39 = > x = 35 years answer : d"
Answer: d
Problem: what is the sum of the digits of integer k , if k = ( 10 ^ 40 - 79 )
Options: a ) 345 , b ) 340 , c ) 343 , d ) 349 , e ) 338
Rationale: "there are 41 digits in 10 ^ 40 when we subtract 79 from it , there will be 40 digits left . 10 ^ 40 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 79 = 9999999 . . . . ( 40 times ) + 1 - 79 = 9999999 . . . . ( 40 times ) - 78 consider the last 2 digits , 99 - 78 = 21 the last 2 digits will be 21 . and our number would be 99999 . . . . . . 99921 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 21 the sum of the digits will be ( 38 * 9 ) + 2 + 1 = 345 answer : - a"
Answer: a
Problem: by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is :
Options: a ) 5760 , b ) 7667 , c ) 4445 , d ) 4566 , e ) 3344
Rationale: "explanation : to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c ) 5760"
Answer: c
Problem: if 80 percent of 600 is 50 percent of x , then x = ?
Options: a ) 960 , b ) 1000 , c ) 1020 , d ) 1080 , e ) 1075
Rationale: 0.8 * 600 = 0.5 * x x = 8 / 5 * 600 = 960
Answer: a
Problem: if a 2 + b 2 + c 2 = 560 and ab + bc + ca = 8 , then a + b + c is
Options: a ) 4 , b ) 52 , c ) 16 , d ) 24 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 560 and ab + bc + ca = 8 , ( a + b + c ) ^ 2 = 560 + 2 ( 8 ) = 576 = 24 ^ 2 therefore : a + b + c = 24 answer : d"
Answer: d
Problem: a man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph , find his average speed for the total journey ?
Options: a ) 1 kmph , b ) 5 kmph , c ) 5.5 kmph , d ) 4 kmph , e ) 7 kmph
Rationale: "explanation : speed of man = 6.5 kmph speed of stream = 2.5 kmph speed in downstream = 9 kmph speed in upstream = 4 kmph average speed = ( 2 x 9 x 4 ) / 13 = 5.5 kmph . answer : c"
Answer: c
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 15 % profit on the first article and 15 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 768 , c ) 150 , d ) 280 , e ) 279
Rationale: "profit on first article = 150 % of 1000 = 150 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : c"
Answer: c
Problem: a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 8 , e ) 9
Rationale: "let the total units of work be 48 . units of work completed by a and b in one day = 6 . units of work completed by b and c in one day = 4 units of work completed by a , b , and c in one day = 8 . from the above information we get the work completed by a and c in one day is 6 units . therefore , the number of days taken by a and c to complete the whole work = 48 / 6 = 8 days . answer : d"
Answer: d
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 288 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 10,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 288 pi r = 6 so area = 4 . pi . r ^ 2 = 144 . pi = 324 x 3.14 = 400 ( approx ) c"
Answer: c
Problem: the percentage increase in the area of rectangle , if each of its side is increased by 10 % is ?
Options: a ) 21 % , b ) 30 % , c ) 25 % , d ) 40 % , e ) 50 %
Rationale: "let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a"
Answer: a
Problem: a fill pipe can fill 1 / 2 of cistern in 35 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 20 min , b ) 25 min , c ) 30 min , d ) 35 min , e ) 40 min
Rationale: "required time = 35 * 2 * 1 / 2 = 20 minutes answer is d"
Answer: d
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 1 per sq m ?
Options: a ) 675 , rs . 1350 , b ) 575 , rs . 675 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 1 = rs . 675 answer : b"
Answer: b
Problem: the diameter of a cylindrical tin is 6 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33
b ) 45
c ) 66
d ) 77
e ) 21
Rationale: r = 3 h = 5 π * 3 * 3 * 5 = 45 π cc answer : b
Answer: b
Problem: b completes a work in 9 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.73 days , c ) 5.75 days , d ) 6.75 days , e ) 7.73 days
Rationale: "1 / 9 + 1 / 10 = 19 / 90 90 / 19 = 4.73 days answer : b"
Answer: b
Problem: if a ( a + 7 ) = 18 and b ( b + 7 ) = 18 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) − 7 , d ) 46 , e ) 48
Rationale: "a ( a + 7 ) = 18 = > we have a = 2 or - 9 also b ( b + 7 ) = 18 = > b = 2 or - 9 given a ≠ b 1 ) when a = 2 , b = - 9 and a + b = - 7 1 ) when a = - 9 , b = 2 and a + b = - 7 answer choice c"
Answer: c
Problem: the average ( arithmetic mean ) of the even integers from 0 to 80 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 40 inclusive ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 36 , e ) 40
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 80 is 80 / 2 = 40 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the answer is a ."
Answer: a
Problem: the number of sailors on a ship is 80 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 9 : 5 , c ) 47 : 25 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.80 * officer sailor / officer = 1.80 / 1 = 180 / 100 = 9 / 5 answer will be b"
Answer: b
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 550 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 23500 answer : a"
Answer: a
Problem: a small college reduced its faculty by approximately 20 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 244
Rationale: "if x is the original number of faculty members , then after 20 % reduction in faculty members number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of faculty members is 244 correct answer - e"
Answer: e
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15.5 - 2 * 1.5 = 12.5 . answer : e ."
Answer: e
Problem: the greatest number that divides 180 , 565 and 705 leaving remainder 5 , 5 and 5 respectively is :
Options: a ) 31 , b ) 33 , c ) 35 , d ) 38 , e ) 39
Rationale: "explanation : 180 - 5 = 175 , 565 - 5 = 560 and 705 - 5 = 700 highest number that divides 175 , 560 and 700 is hcf of numbers . hcf of 175 , 560 and 700 = 35 answer : c"
Answer: c
Problem: how many positive integers less than 100 have a remainder of 4 when divided by 13 ?
Options: a ) 6 , b ) 7 , c ) 4 , d ) 9 , e ) 10
Rationale: "we have to include 4 also . as 13 * 0 + 4 = 2 if somebody says to divide 4 by 13 , we will be telling we have 0 quotient and remainder as 4 . answer is c"
Answer: c
Problem: how many of the positive divisors f of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . f = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Problem: a circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ?
Options: a ) 4 cm ^ 2
b ) 6 cm ^ 2
c ) 5 cm ^ 2
d ) 7 cm ^ 2
e ) 8 cm ^ 2
Rationale: the radius of the incircle in a equilateral triangle is a / 2 ( sqrt ) 3 where a = side of triangle = 6 cm so the diameter of the circle would be the diagonal of square so diagonal = 2 * a / 2 ( sqrt ) 3 = a / ( sqrt ) 3 so area of square = 1 / 2 * ( diagonal ) ^ 2 = 6 * 6 / 2 * 3 = 6 cm ^ 2 answer : b
Answer: b
Problem: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 60 km and the other at the rate of 90 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.62
Rationale: "t = ( 111 + 165 ) / ( 60 + 90 ) * 18 / 5 t = 6.62 answer : e"
Answer: e
Problem: what is the average of first 20 multiples of 7 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 84 , e ) e ) 82
Rationale: "required average = 7 ( 1 + 2 + . . . . + 20 ) / 20 ( 8 / 20 ) x ( ( 20 x 21 ) / 2 ) ( because sum of first 21 natural numbers ) = 84 d"
Answer: d
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 148 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1184 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a 1184 b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 148 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 148 = 3 k + 148 = > 2 k = 296 = > k = 148 the initial quantity of milk in a = 8 k = 8 * 148 = 1184 liters ."
Answer: a
Problem: in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the dividend is
Options: a ) 5336 , b ) 4306 , c ) 4236 , d ) 4336 , e ) none
Rationale: sol . divisor = ( 5 × 46 ) = 230 . also , 10 × q = 230 ⇒ q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer a
Answer: a
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 40 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 ) 9.1 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 15 + 40 = 55 kg alloy is 0.12 * 15 + 0.08 * 40 = 5 kg , so the percentage is 5 / 55 * 100 = 9.1 % . answer : d ."
Answer: d
Problem: the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 5750 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2299 , b ) 2699 , c ) 2670 , d ) 6725 , e ) 5000
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5750 ( 100 / 115 ) = rs . 5000 answer : e"
Answer: e
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 36 .
Options: a ) 5 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 36 , remainder will be - 4 i . e . n will be 4 less than a multiple of 36 . so you must add 5 to n to make it a multiple of 36 a"
Answer: a
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on october 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 difference between stock on october 1 than were in stock on january 1 will be - c - ( c - 36 ) = 36 hence answer will be ( e )
Answer: e
Problem: when positive integer n is divided by positive integer j , the remainder is 5 . if n / j = 105.20 , what is value of j ?
Options: a ) 10 , b ) 50 , c ) 30 , d ) 15 , e ) 25
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 105.20 here 105 is the quotient . given that remainder = 5 so , 105.20 = 105 + 5 / j so , j = 25 answer : e"
Answer: e
Problem: the speed at which a man can row a boat in still water is 9.5 kmph . if he rows downstream , where the speed of current is 8.5 kmph , what time will he take to cover 45.5 metres ?
Options: a ) 18 seconds , b ) 8.4 seconds , c ) 5 seconds , d ) 9.1 seconds , e ) 9.5 econds
Rationale: "speed of the boat downstream = 9.5 + 8.5 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 45.5 m = 45.5 / 5 = 9.1 seconds . answer : d"
Answer: d
Problem: in what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 7 sec , c ) 2 sec , d ) 6.5 sec , e ) 9 sec
Rationale: "t = 65 / 36 * 18 / 5 = 6.5 sec answer : d"
Answer: d
Problem: of 70 players on a football team , 46 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 62
Rationale: "total = 70 thrower = 46 rest = 70 - 46 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 46 + 16 = 62 so e . 62 is the right answer"
Answer: e
Problem: how many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards ? ( 1 mile = 1,160 yards )
Options: a ) 2 , b ) 5 , c ) 4 , d ) 3.61 , e ) 4.3
Rationale: speed = 9 miles / hr = 4.4 yard / s = 29.33 yards / min distance = 106 yards time = distance / speed = 106 / 29.33 = 3.61 minutes ans - d
Answer: d
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 8 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 8 = 4 / 9 ( t - 8 ) 10 t = 792 - 352 = > t = 44 . answer : b"
Answer: b
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 800 m ?
Options: a ) 122.9 m , b ) 170 m . , c ) 122.2 m , d ) 222.9 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 800 m , the number of meters by which a beats c = ( 800 * 212.5 ) / 1000 = 170 m . answer : b"
Answer: b
Problem: 5 ^ 100 is divided by 18 then what is the remainder ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c
Answer: c
Problem: if ( a + b ) = 4 , ( b + c ) = 7 and ( c + d ) = 5 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 4 b + c = 7 c + d = 5 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 7 + 5 = 2 . option d . . ."
Answer: d
Problem: the average of 45 results is 8 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 470 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 8 * 45 - 15 * 22 + 20 * 22 = 360 - 330 + 440 = 470 answer is b"
Answer: b
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 20 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 4200 , b ) 5400 , c ) 6600 , d ) 7800 , e ) 8900
Rationale: "the distance the sound traveled to the man is 20 * 330 = 6600 meters the answer is c ."
Answer: c
Problem: in the set of positive integers from 1 to 70 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 240 , d ) 200 , e ) 190
Rationale: "reduce 1 - 70 5 - 15 - 25 - 35 - 45 + 55 + 65 are valid multiples 0 f 5 . add them - - > 245 b"
Answer: b
Problem: if the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm , then the altitude of the triangle is
Options: a ) 12 cm
b ) 10 cm
c ) 11 cm
d ) 15 cm
e ) 20 cm
Rationale: area of square = 6 ^ 2 = 36 area of triangle = 36 1 / 2 bh = 36 h = 12 cm answer a
Answer: a
Problem: what is the remainder when 1014 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 6 , c ) 30 , d ) 21 , e ) 18
Rationale: "oa is ' c ' . oe : take the remainder from each of 1044 / 33 , 1047 / 33 and so on . . 1014 / 33 gives remainder = 24 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 24 * 24 * 27 * 30 break them into pairs 24 * 24 / 33 gives remainder 15 and 27 * 30 / 33 gives remainder 18 so 15 * 18 / 33 gives remainder 6 . b"
Answer: b
Problem: a train 600 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 298 m , b ) 279 m , c ) 500 m , d ) 289 m , e ) 700 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 600 + x ) / 60 = 65 / 3 x = 700 m . answer : e"
Answer: e
Problem: walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?
Options: a ) 2 hr , b ) 1 hr , c ) 3 hr , d ) 1.5 hr , e ) 2.5 hr
Rationale: let the original speed be s and time be t if new speed = s ã — 3 / 4 , then new time would be t ã — 4 / 3 ( d = st = constant ) . given , 3 t / 4 â ˆ ’ t = 20 t / 3 â ‡ ’ t = 60 minutes = 1 hour answer : a
Answer: a
Problem: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.86 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.86 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.86 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.86 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Problem: how many odd numbers between 10 and 1,100 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 15 numbers . answer : d ."
Answer: d
Problem: a man deposits $ 1000 in a bank at 2 % per annum and $ 1500 in uti at 7 % per annum . find the rate of interest for the whole sum .
Options: a ) 5 % , b ) 8 % , c ) 3 % , d ) 7 % , e ) 1 %
Rationale: "following the above formula , we have the rate of interest for the whole sum = ( 1000 * 2 ) + ( 1500 * 7 ) / 1000 + 1500 = 12500 / 2500 = 5 % . answer is a"
Answer: a
Problem: a pump can fill a tank with water in 6 hours . because of a leak , it took 12 hours to fill the tank . the leak can drain all the water in ?
Options: a ) 12 hr , b ) 11 hr , c ) 13 hr , d ) 14 hr , e ) 16 hr
Rationale: work done by the leak in 1 hour = 1 / 6 - 1 / 12 = 1 / 12 leak will empty the tank in 12 hours answer is a
Answer: a
Problem: if 10 x = 8 y = 14 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 166 , c ) 84 , d ) 122 , e ) 168
Rationale: "10 x = 8 y = 14 z 5 x = 4 y = 7 z 5 ( 4 * 7 ) = 4 ( 5 * 7 ) = 7 ( 5 * 4 ) addition = 28 + 20 + 35 = 83 answer would be multiple of 83 which is 166 answer : b"
Answer: b
Problem: if x and y are positive integers and 9 + x + y + xy = 23 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 9 + 3 + xy = 23 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 9 + 5 + xy = 23 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 9 + 6 + xy = 23 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 9 + 8 + xy = 23 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 9 + 9 + xy = 23 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Problem: a container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 16
Rationale: container 1 has 15 ounces in the ratio 1 : 2 or , x + 2 x = 15 gives x ( alcohol ) = 5 and remaining water = 10 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 5 + 2 and water = 10 + 6 ratio thus alcohol / water = 7 / 16 answer e
Answer: e
Problem: how many plants will be there in a circular bed whose outer edge measure 31 cms , allowing 4 cm 2 for each plant ?
Options: a ) 19
b ) 750
c ) 24
d ) 120
e ) none of these
Rationale: circumference of circular bed = 31 cm area of circular bed = ( 31 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 31 ) 2 â  „ 4 ï € ã · 4 = 19.11 = 19 ( approx ) answer a
Answer: a
Problem: 3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1 - . 06 = . 94
Options: a ) 0.06 , b ) 0.12 , c ) 0.21 , d ) 0.29 , e ) 0.28
Rationale: the probability that eachdoesn ' thit is : 0.5 , 0.8 , and 0.7 . when we have multiple independent events , we multiply the probabilities : . 5 * . 8 * . 7 = 0.28 . option : e
Answer: e
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 18 years investment will become $ 5,000 * 2 = $ 10,000 and in another 18 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Problem: 2 / 5 of 3 / 7 of 23 / 11 of ? = 64 × 3
Options: a ) 511 , b ) 419 , c ) 616 , d ) 636 , e ) 686
Rationale: "explanation : 2 / 5 & time ; 3 / 7 & time ; 20 / 11 & time ; x = 192 x = 192 & time ; 11 & time ; 7 & time ; 5 / 2 & time ; 3 & time ; 20 = 616 answer : option c"
Answer: c
Problem: the annual interest rate earned by an investment increased by 11 percent from last year to this year . if the annual interest rate earned by the investment this year was 22 percent , what was the annual interest rate last year ?
Options: a ) 17 % , b ) 19 % , c ) 18 % , d ) 20 % , e ) 22 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.11 i ( last year ) = 1.11 i ( last year ) 22 = 1.11 x i ( last year ) i ( last year ) = 22 / 1.1 = 220 / 11 = 20 % answer : d"
Answer: d
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: there are 3 single digit multiple of 3 , that is , 3 , 69 . there are 8 prime nos less than 20 - 23 , 57 , 1113 , 1719 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability = 1 / 24 . answer c .
Answer: c
Problem: if p ^ 2 – 13 p + 40 = h , and p is a positive integer between 1 and 10 , inclusive , what is the probability that h < 0 ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10
Rationale: p 2 – 13 p + 40 = h so ( p – 8 ) ( p – 5 ) = h for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b .
Answer: b
Problem: abcd is a square where ab = â ˆ š 4004 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4004 / 2 = 2002 . correct answer b"
Answer: b
Problem: two - third of a positive number and 16 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 1 / 3 , d ) 144 / 25 , e ) 146 / 25
Rationale: let the number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 = 1 / 9 x = 1 / 3 answer : c
Answer: c
Problem: if x < y < z and y - x > 9 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 13 , e ) 10
Rationale: we have : 1 ) x < y < z 2 ) y - x > 9 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 9 , the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 13 ( y - 2 = 11 , y = 13 ) 2 < 13 < z , since z is odd , the least possible value for z is 15 z - x = 15 - 2 = 13 answer d
Answer: d
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are marketing majors ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 11 , e ) 17
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are marketing majors is r = 7 . the answer is c ."
Answer: c
Problem: if x = 8 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.007 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.007 answer : b"
Answer: b
Problem: a train running at the speed of 60 km / hr crosses a pole in 5 seconds . find the length of the train .
Options: a ) 83.33 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 5 = 83.33 meter . answer : a"
Answer: a
Problem: on a purchase of $ 118 , a store offered a payment plan consisting of a $ 18 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 16.7 % , b ) 16.2 % , c ) 16.5 % , d ) 15.5 % , e ) 15.3 %
Rationale: "12 * 10 + 18 = 138 ( 18 / 118 ) * 100 = 15.3 answer : e"
Answer: e
Problem: if 70 honey bees make 70 grams of honey in 70 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 70
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 70 : : 70 : x honey 70 : 1 = > 1 x 70 x x = 70 x 1 x 70 = > x = 70 . answer : e"
Answer: e
Problem: 3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 26
Rationale: let the three integers be x , x + 2 and x + 4 . then , 3 x = 2 ( x + 4 ) + 3 x = 11 . third integer = x + 4 = 15 . option a
Answer: a
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 10 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 76 km / hr , b ) 66 km / hr , c ) 48 km / hr , d ) 67 km / hr , e ) 22 km / hr
Rationale: let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 10 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 48 km / hr . answer : c
Answer: c
Problem: if a certain number is divided by 9 , the quotient , dividend , and divisor , added together , will amount to 69 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 54
Rationale: let x = the number sought . then x / 9 + x + 9 = 69 . and x = 54 . e
Answer: e
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did b get in a profit of rs . 2400 ?
Options: a ) s . 532 , b ) s . 600 , c ) s . 822 , d ) s . 812 , e ) s . 810
Rationale: "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 b ' s share in the profit of rs . 2400 = 15 ( 2400 / 60 ) = rs . 600 . answer : b"
Answer: b
Problem: if 10 litres of an oil of rs . 50 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 49.17 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "50 * 10 = 500 66 * 5 = 330 830 / 15 = 55.33 answer : d"
Answer: d
Problem: if the price of a book is first decreased by 25 % and then increased by 20 % , then the decrease in the price will be ?
Options: a ) 20 % , b ) 10 % , c ) 25 % , d ) 18 % , e ) 30 %
Rationale: "let the original price be $ 100 new final price = 120 % of ( 75 % of $ 100 ) = 120 / 100 * 75 / 100 * 100 = $ 90 decrease is 10 % answer is b"
Answer: b
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 35 + 20 ) kg = 55 kg the answer is e ."
Answer: e
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 2 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 4 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: the distance traveled by ferry p is 16 km . then the distance traveled by ferry q is 48 km . ferry q travels at a speed of 12 kph . the time of the journey for ferry q is 48 / 12 = 4 hours , which is 2 hours more than ferry p . the answer is b .
Answer: b
Problem: a car takes 6 hours to cover a distance of 324 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 36 kmph , e ) none
Rationale: "time = 6 distence = 324 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 324 / 9 = 36 kmph d )"
Answer: d
Problem: in a renowned city , the average birth rate is 4 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 86,400 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 2 persons are added ( 4 - 2 ) . every second 1 person are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 1 = 86400 option a"
Answer: a
Problem: steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 88 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: average speed = total distance / total time = ( 40 * 5 + 80 * 3 ) / ( 5 + 3 ) = 440 / 5 = 88 answer : b
Answer: b
Problem: if circles x and y have the same area and circle x has a circumference of 20 π , half of the radius of circle y is :
Options: a ) 16 , b ) 5 , c ) 4 , d ) 2 , e ) 1
Rationale: "x b é radius of circle x ý b é radius of circle y given : pi * x ^ 2 = pi * ý ^ 2 also , 2 * pi * x = 20 * pi x = 10 thus ý = 10 y / 2 = 5 ans : b"
Answer: b
Problem: what is theleast number should be added to 1056 , so the sum of the number is completely divisible by 23 ?
Options: a ) 20 , b ) 23 , c ) 25 , d ) 27 , e ) 28
Rationale: ( 1056 / 23 ) gives remainder 21 21 + 2 = 23 , so we need to add 2 b
Answer: b
Problem: ravi and sunil are partners in a business . ravi invests rs . 20,000 for 8 months and sunil invested rs . 16000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4
Rationale: "= ( 15000 * 8 ) : ( 8000 * 10 ) = 160000 : 160000 = 1 : 1 answer : a"
Answer: a
Problem: tanks c and b are each in the shape of a right circular cylinder . the interior of tank c has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank c is what percent of the capacity of tank b ?
Options: a ) 75 %
b ) 80 %
c ) 100 %
d ) 120 %
e ) 125 %
Rationale: b . for c , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi c / b = 160 pi / 200 pi = 0.8
Answer: b
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , the how old is b ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10
Rationale: "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 ⇒ 5 x = 20 ⇒ x = 4 . hence , b ' s age = 2 x = 8 years . answer : c"
Answer: c
Problem: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 78 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 53 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 78 % of 250 = 195 are boys who play soccer . girls who play soccer = 55 . total girls who do not play soccer = 108 - 55 = 53 . correct option : c"
Answer: c
Problem: the price of 3 pants and 6 t - shirts is rs . 1500 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 700 , b ) 300 , c ) 250 , d ) 550 , e ) 800
Rationale: let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 8 t - shirts = 8 * 100 = 800 answer : e
Answer: e
Problem: rs . 770 were divided among a , b , c in such a way that a had rs . 40 more than b and c had rs 30 more than a . how much was b â € ™ s share ?
Options: a ) rs . 260 , b ) rs . 270 , c ) rs . 280 , d ) rs . 290 , e ) rs . 300
Rationale: let b gets rs x . then we can say a gets rs ( x + 40 ) and c gets rs ( x + 70 ) . x + 40 + x + x + 70 = 770 3 x = 660 x = 220 . b â € ™ s share = rs ( 220 + 70 ) = rs . 290 d
Answer: d
Problem: what is the greatest of 3 consecutive integers whose sum is 39 ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "39 / 3 = 13 the three numbers are 12 , 13 , and 14 . the answer is a ."
Answer: a