regisss/math_qa huggingface dataset:
Problem: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 8 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 16 , e ) 1 / 4
Rationale: "say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 8 - - > f = 16 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 16 ) = 3 / 16 . answer : d ."
Answer: d
Problem: share rs . 4320 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1440
Rationale: "amount received by sanjay . 4 / 12 x 4320 = 1440 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1440 . e"
Answer: e
Problem: a man rows his boat 78 km downstream and 56 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 3
Rationale: "speed downstream = d / t = 78 / ( 4 ) = 20 kmph speed upstream = d / t = 56 / ( 4 ) = 14 kmph the speed of the stream = ( 20 - 14 ) / 2 = 3 kmph answer : e"
Answer: e
Problem: tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1040 , b ) 1045 , c ) 1055 , d ) 1060 , e ) 1075
Rationale: "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . c )"
Answer: c
Problem: a car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 35 , b ) 35.5 , c ) 36 , d ) 36.5 , e ) 37
Rationale: "40 * t = 1 km = > t = 1 / 40 km / h v * ( t + 10 / 3600 ) = 1 v ( 1 / 40 + 10 / 3600 ) = 1 v ( 100 / 3600 ) = 1 v = 36 km / h the answer is c ."
Answer: c
Problem: a camera lens filter kit containing 5 filters sells for $ 87.50 . if the filters are purchased individually , 2 of them are priced at $ 16.45 each , 2 at $ 14.05 each , 1 at $ 19.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 7 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) 11 %
Rationale: "cost of kit = $ 87.50 if filters are purchased individually - $ 16.45 * 2 + $ 14.05 * 2 + $ 19.50 = $ 80.50 amount saved = $ 87.50 - $ 80.50 = $ 7 required % age = ( $ 7 / $ 87.50 ) * 100 = 8 % so , the correct answer is b ."
Answer: b
Problem: a man swims downstream 30 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 3 , b ) 8 , c ) 9 , d ) 4 , e ) 2
Rationale: 30 - - - 3 ds = 10 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : b
Answer: b
Problem: if a speaks the truth 75 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.45 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 75 / 100 = 0.75 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.75 × 0.6 = 0.45 answer : c"
Answer: c
Problem: what is the dividend . divisor 16 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 149 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 16 * 9 + 5 d = 144 + 5 d = 149 answer c"
Answer: c
Problem: what is the positive difference between the sum of the squares of the first 3 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 24 , e ) 27
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 = 14 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 14 is 27 . so the answer is ( e ) ."
Answer: e
Problem: the charge for a single room at hotel p is 40 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) e . 150 %
Rationale: "p = 0.6 r = 0.9 g r = 0.9 g / 0.6 = 1.5 * g thus r is 50 % greater than g . the answer is d ."
Answer: d
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6800 ?
Options: a ) 4966 , b ) 6791 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6800 x 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 answer : b"
Answer: b
Problem: in a group of cheerleaders , the group made of 10 males and 16 females . every cheerleader gets to choose between a coke or malt . the number of those that choose malt is double the number that chose coke , if all the 6 males choose malt , how many females chose malt ?
Options: a ) 30 , b ) 5 , c ) 8 , d ) 20 , e ) 10
Rationale: number of cheerleaders = 27 number of male = 10 number of female = 17 coke = 9 maly = 17 female who chose malt = 17 - 9 = 8 answer = c
Answer: c
Problem: if a certain number is divided by 5 , the quotient , dividend , and divisor , added together , will amount to 65 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 50
Rationale: "let x = the number sought . then x / 5 + x + 5 = 65 . x = 50 . e"
Answer: e
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 105 , then what is the value of k ?
Options: a ) 209 , b ) 212 , c ) 215 , d ) 218 , e ) 221
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 105 ) / 5 + 32 = 221 the answer is e ."
Answer: e
Problem: a camera lens filter kit containing 5 filters sells for $ 57.50 . if the filters are purchased individually , 2 of them are priced at $ 10.45 each , 2 at $ 12.05 each , 1 at $ 17.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 7 % , b ) 8 % , c ) 8.5 % , d ) 10 % , e ) 11 %
Rationale: "cost of kit = $ 57.50 if filters are purchased individually - $ 10.45 * 2 + $ 12.05 * 2 + $ 17.50 = $ 62.50 amount saved = $ 62.50 - $ 57.50 = $ 5 required % age = ( $ 5 / $ 62.50 ) * 100 = 8 % so , the correct answer is b ."
Answer: b
Problem: there were two candidates in an election . winner candidate received 75 % of votes and won the election by 500 votes . find the number of votes casted to the winning candidate ?
Options: a ) 228 , b ) 744 , c ) 750 , d ) 199 , e ) 231
Rationale: "w = 75 % l = 25 % 75 % - 25 % = 50 % 50 % - - - - - - - - 500 75 % - - - - - - - - ? = > 750 answer : c"
Answer: c
Problem: if 170 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 47 , b ) 46 , c ) 41 , d ) 48 , e ) 45
Rationale: "the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 170 factorial will have 41 as - 170 / 5 = 34 34 / 5 = 6 6 / 5 = 1 so answer will be ( c ) 41"
Answer: c
Problem: the ratio of spinsters to cats is 2 to 7 . if there are 35 more cats than spinsters , how many spinsters are there ?
Options: a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42
Rationale: let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 35 x = 7 and the number of spinsters is 2 ( 7 ) = 14 . the answer is a .
Answer: a
Problem: chris mixed 3 pounds of raisins with 3 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 3 3 lbs of nuts = $ 9 total value of mixture = 9 + 3 = 12 fraction of the value of raisin = 3 / 12 = 1 / 4 ans : c"
Answer: c
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 9 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 72 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,09 = 9 / 100 x = 80 * 9 / 100 x = 7.2 7.2 / 10 = 0.72 = 72 % , answer b"
Answer: b
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 4 m x 2 m x 25 cm ?
Options: a ) 5600 , b ) 6000 , c ) 1185 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 400 x 200 x 25 ) / ( 25 x 11.25 x 6 ) = 1185 . answer : option c"
Answer: c
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220
Rationale: orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b
Answer: b
Problem: what is the sum of natural numbers between 40 and 100
Options: a ) 4800 , b ) 4270 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 40 and 100 numbers = 61 = > 100 - 40 = 60 + 1 = 61 sn = 61 / 2 ã — 140 = 61 ã — 70 = 4270 answer : b"
Answer: b
Problem: if 4 consecutive letters are selected at random from the english alphabet , then the probability that one of the letters is a vowel is ?
Options: a ) 13 / 23 , b ) 16 / 23 , c ) 11 / 23 , d ) 17 / 23 , e ) 18 / 23
Rationale: total no . of ways of selecting 4 consecutive letters = > 23 [ like abcd , bcde , efgh , . . etc ] no . of ways of having one is a vowel = > abcd , bcde , cdef , defg , efgh , fghi , ghij , hijk , ijkl , lmno , mnop , nopq , opqr , rstu , stuv , tuvw , uvwx . . . = 17 p ( one of letter is vowel ) = 17 / 23 answer : d
Answer: d
Problem: a man is 36 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is
Options: a ) 28 years , b ) 22 years , c ) 18 years , d ) 16 years , e ) 15 years
Rationale: "let ' s son age is x , then father age is x + 36 . = > 3 ( x + 3 ) = ( x + 36 + 3 ) = > 3 x + 9 = x + 39 = > 2 x = 30 years = 15 years answer : e"
Answer: e
Problem: how much 60 % of 50 is greater than 50 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 11 , d ) 17 , e ) 15
Rationale: "( 60 / 100 ) * 50 – ( 50 / 100 ) * 30 30 - 15 = 15 answer : e"
Answer: e
Problem: a pair of articles was bought for $ 50 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 22.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 90 % of x = 25 x = 25 * . 9 = $ 22.50 answer is b"
Answer: b
Problem: a meal cost $ 37.25 adn there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 42 - 45 , b ) 41 - 43 , c ) 39 - 41 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 37.25 ) = 3.725 15 % ( 37.25 ) = 5.5875 total amount could have been 37.25 + 3.725 and 37.25 + 5.5875 = > could have been between 40.975 and 42.8375 = > approximately between 41 and 43 answer is b ."
Answer: b
Problem: a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ?
Options: a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km
Rationale: difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a )
Answer: a
Problem: evaluate 25 % of 450 + 45 % of 250
Options: a ) 225 , b ) 242 , c ) 252 , d ) 262 , e ) 272
Rationale: "explanation : = ( 25 / 100 ) * 450 + ( 45 / 100 ) * 250 = 225 option a"
Answer: a
Problem: if a lends rs . 3500 to b at 10 % p . a . and b lends the same sum to c at 11.5 % p . a . , then the gain of b ( in rs . ) in a period of 3 years is
Options: a ) rs . 154.50 , b ) rs . 155.50 , c ) rs . 156.50 , d ) rs . 157.50 , e ) none of these
Rationale: explanation : we need to calculate the profit of b . it will be , si on the rate b lends - si on the rate b gets gain of b = 3500 × 11.5 × 3 / 100 − 3500 × 10 × 3 / 100 = 157.50 option d
Answer: d
Problem: at a certain high school , the senior class is twice the size of the junior class . if 1 / 8 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 3 / 8 , b ) 3 / 4 , c ) 1 / 3 , d ) 4 / 5 , e ) 1 / 2
Rationale: start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 8 ) * 200 = 25 and ( 3 / 4 ) * 100 = 75 . 25 + 75 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : c
Answer: c
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 25 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 25 % , c ) 10 % , d ) 45 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 25 percent to make square c length of each side of square c = 1.25 * 20 = 25 area of c = 25 ^ 2 = 625 difference in areas of c and cummulative areas of a and b = 625 - ( 400 + 100 ) = 225 percent is the area of square c greater than the sum of the areas of squares a and b = ( 225 / 500 ) * 100 % = 45 % answer d"
Answer: d
Problem: the sum of ages of 5 children born 3 years different each is 55 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . x + 12 = 5 + 12 = 17 a"
Answer: a
Problem: there are 7 girls and 3 chairs . in how many ways girls can occupy the chairs ?
Options: a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800
Rationale: "total girls = 7 total chairs = 3 1 st chair can be occupy in 7 ways 2 nd chair can be occupy in 6 ways 3 rd chair can be occupy in 5 ways total number of ways = 7 * 6 * 5 = 210 ways correct option is b"
Answer: b
Problem: in a mixed college 160 students are there in one class . out of this 160 students 3 / 5 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 64 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 5 = 96 total boys : 160 - 96 = 64 answer is b"
Answer: b
Problem: a train running at 7 / 11 of its own speed reached a place in 22 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 9 hrs , e ) 11 hrs
Rationale: "new speed = 7 / 11 of usual speed new time = 11 / 7 of usual time 11 / 7 of usual time = 22 hrs usual time = 22 * 7 / 11 = 14 hrs time saved = 22 - 44 = 8 hrs answer is c"
Answer: c
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3300 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1980 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 132 so , a ’ s amount = 120 × 15 = rs . 1980 . answer : option c"
Answer: c
Problem: a line that passes through ( – 2 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 2 ) = > 5 k = k + 4 = > k = 1 ans b it is !"
Answer: b
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 33 per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for rs . 36 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 23 : 120 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.33 m = = > revenue = price x quantity = 0.36 ( m + w ) = = > profit = 0.36 ( m + w ) - 0.33 m = 0.3 * ( 0.33 m ) [ 30 % of cost ] = = > 0.36 m + 0.36 w - 0.33 m = 0.099 m = = > 0.069 m = 0.36 w = = > m / w = 0.36 / 0.069 = 120 / 23 - - or - - w / m = 23 / 120 b is correct ."
Answer: b
Problem: carol is 5 times alice ’ s age but only twice as old as betty . alice is 12 years younger than carol . how old is betty ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 18 , e ) 24
Rationale: given that c = 5 a = 2 b . . and a = c - 12 = 5 a - 12 - - > 4 a = 12 - - > a = 3 substituting the values a = 3 , c = 15 and b = 6 . . ans a = 6 . .
Answer: a
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has twice the width , twice the depth , and the same length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 15 , b ) 30 , c ) 20 , d ) 18 , e ) 25
Rationale: "volume of cube = lbh = 5 new cube l , b , h are increases of l , 2 b , 2 h new volume of cube = l * 2 b * 2 h = 4 * lbh = 4 * 5 = 20 answer : c"
Answer: c
Problem: in a box of 10 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 7 / 12 , b ) 11 / 20 , c ) 17 / 30 , d ) 28 / 45 , e ) 51 / 90
Rationale: "# defective pens = 2 # good pens = 8 probability of the 1 st pen being good = 8 / 10 probability of the 2 nd pen being good = 7 / 9 total probability = 8 / 10 * 7 / 9 = 28 / 45 the answer is d ."
Answer: d
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 30 , what is the sum of the first 15 terms of the progression ?
Options: a ) 250 , b ) 275 , c ) 260 , d ) 225 , e ) 230
Rationale: 4 th term + 12 th term = 30 i . e . , ( a + 3 d ) + ( a + 11 d ) = 30 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 30 - - - - - - - - - - - - - - - from ( 1 ) = 225 answer : d
Answer: d
Problem: if x and y are numbers such that ( x + 5 ) ( y - 5 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 4 , c ) 9 , d ) 25 , e ) 16
Rationale: "from ( x + 5 ) ( y - 5 ) = 0 it follows that either x = - 5 or y = 5 . thus either x ^ 2 = 25 or y ^ 2 = 25 . now , if x ^ 2 = 8125 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 25 + 0 = 25 . similarly if y ^ 2 = 25 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 25 = 25 . answer : d ."
Answer: d
Problem: find the value of ( 19 + 43 / 151 ) × 151
Options: a ) 2924 , b ) 2916 , c ) 2614 , d ) 2912 , e ) 2215
Rationale: "= ( 19 + 43 / 151 ) × 151 = ( 2869 + 43 ) / 151 × 151 = 2912 / 151 × 151 = 2912 answer is d ."
Answer: d
Problem: the lcm of two numbers is 2310 and hcf is 61 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 671 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 61 / 210 = 11 * 61 = 671 answer : b"
Answer: b
Problem: the c . p of 30 books is equal to the s . p of 40 books . find his gain % or loss % ?
Options: a ) 23 % , b ) 24 % , c ) 25 % , d ) 50 % , e ) 40 %
Rationale: "explanation : 30 cp = 40 sp 40 - - - 10 cp loss 100 - - - ? = > 25 % loss answer : c"
Answer: c
Problem: a train 280 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 15 , b ) 6 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 280 * 3 / 55 = 15 sec . answer : a"
Answer: a
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 30 paise per sq m is
Options: a ) rs . 223.20 , b ) rs . 323.20 , c ) rs . 423.20 , d ) rs . 523.20 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 30 / 100 ) = rs . 223.20 answer : a"
Answer: a
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 5 men and 2 women will do that task .
Options: a ) 6 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 3 / 16 , e ) 3 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 5 m + 2 w = 12 w answer is 12 / 14 = 6 / 7 answer : a"
Answer: a
Problem: a sum of money at simple interest amounts to rs . 824 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 500 , b ) 698 , c ) 780 , d ) 910 , e ) 725
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 824 ) = rs . 30 . s . i . for 3 years = rs . ( 30 * 3 ) = rs . 90 . â ˆ ´ principal = rs . ( 815 - 90 ) = rs . 725 answer e"
Answer: e
Problem: 6 boysand 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days find time taken by 15 boys and 20 girls to do same work
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: 6 b + 8 g = 1 / 10 ( 1 day work ) - - - - - - > ( i ) 26 b + 48 w = 1 / 2 - - - - - - - - > ( ii ) divide both sides by 2 in ( i ) and multiply both sides by 5 now we get 15 b + 20 b = 1 / 4 so ans . is 4 days . answer : a
Answer: a
Problem: a , b and c have rs . 250 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 300 , b ) b ) 290 , c ) c ) 280 , d ) d ) 270 , e ) e ) 66
Rationale: "a + b + c = 250 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 250 - - - - - - - - - - - - - - - - c = 300 answer : a"
Answer: a
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1947 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 118
Rationale: "factorise 1947 . . 3 * 11 * 59 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 59 = 118 . . ans : e"
Answer: e
Problem: a boat can travel with a speed of 14 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 72 km downstream .
Options: a ) 4.25 hr , b ) 3.6 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 14 km / hr speed of the stream = 6 km / hr speed downstream = ( 14 + 6 ) = 20 km / hr time taken to travel 72 km downstream = 72 â  „ 20 = 3.6 hours answer is b"
Answer: b
Problem: if x is equal to the sum of the integers from 40 to 60 , inclusive , and y is the number of even integers from 40 to 60 , inclusive , what is the value of x + y ?
Options: a ) 1021 , b ) 1041 , c ) 1061 , d ) 1081 , e ) 1101
Rationale: "x = 40 + 41 + . . . + 60 = 21 ( 50 ) = 1050 y = 11 x + y = 1061 the answer is c ."
Answer: c
Problem: the average age of 36 students in a group is 15 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 52 years , d ) 54 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 37 * 16 - 36 * 15 ) years = 52 years . answer : c"
Answer: c
Problem: how many paying stones , each measuring 4 m * 2 m are required to pave a rectangular court yard 40 m long and 20 m board ?
Options: a ) 99 , b ) 18 , c ) 100 , d ) 17 , e ) 12
Rationale: "40 * 20 = 4 * 2 * x = > x = 100 answer : c"
Answer: c
Problem: convert the 12 / 36 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph .
Rationale: "15 / 36 m / s = 12 / 36 * 18 / 5 = 1 ( 1 / 5 ) = 1.2 kmph . answer : c"
Answer: c
Problem: a two digit number is 18 less than the sum of the squares of its digits . how many such numbers are there ?
Options: a ) 22 , b ) 67 , c ) 200 , d ) 288 , e ) 111
Rationale: "option 2 only 47 and 67 satisfy the condition answer : b"
Answer: b
Problem: what is the sum of all remainders obtained when the first 100 natural numbers are divided by 7 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 364
Rationale: a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 364 . answer : e .
Answer: e
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 4 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 3 / 4 , b ) 9 / 16 , c ) 16 / 3 , d ) 4 / 3 , e ) 3 / 16
Rationale: "the area of rectangle a is ab . c = 4 a / 3 and d = 4 b / 3 . the area of rectangle b is cd = 16 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 16 ab / 9 ) = 9 / 16 . the answer is b ."
Answer: b
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7 / 10 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 35.71429 , e ) 64.5
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 7 x / 10 hence , number of buckets needed = 25 x / ( 7 x / 10 ) = ( 25 × 10 ) / 7 = 35.71429 answer is d ."
Answer: d
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 46 kg , then the weight of b is :
Options: a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 37 kg
Rationale: "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 46 = 92 hence 80 + 92 - 144 = 37 ans = 37 answer : e"
Answer: e
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 2 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 9 : 5
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 4 and 2 parts , respectively . this will give us in the final mixture ( 5 + 4 ) : ( 3 + 2 ) , which means 9 : 5 answer e ."
Answer: e
Problem: in covering a distance of 30 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "abhay speed = x sameer speed = y ( 30 / x ) - ( 30 / y ) = 2 . . . . 1 - ( 30 / 2 x ) + ( 30 / y ) = 1 . . . - 2 solving 1 and 2 we get 6 x = 30 x = 5 answer e"
Answer: e
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.05 ?
Options: a ) 980 , b ) 1130 , c ) 1440 , d ) 1610 , e ) 1820
Rationale: the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.05 - $ 0.65 = $ 1.40 the charge for the next 1300 grams is $ 1.30 which leaves a charge of $ 0.10 the weight is somewhere between 1550 and 1650 . the answer is d .
Answer: d
Problem: the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 14.25 , what is the perimeter of the garden , in feet ?
Options: a ) 38
b ) 36
c ) 40
d ) 56
e ) 64
Rationale: perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 14.25 ( p ^ 2 ) / 16 = 2 p + 9 p ^ 2 = 32 p + 228 p ^ 2 - 32 p - 228 = 0 p ^ 2 - 38 p + 6 p - 228 = 0 p ( p - 38 ) + 6 ( p + 38 ) = 0 ( p - 38 ) ( p + 6 ) = 0 p = 38 or - 6 discarding negative value , p = 38 answer is a
Answer: a
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 2 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 223.78 , b ) 37.78 , c ) 24.6 , d ) 278.88 , e ) 123.0
Rationale: "explanation : capital = rs . x , then 1 / 2 x = 61.5 x = 123.00 answer : e ) rs . 123.00"
Answer: e
Problem: a fruit seller had some oranges . he sells 20 % oranges and still has 380 oranges . how many oranges he had originally ?
Options: a ) 475 , b ) 700 , c ) 220 , d ) 400 , e ) none of these
Rationale: explanation : he sells 20 % of oranges and still there are 380 oranges remaining = > 80 % of oranges = 380 ⇒ ( 80 × total oranges ) / 100 = 380 ⇒ total oranges / 100 = 4.75 ⇒ total oranges = 4.75 × 100 = 475 answer : option a
Answer: a
Problem: find the mean proportional between 25 & 36 ?
Options: a ) a ) 59 , b ) b ) 30 , c ) c ) 63 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 25 and b = 36 √ 25 × 36 = 5 × 6 = 30 b"
Answer: b
Problem: the compound ratio of 2 / 5 , 6 / 7 , 1 / 3 and 1 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 70 , c ) 1 / 98 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 5 * 6 / 7 * 1 / 3 * 1 / 8 = 12 / 840 = 1 / 70 answer : b"
Answer: b
Problem: p , q and r can do a work in 5 , 7 and 10 days respectively . they completed the work and got rs . 310 . what is the share of q and r respectively ?
Options: a ) 100 and 80 , b ) 100 and 90 , c ) 100 and 110 , d ) 70 and 100 , e ) 100 and 70
Rationale: the ratio of their working rates = 1 / 5 : 1 / 7 : 1 / 10 = 14 : 10 : 7 . since , they work together , the share of q = 10 / 31 * 310 = rs . 100 the share of r = 7 / 31 * 310 = rs . 70 the share of q and r respectively is rs . 100 and rs . 70 answer : e
Answer: e
Problem: what is the average ( arithmetic mean ) of the numbers 16 , 17 , 18 , 19 and 20 ?
Options: a ) 14.2 , b ) 16.5 , c ) 17 , d ) 17.5 , e ) 18
Rationale: "{ 16 , 17 , 18 , 19 , 20 } = { 18 - 2,18 - 1 , 18 , 18 + 1,18 + 2 } - - > the average = 18 . answer : e ."
Answer: e
Problem: a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 267 , d ) 261 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 841 = 261 answer : d"
Answer: d
Problem: a reduction of 21 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.66 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 21 / 100 ) = 21 - - - 10 ? - - - 1 = > rs . 2.1 100 - - - 79 ? - - - 2.1 = > rs . 2.66 answer : a"
Answer: a
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 500 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 500 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 1000 n = 10 satisfies this . a"
Answer: a
Problem: what is the least number should be added to 1156 , so the sum of the number is completely divisible by 25 ?
Options: a ) 19 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "( 1156 / 25 ) gives remainder 6 6 + 19 = 25 , so we need to add 19 answer : a"
Answer: a
Problem: the youngest of 4 children has siblings who are 4 , 5 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: x + ( x + 4 ) + ( x + 5 ) + ( x + 7 ) = 84 4 x + 16 = 84 4 x = 68 x = 17 the answer is d .
Answer: d
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 500 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 6250
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 500 b capital = 37500 * 1 / 6 = 6250 . answer : e"
Answer: e
Problem: in a kilometer race , a beats b by 50 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 50 sec , b ) 190 sec , c ) 287 sec , d ) 74 sec , e ) 697 sec
Rationale: "explanation : time taken by b run 1000 meters = ( 1000 * 10 ) / 50 = 200 sec . time taken by a = 200 - 10 = 190 sec . answer b"
Answer: b
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 6 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 8 1 / 8 km , d ) 9 km , e ) 5 km
Rationale: rs = 5 ¾ - 4 ½ = 1 ¼ t = 6 ½ h . d = 5 / 4 * 13 / 2 = 65 / 8 = 8 1 / 8 km answer : c
Answer: c
Problem: the average of 8 numbers is 25 , that of the first 2 is 20 and of the next 3 is 26 . the sixth number is less than the seventh by 4 , and less than the eighth by 6 . the last number is
Options: a ) 30 , b ) 32 , c ) 40 , d ) 36 , e ) 38
Rationale: explanation : sum of all the numbers = 25 * 8 = 200 sum of first two numbers = 40 sum of next three numbers ( i . e . , 3 rd , 4 th and 5 th ) = 78 so , sum of first five numbers = 118 and sum of 6 th , 7 th and 8 th number = 82 assuming sixth number to be x , we get 7 th number = x + 4 and 8 th number = x + 6 . so , x + ( x + 4 ) + ( x + 6 ) = 82 = > x = 24 . hence , last number ( 8 th number ) = 30 . answer : a
Answer: a
Problem: 18 : 12 seconds : : ? : 6 minutes
Options: a ) 10 , b ) 9 , c ) 20 , d ) 25 , e ) 30
Rationale: 18 * 6 = 12 * x x = 9 answer : b
Answer: b
Problem: a ship going at the speed of 18 km / hr crosses a light house in 20 seconds . what is the length of the train ?
Options: a ) 120 , b ) 150 , c ) 100 , d ) 240 , e ) 200
Rationale: speed = ( 18 x 5 / 18 ) = 5 m / sec . length of the train = ( speed x time ) . length of the train = 5 x 20 m = 100 m . answer : c
Answer: c
Problem: matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days peter stops and peter completes the remaining work in 10 days . in how many days matt complete the work separately .
Options: a ) 28 , b ) 27 , c ) 26 , d ) 25 , e ) 29
Rationale: together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 8 / 20 ) = 25 d
Answer: d
Problem: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 7 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 7 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Problem: a number is increased by 30 % and then decreased by 30 % . find the net increase or decrease per cent .
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 3 % , e ) 6 %
Rationale: "let the number be 100 . increase in the number = 30 % = 30 % of 100 = ( 30 / 100 ã — 100 ) = 30 therefore , increased number = 100 + 30 = 130 this number is decreased by 30 % therefore , decrease in number = 30 % of 130 = ( 30 / 100 ã — 130 ) = 3900 / 100 = 39 therefore , new number = 130 - 39 = 91 thus , net decreases = 100 - 91 = 9 hence , net percentage decrease = ( 9 / 100 ã — 100 ) % = ( 900 / 100 ) % = 9 % answer : a"
Answer: a
Problem: if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 27 , find the value of ab .
Options: a ) 5 , b ) 9 , c ) 4 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 27 - 9 = 18 ab = 9 . answer is b ."
Answer: b
Problem: a man can row his boat with the stream at 19 km / h and against the stream in 11 km / h . the man ' s rate is ?
Options: a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 19 us = 11 s = ? s = ( 19 - 11 ) / 2 = 4 kmph answer : a"
Answer: a
Problem: kamal ' s salary was decreased by 50 % and subsequently increased by 30 % . how much percent does he lose ?
Options: a ) 30 % , b ) 37 % , c ) 65 % , d ) 35 % , e ) 45 %
Rationale: explanation : solution : let original salary = rs . 100 . new final salary = 130 % of ( 50 % of rs . 100 ) = rs . ( 130 / 100 * 50 / 100 * 100 ) = rs . 65 . . ' . decrease = 35 % answer : d
Answer: d
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 9 / 10 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 6 / 100 * 1 + ( 20000 - x ) * 10 / 100 * 1 = 1440 6 x - 8 x = 144000 - 200000 = > - 2 x = - 4000 = > x = 2000 so 18000 / 20000 = 9 / 10 answer - b"
Answer: b
Problem: the ratio of a to b to c is 2 to 3 to 4 , and a , b , c are positive integers . if the average ( arithmetic mean ) of the 3 numbers is 42 , what is the value of a ?
Options: a ) 24 , b ) 25 , c ) 28 , d ) 30 , e ) 32
Rationale: let a = 2 k , b = 3 k , and c = 4 k . a + b + c = 2 k + 3 k + 4 k = 9 k since the average is 42 : 9 k / 3 = 42 3 k = 42 k = 14 then a = 28 . the answer is c .
Answer: c
Problem: what is the dividend . divisor 18 , the quotient is 9 and the remainder is 4
Options: a ) a ) 166 , b ) b ) 148 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158
Rationale: "d = d * q + r d = 18 * 9 + 4 d = 166 answer : a"
Answer: a
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 174 votes . find the total number of valid votes ?
Options: a ) 435 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 174 = > 4 x / 10 = 174 = > 4 x = 1740 = > x = 435 . answer : a"
Answer: a
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 1320 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 1320 = > x = 15 answer : a"
Answer: a
Problem: a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 37 km / hr , b ) 53 km / hr , c ) 36 km / hr , d ) 26 km / hr , e ) 87 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 8 = 45 = > x = 53 km / hr . answer : b"
Answer: b
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 3 : 1 , d ) 1 : 5 , e ) 1 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 2 + 7 / 2 = 6 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6 : 2 = 3 : 1 . answer : c"
Answer: c
Problem: the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 880 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 880 d = 80 the answer is d ."
Answer: d
Problem: 1 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.02775 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 1 / 36 = . 02 something answer ( b )
Answer: b
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 162 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.8 , e ) 2.22
Rationale: "speed = 162 * 5 / 18 = 45 m / sec time taken = 100 / 45 = 2.22 sec . answer : e"
Answer: e
Problem: which number need to add to 956734 to get a number exactly divisible by 412 ?
Options: a ) 345 , b ) 342 , c ) 343 , d ) 342 , e ) 341
Rationale: "956734 / 412 = 2322 and reminder = 70 . 412 - 70 = 342 so , the next number divisible by 412 is 342 places in front of 956734 which means 342 + 956734 = 957076 342 should be added to 956734 b"
Answer: b
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 40 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 2000 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 40 minutes = 15 / 18 * 40 * 60 = 2000 m answer is c"
Answer: c
Problem: a circular wheel radius is 1.75 m . for covering 11 k . m how much time it revolve ?
Options: a ) 10
b ) 100
c ) 1000
d ) 10000
e ) 50
Rationale: distance traveled in 1 round = perimeter = { 2 * 22 / 7 * 175 / 100 } m = 11 m total no . of revolution in covering 11 km = 11000 / 11 = 1000 answer c
Answer: c
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b"
Answer: b
Problem: 0.0006688 / 0.0000150 x 19.85 = ?
Options: a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000
Rationale: "explanation : ? = 6688 / 150 x 19.85 = 45 x 20 = 900 answer : option b"
Answer: b
Problem: find the highest value of ' a ' so that 365 a 24 is divisible by 8 .
Options: a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1
Rationale: "explanation : given , number is divisible by 8 only if ' a 24 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b"
Answer: b
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 70 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 40 , e ) 25
Rationale: "12 * 70 = 840 840 % 21 = 40 answer : d"
Answer: d
Problem: last year a certain bond price with a face value of 5000 yielded 6 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4615 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: interest = 0.06 * 5000 = 0.065 * selling price - - > selling price = 0.06 * 5000 / 0.065 - - > selling price = ~ 4,615 answer : a .
Answer: a
Problem: if 5 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 8 , b ) 6 , c ) 7 , d ) 10 , e ) 9
Rationale: "5 ( log 2 ^ 2 * 5 ^ 2 ) = x 5 log ( 5 * 2 ) ^ 2 = x 5 * 2 log ( 5 * 2 ) = x 10 log 10 = x log 10 base 10 = 1 so 10 * 1 = x x = 10 answer : d"
Answer: d
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 58 %
Options: a ) 18.75 , b ) 19.75 , c ) 26.89 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 58 / 100 = 50.40 so x = 26.89 answer : c"
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 14 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 14 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 14 x = 14 answer : b"
Answer: b
Problem: the population of a town is 7500 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9300 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7500 ã — 100 / 90 ã — 100 / 90 = 9259 a )"
Answer: a
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 7 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 880 , b ) $ 1050 , c ) $ 1280 , d ) $ 1460 , e ) $ 1640
Rationale: "the total surface area is 2 ( 2 * 3 + 3 * 7 + 2 * 7 ) = 82 square feet the total cost is 82 * $ 20 = $ 1640 the answer is e ."
Answer: e
Problem: how many of the positive factors of 24 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 8 , 12 and 24 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 4 answer d"
Answer: d