regisss/math_qa huggingface dataset:
Problem: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 17 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 1,785
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 17 and c = 1 / 2 into the equation and simplify to get the answer 1785 . option e ."
Answer: e
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 180 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 12 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 180 rs . 5 m + 5 m + 5 m - - - - - 180 rs . 15 m - - - - - - 180 rs . = > 1 m = 12 rs . answer : e"
Answer: e
Problem: a train is 250 meter long is running at a speed of 36 km / hour . in what time will it pass a station of 200 meter length ?
Options: a ) 28 seconds , b ) 27 seconds , c ) 45 seconds , d ) 26 seconds , e ) 18 seconds
Rationale: "speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 250 + 200 = 450 meter time = distance / speed = 450 * ( 10 ) = 45 seconds answer : c"
Answer: c
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 72.25 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 85 , e ) 97
Rationale: "explanation : money collected = ( 72.25 x 100 ) paise = 7225 paise . ∴ number of members = √ ( 7225 ) = 85 . answer : d"
Answer: d
Problem: triangle atriangle b are similar triangles with areas 2023 units square and 1792 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 17 : 16 , c ) 23 : 27 , d ) 13 : 17 , e ) 15 : 23
Rationale: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 2023 / 1792 ( x ^ 2 / y ^ 2 ) = ( 17 * 17 * 7 ) / ( 16 * 16 * 7 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 16 ^ 2 x / y = 17 / 16 ans = b you need to take a hint from given options to find factors of 2013 and 2527 ."
Answer: b
Problem: two trains each 120 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 85 km / h while the other travels at 65 km / h . how long will it take for them to pass each other completely .
Options: a ) 11.07 sec , b ) 10.07 sec , c ) 13.07 sec , d ) 12.07 sec , e ) 14.07 sec
Rationale: "explanation : d = 120 m + 120 m = 240 m rs = 85 + 65 = 150 * 5 / 18 = 417 / 10 t = 420 * 10 / 417 = 10.07 sec answer : option b"
Answer: b
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 15,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 20000 , b ) 30000 , c ) 40000 , d ) 30301.5 , e ) 50000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 15,000 ( 1 + 0.04 / 4 ) ^ 4 - 15,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 15,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 15,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 15,000 ( 1.0201 + 1 ) = 30301.5 hence answer is d ."
Answer: d
Problem: the length of a rectangle is reduced by 20 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 14 % , b ) 15 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 20 * 100 ) / ( 100 - 20 ) = 25 % c"
Answer: c
Problem: find the area of a parallelogram with base 10 cm and height 20 cm .
Options: a ) 200 , b ) 384 , c ) 200 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 10 * 20 = 200 cm 2 answer : option c"
Answer: c
Problem: a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be .
Options: a ) 60 kmph , b ) 63 kmph , c ) 57 kmph , d ) 70 kmph , e ) 61 kmph
Rationale: time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer is a .
Answer: a
Problem: if y > 0 , ( 2 y ) / 10 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to y / 5 + 3 y / 10 = 2 y / 5 = 50 % b"
Answer: b
Problem: 200 pupil total , out of 125 like pizza , 115 like burger , then how many like both ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: n ( a u b ) = n ( a ) + n ( b ) - n ( a intersection b ) 200 = 125 + 115 - both both = 240 - 200 = 40 . answer : a
Answer: a
Problem: the area of a rectangular plot is 15 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 15 × b ∴ l = 15 m and l – b = 10 ∴ b = 15 – 10 = 5 m answer b"
Answer: b
Problem: what could be the range of a set consisting of odd multiples of 9 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 72 , e ) 70
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 9 * ( 2 n + 1 ) where n is any positive integer . range = 9 * ( 2 m + 1 ) - 9 * ( 2 n + 1 ) = 9 * 2 * ( m - n ) = 18 * ( m - n ) . m , n - any positive integers the answer must be divisible by 18 , which is only 72 . the correct answer is d"
Answer: d
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 10 % p . a . was rs . 420 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 2530 , b ) rs . 2430 , c ) rs . 2420 , d ) rs . 2410 , e ) rs . 2440
Rationale: "let the sum be rs . p p { [ 1 + 10 / 100 ] 2 - 1 } = 420 p ( 10 / 100 ) ( 2 + 10 / 100 ) = 420 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 420 / ( 0.1 ) ( 2.1 ) = 2000 . amount = 2000 + 420 = rs . 2420 answer : c"
Answer: c
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 25 meters . what distance is she from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 45 m east
Rationale: the net distance is 20 + 25 = 45 meters to the east . the answer is e .
Answer: e
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 4 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 5 : 4 , b ) 7 : 6 , c ) 9 : 8 , d ) 11 : 10 , e ) 13 : 12
Rationale: "3 b = 7 c and so b = 7 c / 3 7 a = 4 b and so a = 4 b / 7 = 4 c / 3 a + b = 4 c / 3 + 7 c / 3 = 11 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 11 : 10 the answer is d ."
Answer: d
Problem: a man can swim in still water at 3 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 1.4 , c ) 1.1 , d ) 1.5 , e ) 1
Rationale: "m = 3 s = x ds = 3 + x us = 3 + x 3 + x = ( 3 - x ) 2 3 + x = 6 - 2 x 3 x = 3 x = 1 answer : e"
Answer: e
Problem: a man gains 30 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 140 % , c ) 150 % , d ) 260 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 130 / 100 ) x = 13 x / 10 new s . p . = 2 ( 13 x / 10 ) = 26 x / 10 profit = 26 x / 10 - x = 26 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 26 x / 10 ) * ( 1 / x ) * 100 = 260 % option d"
Answer: d
Problem: a train traveled the first d miles of its journey it an average speed of 50 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 96 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 90 , d ) 120 , e ) 160
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 50 + d / y + d / 160 = 96 solving for d and y , 15 y = 11 y + 480 3 y = 480 y = 160 answer e"
Answer: e
Problem: 2 persons can finish a job in 8 days . first person alone can finish the work in 24 days . how many days does the second person take to finish the job ?
Options: a ) 10 days , b ) 12 days , c ) 14 days , d ) 16 days , e ) 18 days
Rationale: 2 persons can do work in 1 day = 1 / 8 first person can do work in 1 day = 1 / 24 second person can do work in 1 day = 1 / 8 - 1 / 24 = 1 / 12 so second person can finish work in 12 days answer : b
Answer: b
Problem: a cistern is filled by pipe a in 12 hours and the full cistern can be leaked out by an exhaust pipe b in 18 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 36 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 12 - 1 / 18 ) hrs = 1 / 36 = 36 hrs answer : c"
Answer: c
Problem: | x + 3 | – | 4 - x | = | 8 + x | how many x solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "x = | x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
Answer: a
Problem: of the 100 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 20 answer : option a"
Answer: a
Problem: a number x is multiplied by 3 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 3 / 7 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 3 x / 7 ) to be perfect square x has to 3 / 7 ans : b"
Answer: b
Problem: the list price of an article is rs . 70 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 10.85 % , b ) 14.85 % , c ) 15.85 % , d ) 16.85 % , e ) 17.85 %
Rationale: "70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 10.85 % answer : a"
Answer: a
Problem: a man swims downstream 42 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 6 , e ) 10
Rationale: "42 - - - 3 ds = 14 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 14 + 6 ) / 2 = 10 answer : e"
Answer: e
Problem: a starts business with rs . 3500 and after 8 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 15750 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 8 = 4 months . so there profit ratio = ( 3500 ã — 12 ) : ( 4 x ) = 2 : 3 â ‡ ’ x = 15750 answer : d"
Answer: d
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 914800 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 9 , e ) 13
Rationale: joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 914800 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 9148 so we have 1 , 3 , 9 , 27 . . . . . 914800 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 9148 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 9148 x - 2 = 1 - 3 ^ n - 19682 = 1 - 3 ^ n - 19682 = - 3 ^ n 19683 = 3 ^ n ( negatives cancel out ) 19863 can also be re written as 3 ^ 9 therefore ; 3 ^ 9 = 3 ^ n thus n = 9 ( d )
Answer: d
Problem: 5 20 380 144020 ?
Options: a ) 20741616380 , b ) 20841616380 , c ) 21741616380 , d ) 22741616380 , e ) 20791616380
Rationale: "if number = n , then next number = n * ( n - 1 ) so 5 , ( 5 * 4 = 20 ) , ( 20 * 19 = 380 ) , ( 380 * 379 = 144020 ) , ( 144020 * 144019 = 20741616380 ) answer : a"
Answer: a
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4538 , b ) s . 6342 , c ) s . 4518 , d ) s . 4530 , e ) s . 4517
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 7 = rs . 6342 answer : b"
Answer: b
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) 160 m
Rationale: "relative speed = 81 km / h = 81 x 5 / 18 m / sec = 22.5 m / sec length of slower train = speed x time = 36 x 8 km / hr = 288 x 5 / 18 m / sec = 80 m / sec let length of faster train = b time cross to each other 8 = ( 80 + b ) x 18 / ( 81 x 5 ) = 3240 - 1440 = 18 b 1800 / 18 = b b = 100 m answer : b"
Answer: b
Problem: if the mean of numbers 28 , x , 42 , 78 and 104 is 62 , then what is the mean of 128 , 255 , 280 , 511 , 1023 and x ?
Options: a ) 395 , b ) 375.8 , c ) 355 , d ) 415 , e ) 365
Rationale: "the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 62 * 5 - - > x = 58 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 280 + 511 + 1023 + 58 ) / 6 = 375.8 . answer : b ."
Answer: b
Problem: the grade point average of the entire class is 80 . if the average of one fourth of the class is 92 , what is the average of the rest of the class ?
Options: a ) 73 , b ) 74 , c ) 75 , d ) 76 , e ) 77
Rationale: let x be the number of students in the class . let p be the average of the rest of the class . 80 x = ( 1 / 4 ) 92 x + ( 3 / 4 ) ( p ) x 320 = 92 + 3 p 3 p = 228 p = 76 . the answer is d .
Answer: d
Problem: the compound interest earned on a sum for the second and the third years are $ 1200 and $ 1260 respectively . what is the rate of interest ?
Options: a ) 5 % , b ) 8 % , c ) 11 % , d ) 14 % , e ) 18 %
Rationale: "1260 - 1200 = 60 is the rate of interest on $ 1200 for one year . the rate of interest = ( 100 * 60 ) / ( 1200 ) = 5 % the answer is a ."
Answer: a
Problem: a fair 2 sided coin is flipped 7 times . what is the probability that tails will be the result at least twice , but not more than 7 times ?
Options: a ) 119 / 128 , b ) 120 / 113 , c ) 114 / 210 , d ) 121 / 141 , e ) 104 / 117
Rationale: "at least twice , but not more than 7 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 7 c 2 / 2 ^ 7 + 7 c 3 / 2 ^ 7 + 7 c 4 / 2 ^ 7 + 7 c 5 / 2 ^ 7 + 7 c 6 / 2 ^ 7 = 119 / 128 option : a"
Answer: a
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent q of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march q = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e
Answer: e
Problem: the s . i . on a certain sum of money for 2 years at 4 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 5250 , b ) 1267 , c ) 5750 , d ) 2267 , e ) 5262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 5250 answer : a"
Answer: a
Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 181 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 6564
b ) 7372
c ) 8281
d ) 9331
e ) can not be determined
Rationale: let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 181 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 181 ( x + y ) ( x - y ) = 181 181 is a prime number and thus it will be ( 91 + 90 ) * ( 91 - 90 ) . thus x = 91 and y = 90 x ^ 2 = 91 ^ 2 = 8281 the answer is c .
Answer: c
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 9.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 8 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.095 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 95 f - - > s = f - - > f / s = 1 / 12 - - > f / ( s + f ) = 1 / ( 1 + 12 ) = 1 / 13 = 0.08 . answer : b ."
Answer: b
Problem: how many of the positive divisors of 720 are also multiples of 4 not including 720 ?
Options: a ) 11 , b ) 12 , c ) 17 , d ) 18 , e ) 24
Rationale: "720 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 ^ 2 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 2 , and 1 . there are ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 720 . the answer is c ."
Answer: c
Problem: ( p / q - q / p ) = 21 / 10 . then find 4 p / q + 4 q / p ?
Options: a ) 58 / 9 , b ) 58 / 5 , c ) 58 / 7 , d ) 58 / 2 , e ) 58 / 1
Rationale: let p / q = a , then ( a - 1 / a ) = 21 / 10 ⇒ a 2 − 1 = a . 2110 ⇒ a 2 − 1 = a . 2110 ⇒ 10 a 2 − 21 a − 10 ⇒ 10 a 2 − 21 a − 10 = 0 roots of the equation = − b ± b 2 − 4 ac − − − − − − − √ 2 a − b ± b 2 − 4 ac 2 a a = 21 ± 441 + 400 − − − − − − − − √ 2021 ± 441 + 40020 a = 21 ± 292021 ± 2920 = 5 / 2 or - 2 / 5 for a = 5 / 2 , 4 p / q + 4 q / p = 58 / 5 for a = - 2 / 5 , 4 p / q + 4 q / p = - 58 / 5 answer : b
Answer: b
Problem: a jar was full with honey . a person used to draw out 20 % of the honey from the jar and replaced it with sugar solution . he has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar , the rest part of the jar was filled with the sugar solution . the initial amount of honey in the jar was filled with the sugar solution . the initial amount of honey in the jar was :
Options: a ) 1.25 kg , b ) 1.29 kg , c ) 1.85 kg , d ) 3.25 kg , e ) 1.23 kg
Rationale: answer : a ) 1.25 kg
Answer: a
Problem: a pupil ' s marks were wrongly entered as 85 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 26
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 45 ) = > x / 2 = 40 = > x = 80 . answer : b"
Answer: b
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 8,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 1600
Rationale: "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 20 % . here you find per quarter rate as ( 20 / 4 ) % = 5 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 8,000 = $ 1600 as our answer . but since , the interest is compounded , it will be a bit more than $ 1600 . option ( e ) looks correct ."
Answer: e
Problem: the ratio of two numbers is 2 / 3 , and if a 1 is subtracted from the numerator and a 1 is added to the remainder the ratio becomes 1 / 2 , then the numbers are .
Options: a ) 6 and 9 , b ) 6 and 10 , c ) 6 and 8 , d ) 6 and 7 , e ) 6 and 11
Rationale: a : b = 2 : 3 b = 3 / 2 a a - 1 / b + 1 = 1 / 2 solving this we get a = 6 and b = 9 answer : a
Answer: a
Problem: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 280 , c ) 322 , d ) 345 , e ) 354
Rationale: "clearly , the numbers are ( 20 x 13 ) and ( 20 x 14 ) . larger number = ( 20 x 14 ) = 280 . answer : option b"
Answer: b
Problem: two cubes of their volumes in the ratio 64 : 125 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5
Rationale: "the ratio of their surface area is 64 : 125 4 : 5 answer is e ."
Answer: e
Problem: if the average of 16 x and 8 y is greater than 80 , and x is twice y , what is the least integer value of x ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 16 x and 4 x is greater than 80 . average of 16 x and 4 x is 10 x . so , 10 x > 80 x > 8 answer : a"
Answer: a
Problem: what is the square root of 168,921 ?
Options: a ) 476 , b ) 389 , c ) 497 , d ) 411 , e ) 524
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) b = 389 ^ 2 and d = 411 ^ 2 b = ( 400 - 11 ) ^ 2 and d = ( 400 + 11 ) ^ 2 since we need the answer less than 160000 = > b is out . thus we have d as the ans ."
Answer: d
Problem: if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22 , what is the value of r - p ?
Options: a ) 20 , b ) 10 , c ) 30 , d ) 24 , e ) 5
Rationale: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 44 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 24 hence , the correct answer is d"
Answer: d
Problem: a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 26 , e ) 10
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . ( x + 28 ) + 2 = 2 ( x + 2 ) x + 30 = 2 x + 4 = > x = 26 . answer : d"
Answer: d
Problem: in an examination , 30 % of total students failed in hindi , 42 % failed in english and 28 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 37 , c ) 56 , d ) 40 , e ) 81
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 30 + 42 â € “ 28 = 44 therefore students who passed = 100 â € “ 44 = 56 . answer : c"
Answer: c
Problem: a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is : ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 67 , e ) 30
Rationale: "let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c"
Answer: c
Problem: two trains travelling in the same direction at 50 and 40 kmph completely pass off another in 1 1 / 2 minute . if the length of the first train is 125 m , what is the length of the second train ?
Options: a ) 300 m , b ) 287 m , c ) 125 m , d ) 250 m , e ) 167 m
Rationale: rs = 50 â € “ 40 = 10 * 5 / 18 = 25 / 9 mps t = 90 sec d = 25 / 9 * 90 = 250 m 125 - - - - - - - - 125 m answer : c
Answer: c
Problem: a man can row upstream at 25 kmph and downstream at 31 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 28 , c ) 30 , d ) 27 , e ) 18
Rationale: "us = 25 ds = 31 m = ( 31 + 25 ) / 2 = 28 answer : b"
Answer: b
Problem: a , b , c can complete a piece of work in 24 , 8,12 days . working together , they complete the same work in how many days ?
Options: a ) 4 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 24 + 1 / 8 + 1 / 12 = 6 / 24 = 1 / 4 a , b , c together will complete the job in 4 days answer is a"
Answer: a
Problem: a cricket player whose bowling average was 23.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 131 , d ) 456 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 23.5 w + 52 total wickets after last match = w + 5 ( 23.5 w + 52 ) / ( w + 5 ) = 23.5 - 0.5 = 23 w = 126 so total wickets aftr last match = w + 5 = 131 answer : c"
Answer: c
Problem: on dividing 52 by a number , the quotient is 16 and the remainder is 4 . find the divisor ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = ( d - r ) / q = ( 52 - 4 ) / 16 = 48 / 16 = 3 b )"
Answer: b
Problem: how many different positive integers are factors of 20 ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 10 , e ) 12
Rationale: "2 * 10 4 * 5 answer : c"
Answer: c
Problem: jim â € ™ s taxi service charges an initial fee of $ 2.5 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.65 , e ) $ 5.40
Rationale: "let the fixed charge of jim â € ™ s taxi service = 2.5 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.5 + ( 3.6 / . 4 ) * . 35 = 2.5 + 9 * . 35 = 5.65 $ answer d"
Answer: d
Problem: if the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches , then the face of greatest area is of what area ?
Options: a ) 225 square inches
b ) 45 square inches
c ) 25 square inches
d ) 15 square inches
e ) 10 square inches
Rationale: definitely ( d ) 5 * 3 = 15 sq inches the question asks to find the greatest area of the faces of a cuboid the possible area of the faces are - length * breadth , breadth * height & height * length the possible areas are - 6 , 10 & 15 thus 15 is the greatest possible area . . . . answer : d
Answer: d
Problem: at a certain university , 66 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 60 , d ) 62.5 , e ) 75
Rationale: "answer is 75 % total women = 66 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 24 % but question wants to know the percent of men that are tenured 24 % / 40 % = 60 % c"
Answer: c
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 50 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 49 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.5 = $ 14 - - > x = $ 28 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 28 + 21 = $ 49 . answer : b .
Answer: b
Problem: excluding stoppages , the speed of a bus is 58 kmph and including stoppages , it is 40 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 19 , b ) 19.13 , c ) 10.5 , d ) 11.35 , e ) none of these
Rationale: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( ( 18 / 58 ) ã — 60 ) = 19 min . option ( a ) is correct"
Answer: a
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 430 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 465 , c ) 430 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 430 + x * 110 = ( x + 15 ) 120 x = 465 b"
Answer: b
Problem: what is the 149 th digit to the right of the decimal point in the decimal form of 30 / 33 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 0 , e ) 1
Rationale: to solve , we first have to use some long division . long division allows us to get 30 / 33 in decimal form , which is 0.909090 … where “ 90 ” is repeating . we see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 9 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 0 . in other words , each odd - positioned digit is a 9 , and each even - positioned digit is a 0 . then the 149 th digit to the right of the decimal point and we see that 149 is odd , then 149 th digit is a 9 . answer c .
Answer: c
Problem: the salary of a person was reduced by 14 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 16.3 % , c ) 13.7 % , d ) 15.1 % , e ) 12.3 %
Rationale: let the original salary be $ 100 new salary = $ 86 increase on 86 = 14 increase on 100 = 14 / 86 * 100 = 16.3 % answer is b
Answer: b
Problem: 11 times a number gives 132 . the number is
Options: a ) 11 , b ) 12 , c ) 13.2 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 11 × n = 132 ⇒ n = 12 correct option : b"
Answer: b
Problem: a bullet train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the bullet train must run to reduce the time of journey to 40 min will be .
Options: a ) 80 kmph , b ) 40 kmph , c ) 60 kmph , d ) 90 kmph , e ) 30 kmph
Rationale: c 60 kmph time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph
Answer: c
Problem: the area of a triangle is with base 12 m and height 5 m ?
Options: a ) 88 m 2 , b ) 30 m 2 , c ) 66 m 2 , d ) 77 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 12 * 5 = 30 m 2 answer : b"
Answer: b
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 2 / 7 , d ) 10 / 21 , e ) 5 / 11
Rationale: from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 7 . the answer is c .
Answer: c
Problem: one half of a two digit number exceeds its one third by 9 . what is the sum of the digits of the number ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 7 , d ) d ) 9 , e ) e ) 11
Rationale: "x / 2 – x / 3 = 9 = > x = 54 5 + 4 = 9 answer : d"
Answer: d
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 360 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 360 per week 36 x = 360 x = 10 correct option : b"
Answer: b
Problem: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 15 and 12 . the larger of the two numbers is
Options: a ) 476 , b ) 399 , c ) 450 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 30 x 15 ) and ( 30 x 12 ) . larger number = ( 30 x 15 ) = 450 . answer c"
Answer: c
Problem: the difference between the place values of two nines in the numerical 62039295 is
Options: a ) 89 , b ) 891 , c ) 8910 , d ) 0 , e ) none of them
Rationale: "required difference = ( 9000 - 90 ) = 8910 . answer is c"
Answer: c
Problem: dacid obtained 90 , 92 , 85 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 88 , d ) 90 , e ) 75
Rationale: "average = ( 90 + 92 + 85 + 87 + 85 ) / 5 = 439 / 5 = 87.8 . answer : c"
Answer: c
Problem: in a group of 6 boys and 4 girls , four children are to be selected . in how many different ways can they be selected ?
Options: a ) 159 , b ) 194 , c ) 210 , d ) 209 , e ) 166
Rationale: "out of 10 students 4 children should to be selected . so the combination will be 10 c 4 . 10 c 4 = 10 ! / 6 ! * 4 ! = 10 * 9 * 8 * 7 * 6 ! / 6 ! * ( 4 * 3 * 2 * 1 ) 10 c 4 = 210 there are 210 differect possible ways to select 4 children out of 10 students ."
Answer: c
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 360 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 96
b ) 108
c ) 120
d ) 132
e ) 140
Rationale: the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 360 = 96 the answer is a .
Answer: a
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 55 years . what is the age of the youngest child ?
Options: a ) 5 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
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 . age of the youngest child = x = 5 years . a )"
Answer: a
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 25 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 576 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 125 ) = 115.2 . face value = rs . ( 100 x 115.2 ) = rs . 11520 . annual income = rs . ( 5 / 100 x 11520 ) = rs . 576 . answer a"
Answer: a
Problem: a ladder 22 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 7 feet from the base of the wall . if the top of the ladder slips down 3 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 12.86 , b ) 15 , c ) 18 , d ) 19 , e ) 25
Rationale: "22 ^ 2 - 7 ^ 2 = 435 it means that the height is equal to 20.85 . since the top of the ladder slips down 4 feet , then the height of the wall = 20.85 - 3 = 17.85 the bottom = sqrt ( 22 ^ 2 - 17.85 ^ 2 ) = sqrt ( 484 - 318.62 ) = 12.86 ans is a"
Answer: a
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 117 grams of water ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: ( 2 / 18 ) * 117 = 13 grams the answer is d .
Answer: d
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 24 km / h , what is the circumference of the tire ?
Options: a ) 1 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 24,000 m : c is the circumference c = 1 meters correct answer a"
Answer: a
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 7 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 15 , d ) 8 / 15 , e ) 11 / 60
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 7 = 245 remaining work is 300 - 245 = 55 remaining fraction of work is = 55 / 300 = 11 / 60 answer e"
Answer: e
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.75 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 500 , d ) 1500 , e ) 590
Rationale: n * 50 = ( 375000 - 300000 ) = 75000 n = 75000 / 50 = 1500 d
Answer: d
Problem: 40 % of a number is added to 60 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 100 , e ) 281
Rationale: "( 40 / 100 ) * x + 60 = x 4 x + 600 = 10 x 6 x = 600 x = 100 answer : d"
Answer: d
Problem: in right triangle abc , ac is the hypotenuse . if ac is 35 and ab + bc = 55 , what is the area of the triangle abc ?
Options: a ) 225 , b ) 450 , c ) 25 √ 2 , d ) 200 , e ) 200 √ 2
Rationale: "square ab + bc = 55 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 3025 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 35 ^ 2 = 1225 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 1225 + 2 * ab * bc = 3025 . 1225 + 2 * ab * bc = 3025 . ab * bc = 900 . the area = 1 / 2 * ab * bc = 450 . answer : b ."
Answer: b
Problem: what is the smallest integer that is multiple of 5 , 711
Options: a ) a ) 70 , b ) b ) 35 , c ) c ) 385 , d ) d ) 280 , e ) e ) 140
Rationale: it is the lcm of 5 , 7 and 11 which is 385 . the answer is c .
Answer: c
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 7 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 5 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 7 = 6 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = 6 / 10 = 3 / 5 answer c"
Answer: c
Problem: the average waight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 23 kg , b ) 43 kg , c ) 21 kg , d ) 31 kg , e ) 43 kg
Rationale: sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d
Answer: d
Problem: a father is now 3 times as old as his son . 8 years back , he was 4 times as old as his son . the age of the son ( in years ) is
Options: a ) 12 , b ) 24 , c ) 18 , d ) 27 , e ) 25
Rationale: if father ' s age is f and son ' s age is s , then f = 3 s and f - 8 = 4 * ( s - 8 ) 3 s - 5 = 4 s - 32 s = 24 f = 72 years answer : b
Answer: b
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 40 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,360 , e ) $ 30,960
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 40 % of the benefit ; benefit received = 12000 - 0.4 * 12000 = 12000 - 4800 x = 7200 earning becomes 9360 + 3 x = 9360 + 3 * 7200 = 30960 ans : e"
Answer: e
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 40 per square m ?
Options: a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 38000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 40 * 950 = rs . 38000 d"
Answer: d
Problem: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses e at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) e = 256 , d ) e = 384 , e ) e = 480
Rationale: "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Problem: rajani has to read a book of 445 pages . she has already read the first 157 pages of the book and if she reads 24 pages of the book everyday then how long will she take now to complete the book ?
Options: a ) 25 days , b ) 20 days , c ) 46 days , d ) 21 days , e ) none of these
Rationale: remaining pages to read = 445 – 157 = 288 ∴ reqd . number of days = 288 ⁄ 24 = 12 answer e
Answer: e
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer k such that k + n is a multiple of 21 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 7 q + 5 n + 2 = 3 p + 3 = 7 q + 7 n + 2 is a multiple of 3 and 7 , so it is a multiple of 21 . the answer is a ."
Answer: a
Problem: a sum of money becomes 7 / 6 of itself in 7 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 13 , b ) 50 / 17 , c ) 50 / 19 , d ) 50 / 21 , e ) 50 / 23
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 7 years . rate = ( 100 * x ) / ( x * 6 * 7 ) = 50 / 21 % . answer : d"
Answer: d
Problem: a ship 77 km from the shore , springs a leak which admits to 9 / 4 tonnes of water in 11 / 2 minutes . 92 tonnes of water would sink it . but the pumps can throw out 12 tonnes of water per hour . find the average rate of sailing so that the ship may just reach the shore as it begins to sink .
Options: a ) 10.5 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: leak admits 9 / 4 tonnes water in 11 / 2 min = 11 / 2 * 4 / 9 = 22 / 9 leak admits 9 / 22 tonne of water in 5 min in 1 min in thrws 1 / 5 tonne of water = 9 / 22 - 1 / 5 = 23 / 110 92 / 23 / 11 min = 440 min 22 / 3 min = 7 / 22 / 22 / 3 = > 10.5 km / hr answer a
Answer: a
Problem: a library has an average of 600 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 260 , c ) 300 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 600 x 5 + 240 x 25 ) / 30 ) = 300 answer : option c"
Answer: c
Problem: the lcm of two numbers is 2310 and hcf is 30 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 30 / 210 = 11 * 30 = 330 answer : c"
Answer: c