regisss/math_qa huggingface dataset:
Problem: in a group of cows and hens , the number of legs are 18 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 18 4 x + 2 y = 2 x + 2 y + 18 2 x = 18 x = 9 . answer : c"
Answer: c
Problem: the area of rectangular field is 460 square metres . if the length is 15 per cent more than the breadth , what is the breadth of the rectangular field ?
Options: a ) 15 metres
b ) 26 metres
c ) 34.5 metres
d ) can not be determined
e ) none of these
Rationale: let the breadth of the rectangular field be ‘ x ’ m . then , length of the field will be x + x × 15 / 100 = 23 x / 20 now , x × 23 x / 20 = 460 or , 23 x 2 = 460 × 20 or , x 2 = 20 × 20 or , x = 20 m answer e
Answer: e
Problem: sum of the squares of 3 no . is 252 and the sum of their products taken two at a time is 116 . find the sum ?
Options: a ) 24 , b ) 33 , c ) 22 , d ) 20 , e ) 21
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 252 + 2 * 116 a + b + c = â ˆ š 484 = 22 answer c"
Answer: c
Problem: a train 120 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 450 m , d ) 380 m , e ) 250 m
Rationale: "d 350 d = 72 * 5 / 18 = 25 = 500 â € “ 120 = 380"
Answer: d
Problem: an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 60 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 35 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 35 / 256 . d"
Answer: d
Problem: the positive numbers w , x , y , and z are such that x is 35 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 20 - answer c"
Answer: c
Problem: evaluate : 22 + sqrt ( - 4 + 6 * 4 * 3 ) = ?
Options: a ) 4 , b ) 14 , c ) 24 , d ) 34 , e ) 44
Rationale: "according to order of operations , inner brackets first where 6 ? 4 ? 3 is first calculated since it has a multiplication and a division . 6 * 4 * 3 = 24 * 3 = 8 hence 22 + sqrt ( - 4 + 6 * 4 * 3 ) = 22 + sqrt ( - 4 + 8 ) = 22 + sqrt ( 4 ) = 22 + 2 = 24 correct answer c"
Answer: c
Problem: the width of a rectangle is 10 mtr and its area is 150 square meter . if length of the rectangle is increased , then its new area is 1 ( 1 / 3 ) times of the original area . what is the new perimeter of the rectangle ?
Options: a ) 45
b ) 54
c ) 67
d ) 60
e ) 69
Rationale: ans . ( d ) sol . length of original rectangle = 150 / 10 = 15 ( 10 * ( 15 + x ) ) / ( 10 * 15 ) = 4 / 3 x = 5 perimeter of new rectangle = 2 ( 10 + 20 ) = 60
Answer: d
Problem: how long will a boy take to run round a square field of side 40 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 64 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 40 * 4 = 160 m time taken = 160 * 2 / 5 = 64 sec answer is a"
Answer: a
Problem: the side of a square is increased by 40 % then how much % does its area increases ?
Options: a ) 96 , b ) 56.25 , c ) 50.75 , d ) 42.75 , e ) 52.75
Rationale: "a = 100 a 2 = 10000 a = 140 a 2 = 19600 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 9600 100 - - - - - - - ? = > 96 % answer : a"
Answer: a
Problem: a runs twice as fast as b and gives b a start of 83 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 83 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 83 m is 83 / 1 = 83 m so the total time taken by a and b to reach = 2 * 83 = 166 m answer : e"
Answer: e
Problem: two trains 190 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.7 , b ) 10.9 , c ) 10.6 , d ) 12.6 , e ) 18.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 190 + 160 = 350 m . required time = 350 * 9 / 250 = 12.6 sec . answer : d"
Answer: d
Problem: if a square mirror has a 20 - inch diagonal , what is the approximate perimeter w of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter w must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Problem: 10 litres of water are poured into an aquarium of dimensions 50 cm length , 20 cm breadth , and 40 cm height . how high ( in cm ) will the water rise ? ( 1 litre = 1000 cm ³ )
Options: a ) 6 , b ) 8 , c ) 10 , d ) 20 , e ) 40
Rationale: lxbxh = 10000 h = 10000 / 50 * 20 = 10 cm ' c ' is the answer .
Answer: c
Problem: a retailer sells 10 shirts . the first 3 he sells for $ 82 , $ 100 and $ 90 . if the retailer wishes to sell the 10 shirts for an overall average price of over $ 100 , what must be the minimum average price of the remaining 7 shirts ?
Options: a ) $ 100.00 , b ) $ 104.00 , c ) $ 110.00 , d ) $ 115.00 , e ) $ 119.00
Rationale: first 3 shirts are sold for $ 82 , $ 100 and $ 90 = $ 272 . to get average price of $ 100 , total sale should be 10 * $ 100 = $ 1000 so remaining 7 shirts to be sold for $ 1000 - $ 272 = $ 728 answer should be 728 / 7 = $ 104.00 that is b
Answer: b
Problem: a train running at the speed of 90 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 225 meter , b ) 200 meter , c ) 250 meter , d ) 210 meter , e ) 230 meter
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 9 = 225 meter answer : a"
Answer: a
Problem: what is the total number of integers between 20 and 80 ( exclusive ) that are divisible by 10 ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 9 , e ) 3
Rationale: "30 , 40,50 , 60,70 total 5 answer is a"
Answer: a
Problem: a mixture of 85 kg contains milk and water in the ratio 27 : 7 . how much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1 ?
Options: a ) 5 kg , b ) 6.5 kg , c ) 7.5 kg , d ) 8 kg , e ) 9 kg
Rationale: explanation : expl : milk in 85 kg of mix = 85 * ( 27 / 34 ) = 135 / 2 kg . water in it = 85 - 135 / 2 = 35 / 2 kg . let x kg of water be added to it . then , ( 135 / 2 ) / ( 35 / 2 + x ) = 3 / 1 ; 135 / ( 35 + 2 x ) = 3 / 1 ; 105 + 6 x = 135 ; 6 x = 30 ; x = 5 the quantity of water to be added = 5 kg answer : a
Answer: a
Problem: what is the sum of all the multiples of 25 between 30 and 100 ?
Options: a ) 800 , b ) 625 , c ) 600 , d ) 250 , e ) 200
Rationale: "you first have to know all the multiples of 25 between 30 and 100 . they are 25 , 50,75 and 100 . if you add all these numbers together , you get 250 . final answer : d"
Answer: d
Problem: the product of a and b is equal to 12 more than twice the sum of a and b . if b = 10 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 6 , e ) 35
Rationale: ab = 12 + 2 ( a + b ) 10 a = 12 + 2 a + 20 8 a = 32 a = 4 b - a = 10 - 4 = 6 d is the answer
Answer: d
Problem: a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 5.4 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 6 min , e ) 3 min
Rationale: "s = 600 / 40 = 15 mps s = 5400 / 15 = 360 sec = 6 min . answer : d"
Answer: d
Problem: there are 7 stores in town that had a total of 21 visitors on a particular day . however , only 11 people went shopping that day ; some people visited more than one store . if 7 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 9 , e ) 2
Rationale: "7 people visited 2 stores each for 14 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 14 - 3 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Problem: what is the largest 4 digit number exactly divisible by 12 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9996
Rationale: "largest 4 digit number = 9999 9999 ÷ 12 = 833 , remainder = 3 hence largest 4 digit number exactly divisible by 12 = 9999 - 3 = 9996 answer : e"
Answer: e
Problem: the length of a rectangulat plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 40 , b ) 50 , c ) 200 , d ) 120 , e ) none
Rationale: solution let breadth = x metres then , length = ( x + 20 ) metres . perimeter = ( 5300 / 26.50 ) m = 200 m answer c
Answer: c
Problem: if two positive numbers are in the ratio 1 / 8 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 14.3 % . , b ) 70 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: given ratio = 1 / 8 : 1 / 7 = 7 : 8 let first number be 7 x and the second number be 8 x . the second number is more than first number by 1 x . required percentage = 1 x / 7 x * 100 = 14.3 % . answer : a
Answer: a
Problem: ashok secured average of 79 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 104 , b ) 27 , c ) 99 , d ) 17 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 79 therefore total marks in 6 subjects = 79 * 6 = 474 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 474 – 370 = 104 answer : a"
Answer: a
Problem: johnny makes $ 4.75 per hour at his work . if he works 6 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
Rationale: 4.75 * 6 = 28.50 . answer is c .
Answer: c
Problem: the sale price sarees listed for rs . 150 after successive discount is 20 % and 10 % is ?
Options: a ) 187 , b ) 120 , c ) 108 , d ) 178 , e ) 175
Rationale: "150 * ( 80 / 100 ) * ( 90 / 100 ) = 108 answer : c"
Answer: c
Problem: the difference between a number and its three fifth is 50 . what is the number ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 180 , e ) none
Rationale: "solution let the number be x . then , x - 3 / 5 x = 50 ‹ = › 2 / 5 x = 50 ‹ = › x = ( 50 x 5 / 2 ) ‹ = › 125 . answer c"
Answer: c
Problem: a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 20 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 14 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 20 ] = 14 m answer c"
Answer: c
Problem: how many liters of water must be added to 14 liters of milk and water containing 10 % water to make it 30 % water ?
Options: a ) 1 liter , b ) 2 liters , c ) 3 liters , d ) 4 liters , e ) 5 liters
Rationale: by rule of alligation : 30 % - 10 % = 20 % 100 % - 30 % = 70 % quantity of pure water : quantity of the mixture = 2 : 7 there are 14 liters of mixture , so we need to add 4 liters of pure water . the answer is d .
Answer: d
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 4,4 ) , and ( 4,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "if x + y < 4 , then y < - x + 4 . the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 16 . p ( x + y < 4 ) = 8 / 16 = 1 / 2 the answer is a ."
Answer: a
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 6 years ?
Options: a ) 14300 , b ) 29859 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 6 = 29859 b )"
Answer: b
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 58000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 37.4 %
Rationale: ( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 130000 = 36 / 65 . 36 / 65 is a little above 36 / 72 = 1 / 2 . thus , our answer is just a little above 35 . answer : d
Answer: d
Problem: a basketball player is shooting hoops . he shoots a free throw , a high school 3 - pointer , and then a professional 3 - pointer . the probability that he makes the free throw is 4 / 5 , the probability that he makes the high school 3 - pointer is 1 / 2 , and the probability that he makes the professional 3 - pointer is 1 / 3 . what is the probability that he makes at least one of the 3 shots ?
Options: a ) 14 / 15 , b ) 15 / 16 , c ) 17 / 18 , d ) 9 / 10 , e ) 5 / 6
Rationale: the probability that he makes at least one of the three shots = 1 - ( the probability that he misses all of the shots ) the probability that he misses all shots = ( prob that he misses free throw ) * ( prob that he misses 3 - pointer ) * ( prob that he misses the professional 3 - pointer ) prob that he misses the free throw = 1 - 4 / 5 = 1 / 5 ; prob that he misses the 3 - pointer = 1 - 1 / 2 = 1 / 2 ; prob that he misses the professional 3 - pointer = 1 - 1 / 3 = 2 / 3 thus the probability that he misses all shots = ( 1 / 5 ) * ( 1 / 2 ) * ( 2 / 3 ) = 1 / 15 answer : 1 - 1 / 15 = 14 / 15 a
Answer: a
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 28 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 392 , b ) 412 . , c ) 432 . , d ) 502 , e ) 522
Rationale: "solution 1 : given that number of pastries are equally divided in to 28 groups , so the answer should be a multiple of 28 . and in the given choices , only 392 is divisible by 28 with remainder 0 ( make sure others are no multiples of 28 ) . so this is good enough to stop here , but to verify , 392 / 28 = 14 and 392 / 49 = 8 , which confirms the second part of question , 14 - 8 , 6 pastry short of each customer . solution 2 : going mathematical , expressing in the equation form , let x be the number of pastries and , n be the number of customers in 28 groups . so , x = 28 * n , as per second statement , x = 49 * ( n - 6 ) solve the above 2 for n and then we get x as 392 . answer is a : 392 ."
Answer: a
Problem: what decimal of an hour is a second
Options: a ) . 0028 , b ) . 0027 , c ) . 0026 , d ) . 0025 , e ) none of these
Rationale: explanation : 1 / ( 60 * 60 ) = 1 / 3600 = . 0027 option b
Answer: b
Problem: a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 9 , e ) 2
Rationale: "d = 25 * 60 + 1500 = 3000 m t = 3000 / 60 * 18 / 5 = 180 sec = 3 mins answer : b"
Answer: b
Problem: the total cost of 100 paper plates and 200 paper cups is $ 7.50 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 7.50 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.50 therefore oa is d"
Answer: d
Problem: the average age of 20 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 35 , b ) 38 , c ) 45 , d ) 36 , e ) 60
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 20 ) = 36 years answer : d"
Answer: d
Problem: in how many t ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places ? assume that the pieces are distinct .
Options: a ) t = 288 , b ) t = 144 , c ) t = 12 , d ) 48 , e ) 96
Rationale: 4 white chess pieces can be arranged in 4 ! ways and 4 black pieces can be arranged in 3 ! ways . w _ w _ w _ w number of ways = 4 ! * 3 ! = 24 * 6 = 144 answer b
Answer: b
Problem: a baseball card decreased in value 20 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 20 / 100 ) * 100 = 80 after second year , value of baseball card = ( 1 - 10 / 100 ) * 80 = 72 total percent decrease of the card ' s value over the two years = ( 100 - 72 ) / 100 * 100 % = 28 % answer a"
Answer: a
Problem: 1393 x 1393 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1940449 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1393 x 1393 = ( 1393 ) 2 = ( 1400 - 7 ) 2 = ( 1400 ) 2 + ( 7 ) 2 - ( 2 x 1400 x 7 ) = 1960000 + 49 - 19600 = 1960049 - 19600 = 1940449 . answer : c"
Answer: c
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 5 : 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 ) 7 : 9
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 5 and 1 parts , respectively . this will give us in the final mixture ( 5 + 5 ) : ( 3 + 1 ) , which means 10 : 4 , or 5 : 2 . answer c ."
Answer: c
Problem: in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 4 , − 4 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 7 / 14 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Problem: how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 100 / 19 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 24 % of ( 100 + x ) or 20 + x = ( 100 + x ) 6 / 25 500 + 25 x = 600 + 6 x 19 x = 100 x = 100 / 19 ans : d"
Answer: d
Problem: a room 8 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 13636 , b ) 13440 , c ) 13647 , d ) 13431 , e ) 13675
Rationale: "explanation : area of the room = ( 847 x 777 ) cm 2 . size of largest square tile = h . c . f . of 847 cm and 777 cm = 7 cm . area of 1 tile = ( 7 x 7 ) cm 2 . number of tiles required = ( 847 × 777 ) / ( 7 × 7 ) = 13431 answer : option d"
Answer: d
Problem: if x and y are numbers such that ( x + 8 ) ( y - 8 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 4 , b ) 24 , c ) 54 , d ) 64 , e ) 94
Rationale: "from ( x + 8 ) ( y - 8 ) = 0 it follows that either , x = - 8 or y = 8 . thus either x ^ 2 = 64 or y ^ 2 = 64 . now , if x ^ 2 = 64 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 64 + 0 = 64 . similarly if y ^ 2 = 64 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 64 = 64 . answer : d ."
Answer: d
Problem: what will be the compound interest on rs . 50000 after 3 years at the rate of 12 % per annum
Options: a ) rs 20123.20 , b ) rs 20246.4 , c ) rs 20123.40 , d ) rs 20123.50 , e ) none of these
Rationale: "explanation : ( 50000 × ( 1 + 12 / 100 ) 3 ) = > 50000 × 28 / 25 × 28 / 25 × 28 / 25 = > 70246.4 so compound interest will be 70246.4 - 50000 = rs 20246.4 option b"
Answer: b
Problem: dick and jane each saved $ 1000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %
Rationale: 1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d
Answer: d
Problem: calculate the share of y , if rs . 2690 is divided among x , y and z in the ratio 5 : 7 : 9 ?
Options: a ) 890.7 , b ) 826.7 , c ) 895.7 , d ) 896.7 , e ) 816.7
Rationale: "5 + 7 + 9 = 21 2690 / 21 = 128.1 y ' s share = 7 * 128.1 = 896.7 answer : d"
Answer: d
Problem: the perimeter of an equilateral triangle is 45 . if one of the side is the side of an isoceles triangle of perimeter 40 then what is the lenght of base of isoceles triangle .
Options: a ) 10 units , b ) 20 units , c ) 30 units , d ) 40 units , e ) 15 units
Rationale: "base of isoceles triangle is 40 - 15 - 15 = 10 units . answer : a"
Answer: a
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 5 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 5 / 14
Rationale: "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 5 / 6 * 6 = $ 5 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 5 = $ 20 ; fraction of total revenue from large cups : 20 / ( 36 + 20 ) = 5 / 14 . answer : e"
Answer: e
Problem: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 4860 . what was the number of original inhabitants ?
Options: a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800
Rationale: let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4860 ( 27 / 40 ) * x = 4860 x = 4860 * 40 / 27 = 7200 the answer is b .
Answer: b
Problem: worker a takes 7 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 70 / 17 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 7 one day work of b = 1 / 10 so one day work of a and b together = 1 / 7 + 1 / 10 = 17 / 70 so total days required = 70 / 17 answer : a"
Answer: a
Problem: in what time will a train 200 meters long cross an electric pole , if its speed is 128 km / hr
Options: a ) 5 seconds , b ) 5.7 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 128 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 200 / 35 = 5.7 seconds option b"
Answer: b
Problem: 4 , 12 , 48 , 240 , 1440 , 10080,80640 , 725760 ( . . . )
Options: a ) 7257600 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7,8 , 9,10 answer : option a"
Answer: a
Problem: if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is ?
Options: a ) 68.33 , b ) 18.33 , c ) 28.33 , d ) 48.33 , e ) 98.33
Rationale: explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = = rs . 18.33 answer : b
Answer: b
Problem: a train 120 m long running at 60 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 213 , b ) 298 , c ) 350 , d ) 726 , e ) 267
Rationale: "d = 60 * 5 / 18 = 20 = 333 â € “ 120 = 213 answer : a"
Answer: a
Problem: two pipes a and b can fill a tank in 12 hours and 15 hours respectively . if both pipe open together in tank , then how much time it take to fill the tank ?
Options: a ) 15 , b ) 18 , c ) 20 / 3 , d ) 19 / 4 , e ) 25 / 4
Rationale: in 1 hour pipe a fill = 1 / 12 in 1 hour pipe b fill = 1 / 15 pipe ( a + b ) in 1 hour = [ 1 / 12 + 1 / 15 ] = 3 / 20 total time taken to fill the tank = 20 / 3 hour answer c
Answer: c
Problem: when a number is divided by 13 , the remainder is 6 . when the same number is divided by 7 , then remainder is 1 . what is the number ?
Options: a ) 243 , b ) 253 , c ) 312 , d ) 432 , e ) none of these
Rationale: "explanation : take 243 243 ÷ 7 = 34 , remainder = 5 hence this is not the answer take 312 312 ÷ 7 = 44 , remainder = 4 hence this is not the answer take 253 253 ÷ 7 = 36 , remainder = 1 . 253 ÷ 13 = 19 , remainder = 6 this satisfies both the conditions given in the question . hence it is the answer . answer : b"
Answer: b
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 62 units per day , what is the value of n ?
Options: a ) 30 , b ) 14 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 62 * ( n + 1 ) - - > n = 14 . or as 30 extra units increased the average for n + 1 days by 2 units per day then 30 / ( n + 1 ) = 2 - - > n = 14 . answer : b ."
Answer: b
Problem: james took a 3 - hour bike ride . in the second hour he travlled 24 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 74.0 , b ) 54.9 , c ) 55.5 , d ) 57.0 , e ) 63.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 24 , x = 20 . now , the distance travelled in the 3 rd hour = 24 + 1 / 4 â ˆ — 24 = 30 . = 24 + 20 + 30 = 74 answer : a"
Answer: a
Problem: a rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes . find the least possible number of cubes .
Options: a ) 30 , b ) 40 , c ) 10 , d ) 20 , e ) 50
Rationale: "explanation : volume of the block = ( 6 x 12 x 15 ) cm 3 = 1080 cm 3 side of the largest cube = h . c . f . of 6 cm , 12 cm , 15 cm = 3 cm . volume of this cube = ( 3 x 3 x 3 ) cm 3 = 27 cm 3 number of cubes = ( 1080 / 27 ) = 40 . answer : b"
Answer: b
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 390 m long ?
Options: a ) 40 sec , b ) 60 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 140 = 750 m required time = 750 * 2 / 25 = 40 sec answer : b"
Answer: b
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 20 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 300 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 20 gallons then 0.12 a + 0.16 ( 200 - a ) = 20 - - > a = 300 . answer : a ."
Answer: a
Problem: the circus sells two kinds of tickets : lower seats for $ 30 and upper seats for $ 20 . on a certain night , the circus sells 80 tickets and gets $ 2100 in revenue from the sales . how many tickets for lower seats did they sell ?
Options: a ) 40
b ) 45
c ) 50
d ) 55
e ) 60
Rationale: let l be the number of lower seat tickets . let u be the number of upper seat tickets . l + u = 80 and u = 80 - l . 30 l + 20 u = 2100 . 30 l + 20 ( 80 - l ) = 2100 10 l + 1600 = 2100 . 10 l = 500 . l = 50 . the answer is c .
Answer: c
Problem: the average weight of 8 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 8 × 1.5 = 12 kg so the weight of new person = 65 + 12 = 77 kg answer b"
Answer: b
Problem: the speed at which a man can row a boat in still water is 26 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 150 metres ?
Options: a ) 18 , b ) 27 , c ) 28 , d ) 12 , e ) 25
Rationale: speed of the boat downstream = 26 + 4 = 30 kmph = 30 * 5 / 18 = 8.33 m / s hence time taken to cover 150 m = 150 / 8.33 = 18 seconds . answer : a
Answer: a
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 35 instead of 99 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) 73.82
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 35 + 99 = 2584 correct average = 2584 / 35 = 73.82 answer : e"
Answer: e
Problem: two employees m and n are paid a total of $ 572 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 220 , b ) $ 240 , c ) $ 260 , d ) $ 300 , e ) $ 320
Rationale: "1.2 n + n = 572 2.2 n = 572 n = 260 the answer is c ."
Answer: c
Problem: if rs . 527 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 372
Rationale: ( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 527 * 2 / 17 = rs . 62 b ' s share = 527 * 3 / 17 = rs . 93 c ' s share = 527 * 12 / 17 = rs . 372 . answer : e
Answer: e
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 9 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 8.18 % , d ) 10 % , e ) 10.8 %
Rationale: "9 = 1.1 * x x = 8.18 % answer c )"
Answer: c
Problem: in what ratio should a variety of rice costing rs . 6 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 1 / 68 , b ) 62 / 89 , c ) 12 / 68 , d ) 11 / 84 , e ) 5 / 6
Rationale: "explanation : let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 87.5 - 7.50 ) / ( 7.50 - 6 ) = 5 / 6 answer : e"
Answer: e
Problem: a driver goes on a trip of 60 kilometers , the first 30 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: "the time for the first part of the trip was 30 / 60 = 1 / 2 hours . the time for the second part of the trip was 30 / 30 = 1 hour . the total time for the trip was 3 / 2 hours . the average speed for the trip was 60 / ( 3 / 2 ) = 40 kph the answer is c ."
Answer: c
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 7 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 7 so sum of 3 should be 21 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 9 and 9 so a has to be 3 b"
Answer: b
Problem: the perimeter of one square is 48 cm and that of another is 28 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 13.9 √ 2 , e ) 13 √ 9
Rationale: "4 a = 48 4 a = 28 a = 12 a = 7 a 2 = 144 a 2 = 49 combined area = a 2 = 193 = > a = 13.9 d = 13.9 √ 2 answer : d"
Answer: d
Problem: two bullet train s 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "d 10.8 sec . relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 160 ) m = 300 m . required time = 300 x 9 / 250 = 54 / 5 = 10.8 sec ."
Answer: d
Problem: 18 times a positive integer is more than its square by 80 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 18 x = x 2 + 80 = > x 2 - 18 x + 80 = 0 = > ( x - 10 ) ( x - 8 ) = 0 = > x = 10 or 8 answer : b"
Answer: b
Problem: if | x + 3 | = 15 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 12 , c ) - 8 , d ) - 3 , e ) 11
Rationale: "there will be two cases x + 3 = 15 or x + 3 = - 15 = > x = 12 or x = - 18 sum of both the values will be - 18 + 15 = - 3 answer : d"
Answer: d
Problem: a box has 12 shapes ; 3 circles , 5 squares , and 4 triangles . how many groups of 3 shapes can be made with at least 1 triangle ?
Options: a ) 46
b ) 64
c ) 164
d ) 146
e ) 56
Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 3 so , total groups is 12 c 3 = 12 ! / ( 3 ! ( 12 - 3 ) ! ) = 220 , and n = 12 - 4 = 8 r = 3 for groups without a triangle is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , so , groups with at least 1 triangle = 220 - 56 = 164 answer : c
Answer: c
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ?
Options: a ) 35 , b ) 22.5 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 5 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 5 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 5 x = 7.5 since you need a 15 l solution , you must evaporate 22.5 of the original 50 l solution to get a 5 % solution . answer is b ."
Answer: b
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 540 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 30 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 540 . 6 ( 85 - g ) + 7 g = 540 . 510 - 6 g + 7 g = 540 . g = 540 - 510 = 30 . the answer is b ."
Answer: b
Problem: if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 80 / 40 â € “ 10 * 20 + 10 = ?
Options: a ) 185 , b ) 160 , c ) 170 , d ) 145 , e ) 225
Rationale: "explanation : given : 80 / 40 â € “ 10 * 20 + 10 = ? substituting the coded symbols for mathematical operations , we get , 80 * 40 / 20 + 20 â € “ 10 = ? 80 * 2 + 20 â € “ 10 = ? 160 + 20 â € “ 10 = ? 180 â € “ 10 = 170 answer : c"
Answer: c
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 66000 . what is the share of c ?
Options: a ) rs . 15250 , b ) rs . 13375 , c ) rs . 16750 , d ) rs . 18000 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 66000 ] = rs . 18000 answer : option d"
Answer: d
Problem: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 525 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 550 , d ) 625 , e ) 600
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 525 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 825 a + b + c = 75 per hour so for eight hrs = 75 * 8 = 600 = answer = e"
Answer: e
Problem: find number which is 70 % less than 60 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 26 , e ) 98
Rationale: "explanation : 70 % less is 30 % of the given number therefore , 30 % of 60 is 18 . answer : a"
Answer: a
Problem: a person want to give his money of $ 1000 to his 4 children a , b , c , d in the ratio 2 : 4 : 3 : 1 . what is the a + d share ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 300 , d ) $ 500 , e ) $ 600
Rationale: "a ' s share = 1000 * 2 / 10 = $ 200 d ' s share = 1000 * 1 / 10 = $ 100 a + d = $ 300 answer is c"
Answer: c
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 14 candidates . she plans to have one working interview with 3 of the 14 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "333 . answer e"
Answer: e
Problem: an athlete runs 200 metres race in 20 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 37 , d ) 36 , e ) 28
Rationale: "speed = distance / time = 200 / 20 = 10 m / s = 10 * 18 / 5 = 36 km / hr answer : d"
Answer: d
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 6 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 6 so sum of 3 should be 18 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 8 and 8 so a has to be 2 a"
Answer: a
Problem: what is the remainder when 7777 * 8888 * 101010 is divided by 33
Options: a ) 110 , b ) 220 , c ) 330 , d ) 440 , e ) 550
Rationale: "7777 / 33 = = > remainder = 22 8888 / 33 = = > remainder = 11 101010 / 33 = = > remainder = 30 = 22 * 11 * 30 = 7260 / 33 = = > remainder = 220 answer : b"
Answer: b
Problem: find the last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 4
Rationale: explanation : given exp . = a 2 + b 2 - 2 ab , where a = 287 and b = 269 = ( a - b ) 2 = ( 287 - 269 ) 2 = ( 182 ) = 324 answer is e
Answer: e
Problem: at a monthly meeting , 2 / 3 of the attendees were males and 3 / 4 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 3 / 8 , d ) 2 / 9 , e ) 5 / 18
Rationale: "males who did not arrive on time are 1 / 4 * 2 / 3 = 1 / 6 of the attendees . females who did not arrive on time are 1 / 6 * 1 / 3 = 1 / 18 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 6 + 1 / 18 = 2 / 9 the answer is d ."
Answer: d
Problem: the sum of the ages of 4 children born at the intervals of 4 years each is 36 years . what is the age of the youngest child ?
Options: a ) 3 , b ) 18 , c ) 10 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 4 , x + 8 , x + 12 we know that the sum of their ages is 36 . so , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 36 therefore the youngest child is 3 years old answer : a"
Answer: a
Problem: a school has 4 section of chemistry in class x having 50 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.12 , b ) 52.12 , c ) 51.12 , d ) 53.12 , e ) none of the above
Rationale: "required average marks = 50 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 50 + 35 + 45 + 42 = 2500 + 2100 + 2475 + 1890 / 172 = 8965 â  „ 172 = 52.12 answer b"
Answer: b
Problem: what is the least integer that is a sum of 4 different prime numbers each greater than 10 ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 66 , e ) 68
Rationale: the sum of the four smallest primes greater than 10 is 11 + 13 + 17 + 19 = 60 . the answer is a .
Answer: a
Problem: what is the smallest positive integer that can be multiplied by 605 to make it a perfect square ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "605 is multiplied by 5 gives 3025 its a square root of 55 answer is 5 - option c"
Answer: c
Problem: set a consists of the integers from 1 to 12 , inclusive , while set b consists of the integers from 5 to 15 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 9
Rationale: "a = { 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } b = { 5,6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 } common elements = { 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } = 8 elements answer : option a ."
Answer: a
Problem: p , q and r have rs . 6000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2388 , b ) 3722 , c ) 2400 , d ) 2872 , e ) 1231
Rationale: explanation : let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 . answer : c
Answer: c
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 32 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 32 . . 4 x + 12 = 32 . . x = 5 . . ans = x + 4 = 5 + 4 = 9 answer e"
Answer: e
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 260 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 2999 , c ) 2878 , d ) 2990 , e ) 6500
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 260 = > 6500 answer : e"
Answer: e
Problem: a 160 meter long train crosses a man standing on the platform in 4 sec . what is the speed of the train ?
Options: a ) 176 kmph , b ) 144 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 160 / 4 * 18 / 5 = 144 kmph answer : b"
Answer: b
Problem: p and q started a business investing rs 60000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 7 : 5 , b ) 17 : 3 , c ) 4 : 1 , d ) 17 : 7 , e ) 5 : 8
Rationale: explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 60000 : 15000 = 60 : 15 = 4 : 1 option c
Answer: c
Problem: 20 people can write 50 book in 15 days working 8 hour a day . then in how many day 200 can be written by 60 people ?
Options: a ) 200 , b ) 100 , c ) 50 , d ) 70 , e ) 25
Rationale: "work per day epr hour per person = 50 / ( 15 * 8 * 20 ) / / eq - 1 people = 60 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 200 / ( p * 8 * 60 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 100 answer : b"
Answer: b
Problem: if each side of a square is increased by 50 % , the ratio of the area of the resulting square to the area of the given square is :
Options: a ) 5 : 4
b ) 9 : 4
c ) 4 : 5
d ) 4 : 9
e ) 1 : 2
Rationale: let , each side = a . then , original area = a 2 . new side = 150 a / 100 = 3 a / 2 . new area = 9 a 2 / 4 . required ratio = 9 a 2 / 4 : a 2 = 9 : 4 answer : b
Answer: b
Problem: what least number must be added to 1078 , so that the sum is completely divisible by 23 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 5 , e ) 6
Rationale: "47 * 23 = 1081 1081 - 1078 = 3 answer : a"
Answer: a