regisss/math_qa huggingface dataset:
Problem: two brothers took the gmat exam , the higher score is u and the lower one is v . if the difference between the two scores is equal to their average , what is the value of v / u ?
Options: a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) there is n ' t enough data to answer the question .
Rationale: answer is d : 1 / 3 u - v = ( u + v ) / 2 solving for v / u = 1 / 3 d
Answer: d
Problem: two trains 131 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.12 , d ) 7.35 , e ) 7.11
Rationale: "t = ( 131 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.35 answer : d"
Answer: d
Problem: in the rectangular coordinate system , if the line x = 6 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "x = 6 y + 5 , and thus y = x / 6 - 5 / 6 the slope is 1 / 6 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 6 and thus p = 1 / 3 the answer is b ."
Answer: b
Problem: the temperature of a certain cup of coffee 6 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 63.75 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 6 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 6 a ) + 60 60 = 120 * ( 2 ^ - 6 a ) 60 / 120 = 2 ^ - 6 a 1 / 2 = 2 ^ - 6 a 2 ^ - 1 = 2 ^ - 6 a - 1 = - 6 a 1 / 6 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 6 * 30 ) + 60 f = 120 * ( 2 ^ - 5 ) + 60 f = 120 * ( 1 / 2 ^ 5 ) + 60 f = 120 * 1 / 32 + 60 f = 3.75 + 60 = 63.75 answer b !"
Answer: b
Problem: a man can row his boat with the stream at 16 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 4 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 16 us = 8 s = ? s = ( 16 - 8 ) / 2 = 4 kmph answer : a"
Answer: a
Problem: 2.09 can be expressed in terms of percentage as
Options: a ) 2.09 % , b ) 20.9 % , c ) 209 % , d ) 0.209 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.09 * 100 = 209 answer : option c"
Answer: c
Problem: johnny bought 6 peanut butter cans at an average price ( arithmetic mean ) of 36.5 ¢ . if johnny returned two cans to the retailer , and the average price of the remaining cans was 30 ¢ , then what is the average price , in cents , of the two returned peanut butter cans ?
Options: a ) 5.5 , b ) 11 , c ) 47.5 , d ) 66 , e ) 49.5
Rationale: total price of six cans = 6 * 36.5 = 219 total price of 4 cans = 4 * 30 = 120 total rice of two cans = 219 - 120 = 99 average price of two cans = 99 / 2 = 49.5 c another way to do it is this : assume that the four leftover cans were of 30 c each . the avg was 36.5 c initially because the two cans were 36.5 c each and were providing another 6.5 c of cost to other 4 cans . so cost of the two cans = 2 * 36.5 + 4 * 6.5 = 99 avg cost of the two cans = 99 / 2 = 49.5 c answer ( e )
Answer: e
Problem: a clockwise rotation around point z ( that is , a rotation in the direction of the arrow ) transforms the shaded quadrilateral to the unshaded quadrilateral . the angle of rotation is approximately
Options: a ) 180 o , b ) 270 o , c ) 360 o , d ) 45 o , e ) 135 o
Rationale: the measure of \ pzq formed by the bottom edge of the shaded quadrilateral , zq , and this same edge after the rotation , zp , is approximately 90 . the transformation of the shaded quadrilateral to the unshaded quadrilateral is a clockwise rotation around point z through an an - gle equal to the measure of re ex angle pzq . the measure of \ pzq added to the measure of re ex \ pzq is equal to the measure of one complete rotation , or 360 . therefore , the measure of re ex angle pzq is approximately 360 o - 90 o or 270 o . thus the clockwise rotation around point z is through an angle of approximately 270 o correct answer b
Answer: b
Problem: find the compound interest on $ 66,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.12 , b ) 2552.2 , c ) 9524.32 , d ) 10403.25 , e ) 20512.54
Rationale: "principal = $ 66000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 66000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 76403.25 ci . = $ ( 76403.25 - 66000 ) = $ 10403.25 answer d ."
Answer: d
Problem: if | x | = 4 x - 1 , then x = ?
Options: a ) 3 , b ) 1 / 2 , c ) 1 and 1 / 2 , d ) - 1 / 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied ."
Answer: a
Problem: the length of the bridge , which a train 120 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 10 m , b ) 255 m , c ) 245 m , d ) 19 m , e ) 27 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 120 + x ) / 30 = 25 / 2 = > 2 ( 120 + x ) = 750 = > x = 255 m . answer : b"
Answer: b
Problem: what is the area of an equilateral triangle whose one side length is 90 ?
Options: a ) 4025 √ 3
b ) 3525 √ 3
c ) 3025 √ 3
d ) 2525 √ 3
e ) 2025 √ 3
Rationale: - > the area of an equilateral triangle with one side length of a is √ 3 a 2 / 4 . thus , √ 3 ( 90 ^ 2 ) / 4 = 2025 √ 3 and the answer is e .
Answer: e
Problem: an uneducated retailer marks all his goods at 40 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 5 % , d ) 14.50 % , e ) none
Rationale: sol . let c . p . = rs . 100 . then , marked price = rs . 140 . s . p . = 75 % of rs . 140 = rs . 105 . ∴ gain % = 5 % . answer c
Answer: c
Problem: dick and jane each saved $ 4,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 6,500 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 20 % , b ) 70 % , c ) 50 % , d ) 30 % , e ) 40 %
Rationale: "1990 dick saved = $ 4400 jane saved = $ 2100 ( jane saved $ 2800 less than she did the prior year ) jane saved approximately $ 2800 / 4000 $ ( 70 % ) less in 1990 answer : b"
Answer: b
Problem: the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is ?
Options: a ) 0.35 cm 2
b ) 17.5 cm 2
c ) 8.75 cm 2
d ) 55 cm 2
e ) 50 cm 2
Rationale: explanation : ( 5 * 3.5 ) / 2 = 8.75 answer is c
Answer: c
Problem: if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 189 , what is their sum ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 the two numbers are 3 and 6 . the answer is d ."
Answer: d
Problem: there are 16 bees in the hive , then 5 more fly . how many bees are there in all ?
Options: a ) 20 , b ) 33 , c ) 12 , d ) 17 , e ) 25
Rationale: 16 + 5 = 20 . answer is a .
Answer: a
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 250,000 and only 0.1 % on a company ’ s payroll above $ 250,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of
Options: a ) $ 450,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 400,000 , e ) $ 2 , 200,000
Rationale: "answer : a , ( with different approach ) : the 200 paid is 0.1 % of the additional amount above 250,000 . let it be x now 0.1 % of x = 200 therefore x = 200,000 total = 250,000 + x = 450,000"
Answer: a
Problem: for what value of x , is | x – 3 | + | x + 1 | + | x | = 11 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 4 , e ) - 2
Rationale: for what value of x , is | x – 3 | + | x + 1 | + | x | = 11 ? it ' s easiest just to plug in answer choices : ( c ) : - 3 | x – 3 | + | x + 1 | + | x | = 11 ? | - 3 - 3 | + | - 3 + 1 | + | - 3 | = 11 ? | 6 | + | 2 | + | 3 | = 11 ( c )
Answer: c
Problem: an auction house charges a commission of 16 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 210,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.16 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 210,000 ( 16 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c ."
Answer: c
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 11 , b ) 408 , c ) 2881 , d ) 287 , e ) 221
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 13 + 21 = 34 t = 12 d = 34 * 12 = 408 answer : b"
Answer: b
Problem: what should be the least number to be added to the 1202 number to make it divisible by 4 ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 77 , e ) 2
Rationale: answer : 2 option : e
Answer: e
Problem: a sum of money deposited at c . i . amounts to rs . 3250 in 2 years and to rs . 3830 in 3 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 20 % , d ) 17 % , e ) 50 %
Rationale: "3250 - - - 580 100 - - - ? = > 17 % answer : d"
Answer: d
Problem: if | 20 x - 10 | = 150 , then find the product of the values of x ?
Options: a ) - 45 , b ) 56 , c ) - 62 , d ) 35 , e ) - 30
Rationale: "| 20 x - 10 | = 150 20 x - 10 = 150 or 20 x - 10 = - 150 20 x = 160 or 20 x = - 140 x = 8 or x = - 7 product = - 7 * 8 = - 56 answer is b"
Answer: b
Problem: a certain car uses 12 gallons of gasoline in traveling 180 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 8 , e ) 10
Rationale: "180 / 10 = 18 . the difference is 18 - 15 = 3 . answer b"
Answer: b
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 30 years
Rationale: "let present age of the son = x years then present age the man = ( x + 24 ) years given that in 2 years man ' s age will be twice the age of his son x = 22 answer b"
Answer: b
Problem: in the hillside summer camp there are 60 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 . , b ) 45 . , c ) 40 . , d ) 60 . , e ) 25 .
Rationale: "given there are 60 students , 90 % of 60 = 54 boys and remaining 6 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 60 to existing 54 then the count will be 114 and the girls number will be 6 as it . now boys are 95 % and girls are 5 % . ( out of 120 students = 114 boys + 6 girls ) . imo option d is correct ."
Answer: d
Problem: if x and y are integers such that x ^ 2 = 3 y and xy = 36 , then x – y = ?
Options: a ) - 30 , b ) - 20 , c ) - 5 , d ) 5 , e ) 0
Rationale: here x and y are integers . x ^ 2 = 3 y , xy = 36 . substitute ( x ^ 2 ) / 3 = y in xy = > x ^ 3 = 36 * 3 = > x ^ 3 = 108 . here x ^ 3 is positive , x is also positive . x = 6 then y = 6 . x - y = 0 so option e is correct
Answer: e
Problem: 49 pumps can empty a reservoir in 13 / 2 days , working 8 hours a day . if 196 pumps are used for 5 hours each day , then the same work will be completed in :
Options: a ) 2 days , b ) 5 / 2 days , c ) 13 / 5 days , d ) 3 days , e ) none of these
Rationale: explanation : let the required number of days be x . then , more pumps , less days ( indirect proportion ) less working hrs / day , more days ( indirect proportion ) pumps 196 : 49 working hrs / day 5 : 8 : : 13 / 2 : x 96 x 5 x x = 49 x 8 x 13 / 2 x = 49 x 8 x 13 / 2 x 1 / ( 196 x 5 ) x = 13 / 5 answer c
Answer: c
Problem: a couple decides to have 3 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 2 girls and 1 boy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 / 8 , e ) 4
Rationale: "sample space = 2 ^ 3 = 8 . favourable events = { bgg } , { bgb } , { bbb } , { ggg } , { gbg } probability = 5 / 8 = 5 / 8 . ans ( d ) ."
Answer: d
Problem: working together at their respective constant rates , machine a and machine b can produce 600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 600 unit total would it produce ?
Options: a ) 25 , b ) 37 , c ) 50 , d ) 30 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 600 units in 24 hrs , so it can produce 600 * 8 / 24 = 200 units is 8 hrs . 200 is 30 % of 600 . d is the answer"
Answer: d
Problem: some of the 50 % solution of acid was removed and this was replaced with an equal amount of 30 % solution of acid . as a result , a 40 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5
Rationale: "let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.3 ( x ) = 0.4 0.2 x = 0.1 x = 1 / 2 the answer is a ."
Answer: a
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 200 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 42 , b ) 35 , c ) 40 , d ) 33 , e ) 38
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 200 5 x - 10 = 200 5 x = 190 x = 38 answer : e"
Answer: e
Problem: a certain business school has 500 students , and the law school at the same university has 800 students . among these students , there are 30 sibling pairs consisting of 1 business student and 1 law student . if 1 student is selected at random from both schools , what is the probability that a sibling pair is selected ?
Options: a ) 3 / 40000 , b ) 3 / 20000 , c ) 3 / 4000 , d ) 9 / 400 , e ) 6 / 130
Rationale: probability of selecting 1 student from harvard ' s business school - - - 1 / 500 probability of selecting 1 student from harvard ' s law school - - - - - - - - - 1 / 800 probability that these two students are siblings - - - - ( 1 / 500 * 1 / 800 ) since there are 30 siblings , hence ( 1 / 500 * 1 / 800 ) * 30 . 3 / 40000 answer : a
Answer: a
Problem: a number increased by 40 % gives 700 . the number is
Options: a ) 250 , b ) 500 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 40 % = 140 % 140 % - - - - - - - > 700 ( 140 × 5 = 700 ) 100 % - - - - - - - > 700 ( 100 × 5 = 500 ) b )"
Answer: b
Problem: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 41 , what is the remainder when k is divided by 7 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 41 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 41 ) 17 is the only common number in both the sets . hence k = 17 answer : a"
Answer: a
Problem: the profits of qrs company rose 40 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 68 % , e ) 80 %
Rationale: "assume 100 in march , then 140 in april as 40 % increase , then 112 in may as 20 % decrease from april , and then 168 in june which is 150 % of 112 . so overall increase is from 100 to 168 is 68 % answer d"
Answer: d
Problem: find the value of 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 3200 , c ) 900 , d ) 1600 , e ) none
Rationale: "answer 4 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 4 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 4 x 4 x 4 x 50 = 3200 correct option : b"
Answer: b
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 175 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 9 , c ) 6 , d ) 8 , e ) 10
Rationale: "fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 50 % of 500 = 250 step ( 9 ) 70 % of 350 = 175 ( our target ) total 9 steps required . ans b"
Answer: b
Problem: from the sale of sleeping bags , a retailer made a gross profit of 12 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.64 , d ) 25.0 , e ) 31.36
Rationale: cost price * 1.12 = selling price - - > cost price * 1.12 = $ 28 - - > cost price = $ 25 . answer : d . actually even without any math only c and d make any sense , but since 24.64 * 1.12 wo n ' t be an integer ( $ 28 ) then only answer choice d remains .
Answer: d
Problem: there is enough provisions for 700 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ?
Options: a ) 30 days , b ) 40 days , c ) 50 days , d ) 59 days , e ) 65 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 700 * 25 = 300 * d 2 d 2 = 700 * 25 / 300 = 59 days . answer : d"
Answer: d
Problem: the distance between delhi and mathura is 140 kms . a starts from delhi with a speed of 24 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 46 kmph at 8 a . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 23 3 / 4 , c ) 16 1 / 2 , d ) 9 1 / 2 , e ) 98
Rationale: "d = 140 – 24 = 116 rs = 46 + 24 = 70 t = 116 / 70 = 1.6 hours 8 a . m . + 1.6 = 9 1 / 2 a . m . . answer : d"
Answer: d
Problem: 3 distinct single - digit numbers . a , b , c are in gp . if abs ( x ) for real x is the absolute value of x ( x if x is + ve or 0 and - x if x is - ve ) , then the number of different possible values of abs ( a + b + c ) is
Options: a ) 5 , b ) 6 , c ) 3 , d ) 4 , e ) 7
Rationale: a , b , c may be ( 1 , 2,4 ) & ( 4 , 2,1 ) ( 1 , 3,9 ) & ( 9 , 3,1 ) ( 2 , 4,8 ) & ( 8 , 4,2 ) ( 4 , 6,9 ) & ( 9 , 6,4 ) find abs ( a + b + c ) for these 8 gps 7,13 , 15,19 so , we get 4 different values answer : d
Answer: d
Problem: the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 20 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 6 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 80 y thus 75 x = 80 y or x = 1.06 y ans r = 106 y so increase = 6 % answer : e"
Answer: e
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 53 , what is the value of x ?
Options: a ) 52 , b ) 53 , c ) 54 , d ) 55 , e ) 51
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 53 x = 51 answer : e"
Answer: e
Problem: a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 12 cm by 6 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18000 , c ) 20000 , d ) 30000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 1800 ã — 1200 / 12 ã — 6 ) = 30000 option d"
Answer: d
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 52 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3.3 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 52 / 60 47 x / 60 = 52 / 60 = > x = 1.1 total distance = 3 * 1.1 = 3.3 km ."
Answer: c
Problem: a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction w of the cookies that were placed in the other tins were placed in the green tin ?
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction w = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )
Answer: c
Problem: two trains of equal lengths take 12 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 13 , c ) 77 , d ) 99 , e ) 21
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 10 + 8 = 18 m / sec . required time = ( 120 + 120 ) / 18 = 13 sec . answer : b"
Answer: b
Problem: the difference of two numbers is 11 and one - fifth of their sum is 9 . find the numbers .
Options: a ) 28 and 17 , b ) 27 and 18 , c ) 25 and 15 , d ) 27 and 15 , e ) 25 and 18
Rationale: "let the number be x and y . then , x – y = 11 - - - - ( i ) and 1 / 5 ( x + y ) = 9 = > x + y = 45 - - - - ( ii ) adding ( i ) and ( ii ) , we get : 2 x = 56 or x = 28 . putting x = 28 in ( i ) , we get : y = 17 . hence , the numbers are 28 and 17 . answer is a ."
Answer: a
Problem: 40 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 40 % of companies which offer wireless internet also offer snacks . the answer is b ."
Answer: b
Problem: a boat moves down stream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes . the speed of current is
Options: a ) 2 kmph , b ) 3 kmph , c ) 4 kmph , d ) 5 kmph , e ) 6 kmph
Rationale: if speed ( in kmph ) of the boat = b and current = c , then in downstream time taken ( in hrs . ) = 1 / ( b + c ) = 6 / 60 = 1 / 10 or b + c = 10 - - - ( i ) & in upstream time taken ( in hrs . ) = 1 / ( b - c ) = 10 / 60 = 1 / 6 or b - c = 6 - - - ( ii ) from ( i ) & ( ii ) , b = 8 , c = 2 answer : a
Answer: a
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 15 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 2 - - > e : l = 5 : 2 = 20 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 8 : 15 . answer : b ."
Answer: b
Problem: the sector of a circle has radius of 21 cm and central angle 130 o . find its perimeter ?
Options: a ) 89.7 , b ) 91.4 , c ) 91.7 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 130 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 47.7 + 42 = 89.7 cm answer : a"
Answer: a
Problem: the population of a city increases by 8 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 22.50 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 7 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 7 / 100 ) ^ 3 = 122.5043 ∴ required percentage = 22.50 % answer : c"
Answer: c
Problem: pipe a can fill a tank in 3 hours . due to a leak at the bottom , it takes 9 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 4.5 , b ) 17 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 3 - 1 / x = 1 / 9 = > 1 / x = 1 / 3 - 1 / 9 = ( 3 - 1 ) / 9 = 2 / 9 = > x = 9 / 2 = 4.5 . answer : a"
Answer: a
Problem: the radius of a semi circle is 4.8 cm then its perimeter is ?
Options: a ) 32.51 , b ) 32.4 , c ) 32.1 , d ) 32.92 , e ) 24.69
Rationale: "36 / 7 r = 4.8 = 24.69 answer : e"
Answer: e
Problem: the number of stamps that p and q had were in the ratio of 9 : 2 respectively . after p gave q 33 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 6 : 5 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 11 , b ) 33 , c ) 45 , d ) 67 , e ) 80
Rationale: "p started with 9 k stamps and q started with 2 k stamps . ( 9 k - 33 ) / ( 2 k + 33 ) = 6 / 5 45 k - 12 k = 178 + 165 33 k = 343 k = 11 p has 9 ( 11 ) - 33 = 66 stamps and q has 2 ( 11 ) + 33 = 55 stamps . the answer is a ."
Answer: a
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 40 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 6 , e ) 5
Rationale: explanation : he covered 5 km in 1 hour , so he might cover 40 km in 8 hours . but he took 10 hours . he would have saved 10 â € “ 8 = 2 hours . answer : a
Answer: a
Problem: how many 3 - digit numerals end with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 160 , d ) 180 , e ) 400
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : e"
Answer: e
Problem: machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 6 hours and 20 minutes . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 24
Rationale: c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 380 minutes , so its rate is 1 / 380 of the work per minute . the combined rate is 20 / 380 = 1 / 19 so the work will be completed in 19 minutes . the answer is c .
Answer: c
Problem: in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 410 $ , d ) 430 $ , e ) 447 $
Rationale: 12 * 1.50 + 0.65 * 12 * 55 = 447 hence - e
Answer: e
Problem: cole drove from home to work at an average speed of 60 kmh . he then returned home at an average speed of 90 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 60 time from work to home = x / 90 total time = 2 hrs ( x / 60 ) + ( x / 90 ) = 2 solving for x , we get x = 72 time from home to work in minutes = ( 72 ) * 60 / 60 = 72 minutes ans = c"
Answer: c
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has 80 paisa , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?
Options: a ) rs . 185 , b ) rs . 410 , c ) rs . 285 , d ) rs . 385 , e ) rs . 475
Rationale: "a : b : c = 80 : 65 : 40 = 16 : 13 : 8 8 - - - - 40 37 - - - - ? = > rs . 185 answer : a"
Answer: a
Problem: from a group of 5 boys and 5 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ?
Options: a ) 4 / 15 , b ) 6 / 17 , c ) 8 / 19 , d ) 10 / 21 , e ) 12 / 23
Rationale: "the total number of ways to choose 6 children from 10 is 10 c 6 = 210 the number of ways to choose 3 boys and 3 girls is 5 c 3 * 5 c 3 = 10 * 10 = 100 p ( 3 boys and 3 girls ) = 100 / 210 = 10 / 21 the answer is d ."
Answer: d
Problem: what is the area of square field whose side of length 14 m ?
Options: a ) 225 , b ) 196 , c ) 266 , d ) 288 , e ) 261
Rationale: "14 * 14 = 196 sq m answer : b"
Answer: b
Problem: 3 types of tea the a , b , c costs rs . 95 / kg , 100 / kg and 70 / kg respectively . how many kgs of each should be blended to produce 100 kg of mixture worth rs . 90 / kg , given that the quantities of band c are equal
Options: a ) 70 , 1515 , b ) 50 , 2525 , c ) 60 , 2020 , d ) 40 , 3030 , e ) 20 , 3030
Rationale: given quantities of b and c are equal . therefore instead of considering them as a different quantities take average of both and consider it as a single entity . so the cost of the mixture ` ` d ' ' ( equal quantities of ` ` b ' ' and ` ` c ' ' ) is 170 / 2 = 85 rs / kg now the tea contains only ` ` a ' ' of 95 rs / per and ` ` d ' ' of 85 rs / kg . it is clearly seen that ` ` a ' ' is 5 more and ` ` d ' ' is 5 less than the required cost per kg . therefore 50 / 50 will go well . a = 50 kg and d = 50 kg . ( d = b & c in equal ratio ) . therefore b & c = 25 kg each . ( a : b : c ) = ( 50 , 2525 ) answer : b
Answer: b
Problem: # p is defined as 2 p - 20 for any number p . what is p , if # ( # ( # p ) ) = 6 ?
Options: a ) – 108 , b ) – 44 , c ) 10 , d ) 16 , e ) 18.25
Rationale: # p = 2 p - 20 - - - > # ( # p ) = 2 ( 2 p - 20 ) - 20 = 4 p - 60 and thus # ( 4 p - 60 ) = 2 ( 4 p - 60 ) - 20 = 8 p - 140 = 6 - - - > 8 p = 146 - - - > p = 18.25 , e is the correct answer .
Answer: e
Problem: a watch was sold at a loss of 9 % . if it was sold for rs . 220 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 2876 , c ) 1977 , d ) 2778 , e ) 1692
Rationale: "91 % 104 % - - - - - - - - 13 % - - - - 220 100 % - - - - ? = > rs . 1692 answer : e"
Answer: e
Problem: two persons a and b can complete a piece of work in 30 days and 60 days respectively . if they work together , what part of the work will be completed in 10 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 5 / 3
Rationale: a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 60 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 60 = 1 / 20 the part of the work completed in 10 days = 10 ( 1 / 20 ) = 1 / 2 . answer : d
Answer: d
Problem: by travelling at 30 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 19 kmph , b ) 15 kmph , c ) 12 kmph , d ) 20 kmph , e ) 23 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 30 * 3 x = 90 x km he covered 2 / 3 * 90 x = 60 x km in 1 / 3 * 3 x = x hours so , the remaining 30 x km , he has to cover in 2 x hours . required speed = 30 x / 2 x = 15 kmph . answer : b"
Answer: b
Problem: 33 1 / 3 % of 270 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 270 = 90 b )"
Answer: b
Problem: mr . hernandez , who was a resident of state x for only 8 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 6 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 6 % = 1350 as stated annual tax is prorated as per the duration of stay . prorated tax = 1350 ( 8 / 12 ) = 900 answer a"
Answer: a
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1300 employees , then the no . of female employees who are computer literate ?
Options: a ) 546 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1300 female employees , 60 % of 1300 . = ( 60 * 1300 ) / 100 = 780 . then male employees , = 520 50 % of male are computer literate , = 260 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1300 ) / 100 = 806 computer literate . thus , female computer literate = 806 - 260 = 546 . answer : option a"
Answer: a
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 5 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) 72
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 4 and 5 are adjacent - consider 4 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 4 and 5 can be arranged as 45 or 54 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
Answer: e
Problem: susan drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 60 miles / hr for the remaining 20 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 60 miles total time = 40 / 15 + 20 / 60 = 3 avg . speed = 20 . answer - b
Answer: b
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 480 m , its area is ?
Options: a ) 150 , b ) 240 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 480 = > x = 16 a = 80 , b = 192 , c = 208 s = ( 80 + 192 + 208 ) / 2 = 240 answer : b"
Answer: b
Problem: the perimeter of a semi circle is 113 cm then the radius is ?
Options: a ) 17 , b ) 28 , c ) 19 , d ) 11 , e ) 22
Rationale: "36 / 7 r = 113 = > r = 22 answer : e"
Answer: e
Problem: a boat having a length 4 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 120 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 4 x 3 x 0.01 ) m 3 = 0.12 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.12 x 1000 ) kg = 120 kg . answer : b"
Answer: b
Problem: a train 450 m long running at 108 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 271 , b ) 266 , c ) 350 , d ) 277 , e ) 300
Rationale: "length of the platform = 108 * 5 / 18 * 25 = 750 – 450 = 300 answer : e"
Answer: e
Problem: when the price of sugar was increased by 32 % , a family reduced its consumption in such a way that the expenditure on sugar was only 10 % more than before . if 30 kg were consumed per month before , find the new monthly consumption .
Options: a ) 20 kg , b ) 25 kg , c ) 30 kg , d ) 35 kg , e ) none of these
Rationale: since , expenditure = price × consumption ∴ 110 % of 30 = 132 ⁄ 100 × new consumption ⇒ 110 ⁄ 100 × 30 = 132 ⁄ 100 × new consumption ⇒ new consumption = 25 kg answer b
Answer: b
Problem: find the 25 th term of an arithmetic progression whose first term is 5 and the common difference is 7 .
Options: a ) 145 , b ) 38 , c ) 173 , d ) 156 , e ) 189
Rationale: n th term of a . p = a + ( n - 1 ) * d = 5 + ( 25 - 1 ) * 7 , = 5 + 168 = 173 . answer : c
Answer: c
Problem: in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.56 , b ) 0.62 , c ) 0.68 , d ) 0.74 , e ) 0.8
Rationale: let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.7 * 0.6 x = 0.62 x the answer is b .
Answer: b
Problem: the function g ( a ) is defined for integers a such that if a is even , g ( a ) = a / 2 and if a is odd , g ( a ) = a + 5 . given that g ( g ( g ( g ( g ( a ) ) ) ) ) = 19 , how many possible values for a would satisfy this equation ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 11
Rationale: let me define terms : in g ( a ) = r a is argument , r is result , g ( ) is function , in g ( g ( g ( g ( g ( a ) ) ) ) ) , g 1 is inner most , g 5 is outermost for identification . from definition of function g , we can deduce that : if result is even then two possibilities for argument = 1 even 1 odd if result is odd then one possibility for argument = 1 even since final result = 19 = odd possibilities : g 1 : 1 even g 2 : 1 * ( even , odd ) = 1 even 1 odd g 3 : 1 * ( even , odd ) + 1 even = 2 even 1 odd g 4 : 2 * ( even , odd ) + 1 even = 3 even 2 odd g 5 : 3 * ( even , odd ) + 2 even = 5 even 3 odd = total 8 ans d it is !
Answer: d
Problem: there are 16 bees in the hive , then 9 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 25
Rationale: 16 + 9 = 25 . answer is e .
Answer: e
Problem: seller selling an apple for rs . 20 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 21 , d ) 18 , e ) 20
Rationale: "sp = 20 loss = cp 21 loss = cp − sp = cp − 20 ⇒ cp 21 = cp − 20 ⇒ 20 cp 21 = 20 ⇒ cp 21 = 1 ⇒ cp = 21 c"
Answer: c
Problem: what are the last two digits of ( 301 * 402 * 503 * 604 * 645 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 00
Rationale: ( ( 301 * 402 * 503 * 604 * 645 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 5,7 , 8,9 ; 6 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,45 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 45 ) ( 56 * 49 ) ) ^ 2 = ( 00 * 44 ) ^ 2 = 00 ^ 2 = 00 hence answer is e
Answer: e
Problem: nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.15 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 27.6 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "b its is . let price = x ( x - 1.15 ) 8 = 6 x x = 4.6 hence total money = 6 * 4.6 = 27.6"
Answer: b
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 60 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 12 % , d ) 20 % , e ) 80 %
Rationale: the actual answer is obtained by multiplying 160 % by 70 % and subtracting 100 % from this total . that is : 160 % × 70 % = 112 % ; 112 % − 100 % = 12 % . answer : c
Answer: c
Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 tails ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 2 , d ) 3 / 4 , e ) 1 / 4
Rationale: "let ' s find the probability of 2 tails , 3 tails p ( ttt ) = ( ( 1 / 2 ) ^ 3 = 1 / 8 . p ( htt ) = ( 3 ! / 2 ! ) * ( 1 / 2 ) ^ 3 = 3 / 8 total probablity = 1 / 8 + 3 / 8 = 1 / 2 answer ( c )"
Answer: c
Problem: a 75 - liter solution of cool - drink is made from 10 % jasmine water . if 3.5 liters of jasmine and 9.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 12.5 % , b ) 14 % , c ) 15.5 % , d ) 17 % , e ) 18.5 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 75 ) + 3.5 ) / 88 = 11 / 88 = 1 / 8 = 12.5 % the answer is a ."
Answer: a
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1200 m long ?
Options: a ) 200 sec , b ) 240 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2400 m t = d / s t = 2400 / 10 t = 240 sec answer : b"
Answer: b
Problem: a 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform .
Options: a ) 310 meter , b ) 335 meter , c ) 345 meter , d ) 350 meter , e ) none of these
Rationale: "explanation : speed = distance / time = 300 / 18 = 50 / 3 m / sec let the length of the platform be x meters then distance = speed ∗ time x + 300 = 50 / 3 ∗ 39 = > 3 ( x + 300 ) = 1950 = > x = 350 meters option d"
Answer: d
Problem: a and b go around a circular track of length 100 m on a cycle at speeds of 18 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 20 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 100 / ( 18 * 5 / 18 ) , 100 / ( 36 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : e"
Answer: e
Problem: zoey won the lottery and got $ 7 , 348340 . she wants to split it among herself and 5 friends evenly . how much money must she add if she wants to split it evenly ?
Options: a ) $ 3 , b ) $ 2 , c ) $ 9 , d ) $ 1 , e ) $ 4
Rationale: zoey and her 5 friends is 6 people in all . $ 7 , 348340 must be divisible by 6 if she wants to split it evenly . the money is divisible by 6 if it ' s divisible by 2 and 3 . 7 + 3 + 4 + 8 + 3 + 4 + 0 = 29 . 2 and 3 cant go into 29 . adding 1 dollar makes it 30 . 2 and 3 can go into 30 so 6 can also . the answer is d .
Answer: d
Problem: in a certain code language , ' book ' is coded as ' pencil ' , ' pencil ' is coded as ' mirror ' , ' mirror ' is coded as ' board ' . then what is useful to write on a paper ?
Options: a ) 2 , b ) 6278 , c ) 277 , d ) 281 , e ) 22
Rationale: we use pencil to write on a paper but here pencil is coded as mirror . so , the answer is mirror . answer : a
Answer: a
Problem: what is the angle between the hands of a clock when time is 8 : 40 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 100 deg
Rationale: "angle between two hands = 40 h - 11 / 2 m = 40 * 8 - 40 * 11 / 2 = 320 - 220 = 100 deg answer : e"
Answer: e
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 6 c + 3 . the minimum is 3 when c = 0 . the maximum is 45 when c = 7 . there are 8 such numbers . the answer is d ."
Answer: d
Problem: a box contains 4 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2
Rationale: "my complicated version of your simple approach let the 4 black balls be bbbband 4 red balls be rrrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 8 ! ) / ( 4 ! x 4 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 4 red ( rrrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 3 ! ) hence required probability = [ ( 8 ! ) / ( 4 ! x 4 ! ) ] / [ ( 7 ! ) / ( 4 ! x 3 ! ) ] = 2 e"
Answer: e
Problem: if 50 % of ( x - y ) = 30 % of ( x + y ) , then what percent of x is y ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 15 % , e ) 50 %
Rationale: "50 % of ( x - y ) = 30 % of ( x + y ) 50 / 100 ( x - y ) = 30 / 100 ( x + y ) x = 4 y required percentage = y / x * 100 = y / 4 y * 100 = 25 % answer is c"
Answer: c
Problem: 30 ^ 10 / 180 ^ 5 = ?
Options: a ) 5 ^ 5 , b ) 5 ^ 6 , c ) 3 ^ 6 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 180 ^ 5 = ? a . 5 ^ 5 b . 5 ^ 6 c . 3 ^ 6 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 180 ^ 5 = ( 30 ^ 10 ) / ( 6 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 6 ^ 5 ) = ( 6 ^ 5 ) ( 5 ^ 5 ) / ( 6 ^ 5 ) = 5 ^ 5 . thus , a is the answer ."
Answer: a
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 245 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 70 % of 500 = 350 step ( 9 ) 70 % of 350 = 245 ( our target ) total 9 steps required . ans e
Answer: e
Problem: when the price of an article was reduced by 30 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 26 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 30 % , the new price is 0.7 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.7 p ) ( 1.8 n ) = 1.26 np , which is 1.26 times the old revenue , so is 26 % greater . answer : a"
Answer: a