Cheukting/mathqa huggingface dataset:
Question (general): the average salary of 15 people in the shipping department at a certain firm is $ 21,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 21,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: "total salary . . . 15 * 21 k = 315 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 6 emp sal = 315 k - 125 k - 64 k = 126 k average = 126 k / 6 = 21000 ans : c"
Answer: c
Question (physics): walking at the rate of 3 kmph a man cover certain distance in 6 hr 40 min . running at a speed of 18 kmph the man will cover the same distance in .
Options: a ) 40 min , b ) 25 min , c ) 54 min , d ) 65 min , e ) 58 min
Rationale: "distance = speed * time 3 * 20 / 3 = 20 km new speed = 18 kmph therefore time = 20 / 18 = 10 / 9 = 54 min answer : c ."
Answer: c
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of thesportformulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15
b ) 30
c ) 45
d ) 75
e ) 90
Rationale: standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 5 . so , x = 325 / 4 ounces . water = ( 60 / 65 ) * ( 325 / 4 ) = 60 * 3 / 4 = 75 ounces . ans d
Answer: d
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (geometry): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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