Cheukting/mathqa huggingface dataset:
Question (physics): a can do a piece of work in 4 hours . a and c together can do it in just 2 hours , while b and c together need 3 hours to finish the same work . in how many hours b can complete the work ?
Options: a ) 10 hours , b ) 12 hours , c ) 16 hours , d ) 18 hours , e ) 20 hours
Rationale: "explanation : work done by a in 1 hour = 1 / 4 work done by b and c in 1 hour = 1 / 3 work done by a and c in 1 hour = 1 / 2 work done by a , b and c in 1 hour = ( 1 / 4 ) + ( 1 / 3 ) = 7 / 12 work done by b in 1 hour = ( 7 / 12 ) – ( 1 / 2 ) = 1 / 12 = > b alone can complete the work in 12 hour option b"
Answer: b
Question (gain): a man can row downstream at the rate of 32 kmph and upstream at 17 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 7.5 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 32 + 17 ) = 24.5 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 32 - 17 ) = 1 / 2 ( 15 ) = 7.5 kmph answer is a ."
Answer: a
Question (general): a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 15 minutes , a combustion reaction creates 15,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: "solution : 15,000 carbon dioxide molecules are created over a period of 15 minutes . therefore 15,000 / 15 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a ."
Answer: a
Question (physics): a train speeds past a pole in 15 seconds and a platform 100 m long in 20 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 300 m , e ) 145 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 20 = x / 15 x = 300 m . answer : d"
Answer: d
Question (general): the smallest number when increased by ` ` 1 ` ` is exactly divisible by 618 , 3648 , 60 is :
Options: a ) 724 , b ) 721 , c ) 720 , d ) 719 , e ) 700
Rationale: lcm = 720 720 - 1 = 719 answer : d
Answer: d
Question (physics): a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days g will the work get over ?
Options: a ) 60 , b ) 70 , c ) g = 75 , d ) g = 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.96 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 3.00 , b ) $ 3.20 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 3.80
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 96 4 x / 15 = 96 x = $ 3.60 = $ 3.60 the answer is d ."
Answer: d
Question (general): how many prime numbers are between 78 / 14 and 55 / 4 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "78 / 14 = 39 / 7 = 6 - 55 / 4 = 14 - prime numbers between 6 and 14 are 7 , 11 and 13 - sign signifies that the number is marginally less . answer b"
Answer: b
Question (physics): a person can swim in still water at 12 km / h . if the speed of water 10 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 10 us = 12 - 10 = 2 d = 12 t = 12 / 2 = 6 answer : d"
Answer: d
Question (gain): if 15 % of a class averages 100 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 63 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 76 % , b ) 77 % , c ) 78 % , d ) 79 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 15 % - 50 % = 35 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.15 x 100 + 0.50 x 78 + 0.35 x 63 = 76.05 the class average ( rounded ) is 76 % final answer a ) 76 %"
Answer: a
Question (general): what is x if x + 3 y = 10 and y = 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 3 in x + 3 y = 10 x + 3 ( 3 ) = 10 x + 9 = 10 if we substitute x by 1 in x + 9 = 10 , we have 1 + 9 = 10 . hence x = 1 correct answer a"
Answer: a
Question (general): arun borrowed a sum of money from jayant at the rate of 8 % per annum simple interest for the first 4 years , 10 % per annum for the next 6 years and 12 % per annum for the period beyond 10 years . if he pays a total of 12160 as interest only at the end of 15 years , how much money did he borrow ?
Options: a ) 8000 , b ) 10000 , c ) 12000 , d ) 9000 , e ) none of these
Rationale: let the principal = p then p × 8 × 4 / 100 + p × 10 × 6 / 100 + p × 12 × 5 / 100 = 12160 ⇒ 152 p = 12160 × 100 or 12160 × 100 / 152 = 8000 answer a
Answer: a
Question (general): what is the largest 4 digit number exactly divisible by 88 ?
Options: a ) 9999 , b ) 9944 , c ) 9988 , d ) 9900 , e ) 9991
Rationale: "largest 4 digit number = 9999 9999 ÷ 88 = 113 , remainder = 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer is b"
Answer: b
Question (physics): a women travels from x to y distance of 1000 miles in 10 hours . she returns to x in 4 hours . find her average speed
Options: a ) 300 mph , b ) 150.2 mph , c ) 142.8 mph , d ) 200 mph , e ) 111.01 mph
Rationale: speed from x to y = 1000 / 10 = 100 mph speed from y to x = 1000 / 4 = 250 mph average speed = 2 * 100 * 250 / 350 = 142.8 mph answer is c
Answer: c
Question (general): in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 45 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 3 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : d . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d"
Answer: d
Question (general): a vendor sells 20 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 20 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.8 ) x = 0.4 x . the remaining pears are ( 0.5 ) ( 0.8 ) x = 0.4 x . on day two , the vendor throws away ( 0.8 ) ( 0.4 ) x = 0.32 x . the vendor throws away a total of 0.4 x + 0.32 x = 0.72 x . the vendor throws away 72 percent of the pears . the answer is e .
Answer: e
Question (general): john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 80 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 80 = 20 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 20 / 100 ) * 100 = ( 0.2 ) * 100 = 20 % . a"
Answer: a
Question (general): a number is doubled and 9 is added . if the resultant is trebled , it becomes 75 . what is that number ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "explanation : let the number be v . then , 3 ( 2 x + 9 ) = 75 . 2 x + 9 = 25 = > 2 x = 16 = > x = 8 answer : d ) 8"
Answer: d
Question (general): the value of 489.1375 x 0.0483 x 1.956 / 0.0873 x 92.581 x 99.749 is closest to :
Options: a ) 0.48 , b ) 5.8 , c ) 0.58 , d ) 0.058 , e ) 0.0058
Rationale: = 489.1375 x 0.0483 x 1.956 / 0.0873 x 92.581 x 99.749 = 489 x 0.05 x 2 / 0.09 x 93 x 100 = 489 / 9 x 93 x 10 = 163 / 279 x 1 / 10 = 0.58 / 10 = 0.058 ( or ) 0.06 . answer is d .
Answer: d
Question (gain): an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 15 % profit , offers a discount of 15 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 27.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 150 . s . p . = 85 % of rs . 150 = rs . 127.5 . ∴ gain % = 27.50 % . answer b"
Answer: b
Question (general): on teacher ' s day , sweets were to be equally distributed among 190 children in a school . actually , on the teacher ' s day , 70 children were absent and therefore each child got 14 sweets extra . how many sweets did each child get on that day ?
Options: a ) 18 , b ) 22 , c ) 28 , d ) 32 , e ) 38
Rationale: total children = 190 . let each student gets x chocolates if all were present . so , total chocolates = 190 x . 70 students were absent . so , no of extra chocolates distributed among 120 students , = 14 * 70 = 980 . now , total chocolates = 190 x 120 * ( x + 14 ) = 190 120 x + 1680 = 190 x 70 x = 1680 x = 24 . total no of chocolates = 24 * 190 = 4560 . no of chocolates each student gets on that day = 4560 / 120 = 38 . answer : option e
Answer: e
Question (general): x , a , z , and b are single digit positive integers . x = ¼ a . z = ¼ b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 33 , b ) 36 , c ) 44 , d ) 63 , e ) 66
Rationale: from the given equations , a = 4 x , b = 4 z ( 10 a + b ) - ( 10 x + z ) = 40 x + 4 z - 10 x - z = 30 x + 3 z = 3 ( 10 x + z ) therefore the resultant should be divisible by 3 which is n ' t possible only in the case of c . hence c is the answer
Answer: c
Question (physics): in what time will a train 140 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 3.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) 6 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 140 / 40 = 3.5 sec . answer : a"
Answer: a
Question (gain): if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 157.20 , b ) 157.29 , c ) 157.50 , d ) 157.30 , e ) 157.23
Rationale: "( 3500 * 1.5 * 3 ) / 100 = > 157.50 answer : c"
Answer: c
Question (general): if a : b is 2 : 3 and b : c is 3 : 4 then a : c is equal to
Options: a ) 2 : 3 , b ) 6 : 7 , c ) 5 : 6 , d ) 1 : 2 , e ) 3 : 4
Rationale: "since a : b = 2 : 3 and b : c = 3 : 4 , we can deduce that a : b : c = 2 : 3 : 4 so , a : c = 2 : 4 = 1 : 2 . d is the correct answer ."
Answer: d
Question (physics): carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 5 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 11 8 / 2 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 30 / 11 = 11 8 / 2 answer is c"
Answer: c
Question (general): on a two - dimensional coordinate plane , the line z = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: apparently it ' s z = x ^ 2 - x ^ 3 instead of z = x ^ 2 - z ^ 3 . in this case : the x - intercept is the value ( s ) of x for z = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c .
Answer: c
Question (general): find the value of 72514 x 9999 = m ?
Options: a ) 725067486 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 357889964
Rationale: "72514 x 9999 = 72514 x ( 10000 - 1 ) = 72514 x 10000 - 72514 x 1 = 725140000 - 72514 = 725067486 a"
Answer: a
Question (geometry): a rectangular parking space is marked out by painting three of its sides . if the length of the unpainted side is 9 feet , and the sum of the lengths of the painted sides is 37 feet , find out the area of the parking space in square feet ?
Options: a ) 120 , b ) 122 , c ) 124 , d ) 128 , e ) 126
Rationale: "length = 9 feet breadth = 37 − 92 = 14 feet area = 9 × 14 = 126 square feet answer is e ."
Answer: e
Question (physics): a man ' s speed with the current is 20 kmph and speed of the current is 1 kmph . the man ' s speed against the current will be
Options: a ) 11 kmph , b ) 12 kmph , c ) 18 kmph , d ) 17 kmph , e ) none of these
Rationale: explanation : speed with current is 20 , speed of the man + it is speed of the current speed in s ɵ ll water = 20 - 1 = 19 now speed against the current will be speed of the man - speed of the current = 19 - 1 = 18 kmph answer : c
Answer: c
Question (general): if | x - 12 | = 100 , what is the sum of all the possible values of x ?
Options: a ) - 12 , b ) - 22 , c ) 24 , d ) 36 , e ) 42
Rationale: "there will be two cases x - 12 = 100 or x - 12 = - 100 = > x = 112 or x = - 88 sum of both the values will be - 88 + 112 = 24 answer is c"
Answer: c
Question (physics): calculate the l . c . m of 4 / 9 , 5 / 7 , 9 / 13 , 7 / 15 is :
Options: a ) 1230 , b ) 1290 , c ) 1260 , d ) 1240 , e ) 2260
Rationale: "required l . c . m = l . c . m . of 4 , 5 , 9 , 7 / h . c . f . of 9 , 7 , 13 , 15 = 1260 / 1 = 1260 answer is c"
Answer: c
Question (gain): kanul spent $ 3000 in buying raw materials , $ 2000 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 5555.555 , b ) $ 5543.22 , c ) $ 5568.000 , d ) $ 5366.521 , e ) $ 5365.66
Rationale: let the total amount be x then , ( 100 - 10 ) % of x = 3000 + 2000 90 % of x = 5000 90 x / 100 = 5000 x = $ 50000 / 9 x = $ 5555.555 answer is a
Answer: a
Question (general): the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 5 | + 4 is equal to :
Options: a ) – 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14
Rationale: x ^ 2 - 8 x + 17 = | x - 5 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 12 = 0 x = 11,4 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 4 + 3 + 2 = 20 ans ( c )
Answer: c
Question (general): 1.20 can be expressed in terms of percentage as
Options: a ) 120 % , b ) 0.120 % , c ) 1.20 % , d ) 0.209 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 1.20 * 100 = 120 answer : option a"
Answer: a
Question (general): if the radius of a cylinder is doubled and height 5 times , what is the new volume of the cylinder divided by the old one ?
Options: a ) 8 . , b ) 2 . , c ) 6 . , d ) 20 . , e ) 10 .
Rationale: "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 2 r ) ^ 2 ( 5 h ) v ' = 20 v d ) 20"
Answer: d
Question (general): ( x ) + 4671 + 6514 - 7687 = 19190 . calculate the value of x
Options: a ) 15615 , b ) 15692 , c ) 15687 , d ) 15112 , e ) 15690
Rationale: "x + 4671 + 6514 - 7687 = 19190 = x + 4671 + 6514 = 19190 + 7687 = x + 11185 = 26877 = x = 26877 - 11185 = 15692 answer is b"
Answer: b
Question (gain): in some quantity of ghee , 60 % is pure ghee and 40 % is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 18 , e ) 22
Rationale: let the original quantity be x then , vanaspati ghee in xkg = 40 x / 100 kg = 2 x / 5 kg ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 2 x / ( 5 x + 50 ) = 1 / 5 x = 10 answer is a
Answer: a
Question (physics): a motorist travels for 6 hours , the first half at 60 kmph and the rest at 48 kmph . find the distance traveled by him .
Options: a ) 234 , b ) 124 , c ) 324 , d ) 452 , e ) 352
Rationale: distance = 3 * 60 + 3 * 48 = 180 + 144 = 324 km answer c .
Answer: c
Question (geometry): in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the error percent in the area calculated from these measurements .
Options: a ) 0.8 % , b ) 0.2 % , c ) 0.4 % , d ) 0.9 % , e ) 0.6 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 * x ) * ( 96 / 100 * y ) = 504 / 500 * xy . error in measurement = 504 / 500 * xy ) - xy = 4 / 500 * xy . error % = [ 4 / 500 * xy * 1 / xy * 100 ] % = 4 / 5 = 0.8 % . answer is a"
Answer: a
Question (general): in a group of ducks and cows , the total number of legs are 24 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 24 more than twice the number of heads = > 2 ( d + 2 c ) = 24 + 2 ( c + d ) = > d + 2 c = 12 + c + d = > 2 c = 12 + c = > c = 12 i . e . , total number of cows = 12 answer is a ."
Answer: a
Question (physics): a can do a piece of work in 6 days . b can do it in 5 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8.7 days , b ) 2.0 days , c ) 6.6 days , d ) 7.5 days , e ) 4.4 days
Rationale: "c = 1 / 2 - 1 / 6 - 1 / 5 = 2 / 15 = > 7.5 days answer : d"
Answer: d
Question (general): if 250 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 65 , b ) 66 , c ) 62 , d ) 69 , e ) 97
Rationale: "the question actually asks the highest power of 10 which divides 250 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 250 factorial will have 62 as - 250 / 5 = 50 50 / 5 = 10 10 / 5 = 2 so answer will be ( c ) 62"
Answer: c
Question (physics): a machine , working at a constant rate , manufactures 72 staplers in 28 minutes . how many staplers does it make in 1 hr 52 min ?
Options: a ) 268 , b ) 262 , c ) 300 , d ) 288 , e ) 250
Rationale: "change 1 hr 52 min to 112 min . for this , we need to set up a simple proportion of staplers per time 72 / 28 = s / 112 . the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . we can cancel the common factor of 28 in the two denominators . 72 / 28 * 28 = s / 112 * 28 72 / 1 = s / 4 s = 4 * 72 s = 288 the machine would be 288 staplers in 1 hr 52 min . answer : d"
Answer: d
Question (probability): wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 1 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 1 / 8 * ( 1 - 3 / 5 ) = 1 / 20 . answer : a ."
Answer: a
Question (general): when a = x + ( 2 / x ) and b = x - ( 2 / x ) , ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = ?
Options: a ) 2 , b ) 256 , c ) 8 , d ) 16 , e ) 32
Rationale: - - > ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = { ( 2 ) ^ ( a ^ 2 - b ^ 2 ) } = 2 ^ ( a - b ) ( a + b ) . since a - b = 4 / x and a + b = 2 x , 2 ^ ( a - b ) ( a + b ) = 2 ^ ( 4 / x ) ( 2 x ) = 2 ^ 8 = 256 answer is b
Answer: b
Question (general): if ( 4 - x ) / ( 4 + x ) = x , what is the value of x ^ 2 + 5 x - 4 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: ( 4 - x ) = x * ( 4 + x ) ( 4 - x ) = 4 x + x ^ 2 0 = x ^ 2 + 5 x - 4 the answer is a .
Answer: a
Question (physics): walking with 4 / 5 of my usual speed , i miss the bus by 5 minutes . what is my usual time ?
Options: a ) 145 , b ) 5617 , c ) 15 , d ) 20 , e ) 12
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 5 4 - - - - - - - - - ? è 20 answer : d"
Answer: d
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 45 kg , then the weight of b is :
Options: a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 35 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 45 x 2 ) = 90 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 170 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 35 . b ’ s weight = 35 kg . answer : d"
Answer: d
Question (general): evaluate : 35 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 27 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 35 - 12 * 3 * 2 = 35 - 8 = 27 correct answer d"
Answer: d
Question (general): a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 5 / 4 = s * 9 / 4 tips = s * 5 / 4 fraction of his income came from tips = ( s * 5 / 4 ) / ( s * 9 / 4 ) = 5 / 9 answer : d"
Answer: d
Question (general): in a fort , there are 1200 soldiers . if each soldier consumes 3 kg per day , the provisions available in the fort will last for 30 days . if some more soldiers join , the provisions available will last for 25 days given each soldier consumes 2.5 kg per day . find the number of soldiers joining the fort in that case ?
Options: a ) 273 , b ) 528 , c ) 539 , d ) 538 , e ) 723
Rationale: "assume x soldiers join the fort . 1200 soldiers have provision for 1200 ( days for which provisions last them ) ( rate of consumption of each soldier ) = 1200 ( 30 ) ( 3 ) kg also provisions available for ( 1200 + x ) soldiers is ( 1200 + x ) ( 25 ) ( 2.5 ) kg as the same provisions are available = > 1200 ( 30 ) ( 3 ) = ( 1200 + x ) ( 25 ) ( 2.5 ) x = [ 1200 ( 30 ) ( 3 ) ] / [ ( 25 ) ( 2.5 ) ] - 1200 x = 528 answer : option b"
Answer: b
Question (general): 19 people went to a hotel for combine dinner party 13 of them spent rs . 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 1496 , e ) none of these
Rationale: solution : let average expenditure of 19 people be x . then , 19 x = 13 * 79 + 6 * ( x + 4 ) ; or , 19 x = 13 * 79 + 6 x + 24 ; or , x = 80.84 ; so , total money spent = 80.84 * 19 = rs . 1536.07 . answer : option e
Answer: e