Cheukting/mathqa huggingface dataset:
Question (physics): a walks at 30 kmph and 30 hours after his start , b cycles after him at 42 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3150 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 42 = 30 x = 3150 km answer is e"
Answer: e
Question (physics): what is the speed of the stream if a canoe rows upstream at 8 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.9 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 8 ) kmph = 2 kmph . answer d"
Answer: d
Question (geometry): obra drove 150 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 %
b ) 12.5 %
c ) 18.75 %
d ) 25 %
e ) 31.25 %
Rationale: area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 150 π / 480 π = 31.25 % hence , answer is e .
Answer: e
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 305 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 610 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 305 ) = 2 + 2 ( extra ) = > 2 x - 610 = x = > x = 610 . answer : b"
Answer: b
Question (gain): at a florist shop on a certain day , all corsages sold for either $ 20 or $ 30 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 10 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000
Rationale: "let , no . of corsages @ $ 20 = x , no . of corsages @ $ 30 = y and revenue = r so , 20 x + 30 y = r . . . . . . . . . ( 1 ) now , given the situation , 20 ( x + 8 ) + 30 ( y - 8 ) = r - . 1 r = > 20 x + 160 + 30 y - 240 = . 9 r = > 20 x + 30 y = . 9 r + 80 . . . . . . . . . . . . ( 2 ) so , r = . 9 r + 80 = > r = 800 the answer is d ."
Answer: d
Question (general): two pots are in side - by - side . one pot , which is 20 inches tall , casts a shadow that is 10 inches long . the other pot is 40 inches tall . compute , in inches , the length of the shadow that the taller pot casts .
Options: a ) 25 , b ) 30 , c ) 10 , d ) 15 , e ) 20
Rationale: the ratio of shadow to height is constant , so if x is the length of the shadow , then 20 / 10 = 40 / x and x = 20 . correct answer e
Answer: e
Question (other): income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 19000 , then find his savings ?
Options: a ) 3800 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 19000 = > x = 3800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3800 . answer : a"
Answer: a
Question (general): ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 7.0 = ?
Options: a ) - 0.61 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 0.61 answer a
Answer: a
Question (general): if 9 a - b = 10 b + 60 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 8 , b ) - 4 , c ) 0 , d ) 4 , e ) 8
Rationale: "( i ) 9 a - 11 b = 60 ( ii ) 2 a + 22 b = - 60 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Question (general): in a fuel station the service costs $ 2.75 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 ) 420 $ , d ) 450 $ , e ) 462 $
Rationale: 12 * 2.75 + 0.65 * 12 * 55 = 462 hence - e
Answer: e
Question (gain): find 20 % of 240
Options: a ) 96 , b ) 94 , c ) 86 , d ) 74 , e ) 48
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 20 % of 240 20 / 100 × 240 = 48 answer : e"
Answer: e
Question (general): if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 12 . what is the value of f ( 6 ) ?
Options: a ) 1 , b ) 0 , c ) - 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 12 then f ( 5 ) = 12 - 5 = 7 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 7 - 6 = 1 . answer : a . questions on funtions to practice :"
Answer: a
Question (general): if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 12.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 318 , b ) $ 289 , c ) $ 282 , d ) $ 274 , e ) $ 286
Rationale: total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 12 = 16 * 12 = 192 $ total charge = 126 + 192 = 318 $ answer a
Answer: a
Question (general): when a number is divided by 3 & then multiply by 12 the answer is 9 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 2.25 , d ) 5.7 , e ) 6.5
Rationale: "if $ x $ is the number , x / 3 * 12 = 9 = > 4 x = 9 = > x = 2.25 c"
Answer: c
Question (gain): an error 2 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 1.04 , b ) 2.04 , c ) 3.04 , d ) 4.04 , e ) none of these
Rationale: "explanation : 100 cm is read as 102 cm . a 1 = ( 100 × 100 ) cm 2 and a 2 = ( 102 × 102 ) cm 2 ( a 2 - a 1 ) = [ 1022 - 1002 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 answer : d"
Answer: d
Question (geometry): juan and his five friends will sit on six fixed seats around a circular table . if juan must sit on the seat closest to the window and jamal must sit next to juan , in how many can juan and his five friends sit ?
Options: a ) 20
b ) 24
c ) 48
d ) 72
e ) 120
Rationale: j = juan , f = jamal since j is always fixed , set j , set f relative to j , then see how many options there are : j f 4 3 2 1 = 24 or f j 4 3 2 1 = 24 24 + 24 = 48 … c answer : c
Answer: c
Question (general): lucia ' s sells kale at x dollar per pound for the first 20 pounds and . 8 x for every subsequent pound . amby ' s price is x per pound for the first 14 pounds and . 9 x for subsequent pounds . what is the minimum number of pounds over 15 for which lucia ' s becomes an equal or better deal ?
Options: a ) 24 , b ) 26 , c ) 25 , d ) 27 , e ) 28
Rationale: for amy ' s deal to be better , the cost has to be less or equal to lucia ' s assuming ' n ' is the number of pounds of kale , the equation is 20 x + ( n - 20 ) ( 0.8 x ) < = 14 x + ( n - 14 ) ( 0.9 x ) resolve it : = = > 20 x + 0.8 nx - 16 x < = 14 x + 0.9 nx - 12.6 x = = > 2.6 x < = 0.1 nx = = > 26 x < = nx = = > x ( n - 26 ) > = 0 as x can not be 0 , = = > n - 26 > = 0 = = > n > = 26 so the minimum value is 26 ' b ' would be the correct answer
Answer: b
Question (general): when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 1 . what is the value of 7 y – x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y - 3 = x 7 y - x = 3 the answer is c ."
Answer: c
Question (general): in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 140800 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 140800 = 1 * 5 ^ 2 * 8 ^ 3 * 11 the factors of 8 must come from the purple point value , so there are 3 purple chips . the answer is c .
Answer: c
Question (general): evaluate 49 / . 07
Options: a ) 400 , b ) 500 , c ) 700 , d ) none of these , e ) 506
Rationale: "explanation : 49 / . 07 = 4900 / 7 = 700 option c"
Answer: c
Question (general): an employee ’ s annual salary was increased 30 % . if her old annual salary equals $ 30,000 , what was the new salary ?
Options: a ) $ 28,000 , b ) $ 25,000 , c ) $ 20,000 , d ) $ 35,000 , e ) $ 39,000
Rationale: "old annual salary = $ 30,000 salary increase = 30 % . original salary = $ 30,000 * 30 / 100 = $ 9000 new salary = $ 30,000 + $ 9000 = $ 39,000 hence e ."
Answer: e
Question (general): 1 , 3,5 , 7,9 , . . . . 50 find term of sequnce
Options: a ) 1000 , b ) 1200 , c ) 1300 , d ) 1800 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Question (gain): david deposited $ 5000 to open a new savings account that earned 6 percent annual interest , compounded semi - annually . if there were no other transactions in the account , what the amount of money in david account one year after the account was opened ?
Options: a ) $ 5306 , b ) $ 6120 , c ) $ 5136 , d ) $ 5405 , e ) $ 5500
Rationale: approach # 1 : 6 percent annual interest compounded semi - annually - - > 3 % in 6 moths . for the first 6 moths interest was 3 % of $ 5000 , so $ 150 ; for the next 6 moths interest was 3 % of $ 5000 , plus 3 % earned on previous interest of $ 150 , so $ 150 + $ 6 = $ 156 ; total interest for one year was $ 150 + $ 156 = $ 306 , hence balance after one year was $ 5000 + $ 306 = $ 5306 . answer : a .
Answer: a
Question (general): ( 1000 ) 7 ÷ ( 10 ) 17 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: explanation : = ( 103 ) 7 / ( 10 ) 17 = ( 10 ) 21 / ( 10 ) 17 = 10 ( 4 ) = 10000 option d
Answer: d
Question (other): how many multiples of 3 are there between 100 and 300 ( both are inclusive ) ?
Options: a ) 67.6 , b ) 1.58 , c ) 2.47 , d ) 3.54 , e ) 6.51
Rationale: "the answer is ( 300 - 100 ) / 3 + 1 = 67.6 answer is a"
Answer: a
Question (probability): find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50
Rationale: let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 } n ( x ) = 15 , n ( s ) = 50 hence , the required probability is 15 / 50 . answer : b
Answer: b
Question (gain): fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 10 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 1.250 kg , e ) none of these
Rationale: "the weight of non - water in 10 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 10 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 1.25 answer : d"
Answer: d
Question (physics): two trains , a and b , started simultaneously from opposite ends of a 200 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 200 - mile trip in 10 hours ; train b , traveling at a constant rate , completed the 200 - mile trip in 6 hours . how many miles had train a traveled when it met train b ?
Options: a ) 70 , b ) 75 , c ) 87.5 , d ) 90 , e ) 92.5
Rationale: "as the ratio of the rates of a and b is 6 to 10 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 6 / ( 6 + 10 ) = 6 / 16 of 200 miles : 200 * 6 / 16 = 75 miles . answer : b ."
Answer: b
Question (general): a mixture of 200 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 11 liters , b ) 11.2 liters , c ) 12.5 liters , d ) 13.78 liters , e ) 13.33 liters
Rationale: "number of liters of water in 200 liters of the mixture = 20 % of 120 = 20 / 100 * 200 = 40 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 40 + p ) and total volume of mixture is ( 200 + p ) . ( 40 + p ) = 25 / 100 * ( 200 + p ) 160 + 4 p = 200 + p p = 13.33 liters . answer : e"
Answer: e
Question (probability): a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 5 from part a & 10 from part b , in how many ways can he choose the questions ?
Options: a ) 100 , b ) 120 , c ) 125 , d ) 350 , e ) 252
Rationale: "there 5 questions in part a out of which 10 question can be chosen as = 10 c 5 similarly , 10 questions can be chosen from 10 questions of part b as = 10 c 10 . hence , total number of ways , = 10 c 5 * 10 c 10 = [ 10 ! / ( 5 ! 5 ! ) ] * [ 10 ! / ( 0 ! * 10 ) ] = { 10 * 9 * 8 * 7 * 6 / ( 5 * 4 * 3 * 2 * 1 ) } * 10 ! / 1 * 10 ! = 252 e"
Answer: e
Question (general): on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 240,000 ?
Options: a ) 27 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 240 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 240,000 = 3 years total 27 years . answer a"
Answer: a
Question (general): 14.02 ã — 0.001 = ?
Options: a ) 0.1402 , b ) 0.001402 , c ) 1.4021 , d ) 0.01402 , e ) none of these
Rationale: "14.02 ã — 0.001 = 0.01402 the answer is d ."
Answer: d
Question (physics): mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 17 candidates . she plans to have one working interview with 3 of the 17 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 420 , c ) 300 , d ) 30 , e ) 333
Rationale: "420 . answer b"
Answer: b
Question (general): the average ( arithmetic mean ) of 5 numbers is 5 . if 2 is subtracted from each of 4 of the numbers , what is the new average ?
Options: a ) 3.4 , b ) 4.5 , c ) 6.2 , d ) 5.7 , e ) 6.9
Rationale: let the numbers be a , b , c , d , e , f so , total of these 5 numbers must be 25 or , a + b + c + d + e = 25 so , 12 must be subtracted from the total sum i . e a + b + c + d + e - 8 or , 25 - 8 = 17 hence average of the 5 numbers now is 17 / 5 = > 3.4 so , answer will be a
Answer: a
Question (geometry): the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many q grams ?
Options: a ) q = 16
b ) q = 32
c ) 64
d ) 128
e ) 512
Rationale: weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )
Answer: b
Question (physics): a man can row upstream at 34 kmph and downstream at 48 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 41 , d ) 32 , e ) 23
Rationale: "us = 34 ds = 48 m = ( 48 + 34 ) / 2 = 41 answer : c"
Answer: c
Question (other): a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 6 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 12 , b ) 18 , c ) 14 , d ) 20 , e ) 22
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 6 ) = ( 7 / 16 ) * v 1 ( v 1 - 6 ) / v 1 = 3 / 4 6 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 6 = 24 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 24 = 14 litres . answer : c"
Answer: c
Question (general): one ton has 2300 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1840 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2300 pound = 13 * 2300 * 16 ounces . hence the answer is ( 13 * 2300 * 16 ) / 260 = 1840 . answer : a ."
Answer: a
Question (physics): a man can row 2 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 1.8 , b ) 1.9 , c ) 1.2 , d ) 1.7 , e ) 1.3
Rationale: "m = 2 s = 1.2 ds = 2.4 us = 0.8 x / 1.2 + x / 0.8 = 1 x = 0.6 d = 0.6 * 2 = 1.2 answer : c"
Answer: c
Question (general): total dinning bill for 10 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 24.26
Rationale: 211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 10 = 24.26 answer : e
Answer: e
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 40 % profit on the first article and 40 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 400 , e ) 270
Rationale: "profit on first article = 40 % of 1000 = 400 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"
Answer: d
Question (general): sawyer is mixing up a salad dressing . regardless of the number of servings , the recipe requires that 5 / 8 of the finished dressing mix be peanut oil , 1 / 4 vinegar , and the remainder an even mixture of salt , pepper and sugar . if sawyer accidentally doubles the vinegar and forgets the sugar altogether , what proportion of the botched dressing will be peanut oil ?
Options: a ) 15 / 29 , b ) 5 / 8 , c ) 5 / 16 , d ) 1 / 2 , e ) 13 / 27
Rationale: peanut oil = 5 / 8 = 15 / 24 - - > 15 parts out of 24 ; vinegar = 1 / 4 = 6 / 24 - - > 6 parts out of 24 ; salt + pepper + sugar = 1 - ( 15 / 24 + 6 / 24 ) = 3 / 24 , so each = 1 / 24 - - > 1 part out of 24 each ; if vinegar = 12 ( instead of 6 ) and sugar = 0 ( instead of 1 ) then total = 15 + 12 + 1 + 1 + 0 = 29 parts out of which 15 parts are peanut oil - - > proportion = 15 / 29 . answer : a .
Answer: a
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 30 % profit on the first article and 30 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 300
Rationale: "profit on first article = 30 % of 1000 = 300 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e"
Answer: e
Question (general): a number is doubled and 11 is added . if resultant is doubled , it becomes 74 . what is that number
Options: a ) 18 , b ) 10 , c ) 13 , d ) 14 , e ) 16
Rationale: "explanation : = > 2 ( 2 x + 11 ) = 74 = > 4 x + 22 = 74 = > 4 x = 52 = > x = 13 option c"
Answer: c
Question (physics): raja and ram can together complete a piece of work in 4 days . if raja alone can complete the same work in 12 days , in how many days can ram alone complete that work ?
Options: a ) 6 days , b ) 5 days , c ) 7 days , d ) 8 days , e ) 10 days
Rationale: ( raja + ram ) ' s 1 days work = 1 / 4 raja 1 day work = 1 / 2 ram 1 day work = ( 1 / 4 - 1 / 12 ) = 1 / 6 = = > 6 days answer a
Answer: a
Question (gain): fresh grapes contain 60 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 37.5 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 60 = 40 % of whole weight ) , so 20 * 0.75 = x * 0.4 - - > x = 37.5 . answer : c"
Answer: c
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 330 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 197 , d ) 660 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 330 ) = 2 + 2 ( extra ) = > 2 x - 660 = x = > x = 660 . answer : d"
Answer: d
Question (general): what is the remainder when 617 + 1176 is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "617 + 1176 mod 7 = > 617 % 7 + 1176 % 7 = > 1 + 0 = > 1 % 7 = > 1 answer : a"
Answer: a
Question (physics): a and b together can complete a piece of work in 4 days . if a alone can complete the same work in 12 days , in how many days can b alone complete that work ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 8
Rationale: "a and b ' s one day work = 1 / 4 a ' s 1 day ' s work = 1 / 12 b ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 12 ) = 2 / 12 = 1 / 6 hence b alone can complete the work in 6 days . answer is option c"
Answer: c
Question (physics): a train 300 m long , running with a speed of 90 km / hr will pass a tree in ?
Options: a ) 17 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec time taken = 300 * 1 / 25 = 12 sec answer : e"
Answer: e
Question (general): tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 75 ?
Options: a ) 4 , b ) 18 , c ) 15 , d ) 20 , e ) 24
Rationale: you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 18 * 50 600 1800 - 900 0900 12 75.00 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is b
Answer: b