Cheukting/mathqa huggingface dataset:
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1300 , what is the reduced price for kg ?
Options: a ) s . 40 , b ) s . 65 , c ) s . 49 , d ) s . 41 , e ) s . 42
Rationale: "1300 * ( 25 / 100 ) = 325 - - - - 5 ? - - - - 1 = > rs . 65 answer : b"
Answer: b
Question (general): how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1 / 2 m board ?
Options: a ) 90 , b ) 99 , c ) 97 , d ) 95 , e ) 65
Rationale: "30 * 33 / 2 = 5 / 2 * 2 * x = > x = 99 answer b"
Answer: b
Question (general): 20 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 4 : 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 20 + x = ( 3 / 7 ) * ( 20 + x ) 280 + 35 x = 300 + 15 x 20 x = 20 x = 1 the answer is a ."
Answer: a
Question (gain): a sum amounts to rs . 5292 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 4000 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 5292 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 5292 = p [ 21 / 20 ] ^ 2 5292 [ 20 / 21 ] ^ 2 4800 answer : d"
Answer: d
Question (physics): express a speed of 56 kmph in meters per second ?
Options: a ) 10.56 mps , b ) 17.56 mps , c ) 97.56 mps , d ) 15.56 mps , e ) 18.56 mps
Rationale: "56 * 5 / 18 = 15.56 mps answer : d"
Answer: d
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 45 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 372 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 45 ) = 21 + 351 = > 372 hence answer will be ( b ) 372"
Answer: b
Question (physics): a group of men decided to do a work in 12 days , but 6 of them became absent . if the rest of the group did the work in 14 days , find the original number of men ?
Options: a ) 15 , b ) 42 , c ) 44 , d ) 45 , e ) 18
Rationale: "original number of men = 6 * 14 / ( 14 - 12 ) = 42 answer is b"
Answer: b
Question (gain): a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 234 for it , the cost price of the cricket bat for a is :
Options: a ) 156 , b ) 120 , c ) 130 , d ) 160 , e ) 210
Rationale: "125 % of 120 % of a = 234 125 / 100 * 120 / 100 * a = 234 a = 234 * 2 / 3 = 156 . answer a"
Answer: a
Question (physics): a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 5 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 5 ] = 56 m answer b"
Answer: b
Question (gain): in town x , 64 percent of the population are employed , and 49 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 20 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 15 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 15 / 64 = 20 b"
Answer: b
Question (physics): the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour . the motor - cyclist stops to wait for the hiker 12 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the motor - cyclist wait until the hiker catches up ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 48 , e ) 60
Rationale: for the 12 minutes the motor - cyclist continues to overtake the hiker , she is going at 24 miles per hour faster than the hiker . once the motor - cyclist stops , the hiker is going at 6 miles per hour while the motor - cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 24 / 6 * 12 or 48 minutes answer is ( d )
Answer: d
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 90 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 26 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 90 m = 90 / 5 = 18 seconds . answer : e"
Answer: e
Question (physics): a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 9 seconds . due to some problem , one boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 8.25 sec , e ) none of these
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 9 = 20 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 â  „ 20 = 8.25 sec . answer d"
Answer: d
Question (gain): a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 2640 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 2640 100 r + 120 r = 2640 r = 12 % answer : b"
Answer: b
Question (general): tickets numbered from 1 to 26 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 4 / 13 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 26 = 4 / 13 the answer is d ."
Answer: d
Question (gain): in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 56 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 400 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 56 , so 0.14 * { total } = 56 - - > { total } = 400 . answer : b ."
Answer: b
Question (geometry): the number 219 can be written as sum of the squares of 3 different positive integers . what is the sum of these 3 different integers ?
Options: a ) 20 , b ) 21 , c ) 19 , d ) 17 , e ) 15
Rationale: "sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now , sum of these 3 different integers = 13 + 7 + 1 = 21 ans - b"
Answer: b
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 7 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 7 / 27 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 7 * x hence , a 1 + a 2 + . . + a 20 + n = 27 x so , the fraction asked = 7 x / 27 x = 7 / 27 answer a"
Answer: a
Question (general): in a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man . what is weight of new comer ?
Options: a ) 70 , b ) 66 , c ) 68 , d ) 69 , e ) 72
Rationale: solution : member in group * age increased = difference of replacement or , 8 * 1 = new comer - man going out or , new comer = 8 + 60 ; or , new comer = 68 years . answer : option c
Answer: c
Question (other): the ratio of a and b is 5 : 3 . after 2 years their ratio is 3 : 2 . what is the age of b ?
Options: a ) 5 , b ) 3 , c ) 6 , d ) 7 , e ) 8
Rationale: the ratio of a and b is 5 x and 3 x years . after 2 years , their ratio will be 3 and 2 . ( i . e ) ( 5 x + 2 ) / ( 3 x + 2 ) = 3 / 2 10 x + 4 = 9 x + 6 x = 2 b ' s age = 3 x = 3 ( 2 ) = 6 years answer is option c
Answer: c
Question (physics): a train leaves delhi at 7 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 840 , c ) 600 , d ) 888 , e ) 121
Rationale: "d = 30 * 7 = 210 rs = 40 – 30 = 10 t = 210 / 10 = 21 d = 40 * 21 = 840 km answer : b"
Answer: b
Question (general): if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 , inclusive ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: one case is rainy - rainy - rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 4 = 1 / 16 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 1 / 16 = 1 / 4 the answer is a .
Answer: a
Question (geometry): eight cubes , each with a volume of 512 cm ^ 3 , are joined to form one large cube . what is the surface area of the large cube ?
Options: a ) 4096 sq cm
b ) 1536 sq cm
c ) 1024 sq cm
d ) 2048 sq cm
e ) 512 sq cm
Rationale: volume = a x a x a = a ^ 3 volume of cube = 8 x 512 = 4096 cm ^ 3 4096 = a ^ 3 a = 16 surface area of cube = 6 a ^ 2 = 6 x 16 ^ 2 = 1536 answer is b
Answer: b
Question (geometry): the length of a rectangle is twice its breadth . if its lengthis decreased by 5 cm & breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle ?
Options: a ) 25 cm , b ) 30 cm , c ) 40 cm , d ) 45 cm , e ) 60 cm
Rationale: let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x 2 + 75 ⇒ 2 x 2 + 10 x − 5 x − 25 = 2 x 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm c
Answer: c
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 51200 ?
Options: a ) 81000 , b ) 81028 , c ) 27772 , d ) 29889 , e ) 64800
Rationale: 51200 * 9 / 8 * 9 / 8 = 64800 . answer : e
Answer: e
Question (general): set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 4 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9
Rationale: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 4 then total increased to 62 + 4 = 66 new avg - 66 / 10 = 6.6 . hence answer is a ."
Answer: a
Question (gain): during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 18 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . d"
Answer: d
Question (general): how many numbers are divisible by 4 between 1 and 100 .
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 25
Rationale: "numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the number between 1 to 100 which are divisible by 4 . so answer is 24 numbers . option : a"
Answer: a
Question (general): if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . what is the actual distance travelled by him ?
Options: a ) 33 , b ) 11 , c ) 38 , d ) 50 , e ) 12
Rationale: "assume that the person would have covered x km if travelled at 10 km / hr ⇒ speed = distancetime = x 10 . . . . . ( equation 1 ) give that the person would have covered ( x + 20 ) km if travelled at 14 km / hr ⇒ speed = distancetime = ( x + 20 ) 14 . . . . . ( equation 2 ) from equations 1 and 2 , x 10 = ( x + 20 ) 1414 x = 10 x + 2004 x = 200 x = 2004 = 50 answer : d"
Answer: d
Question (general): arjun started a business with rs . 40,000 and is joined afterwards by anoop with rs . 80 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 40000 * 12 = 80000 * ( 12 – x ) = > x = 6 . answer : d"
Answer: d
Question (general): 5555 × 9999 = ?
Options: a ) 55500005 , b ) 55511115 , c ) 55522225 , d ) 55533335 , e ) 55544445
Rationale: "e 55544445 5555 × 9999 = 5555 ( 10000 - 1 ) = 5555 × 10000 - 5555 × 1 = 55550000 - 5555 = 55544445"
Answer: e
Question (general): 1397 x 1397 = ?
Options: a ) 1951607 , b ) 1951609 , c ) 1951610 , d ) 1951611 , e ) 1951613
Rationale: "1397 x 1397 = ( 1397 ) 2 = ( 1400 - 3 ) 2 = ( 1400 ) 2 + ( 3 ) 2 - ( 2 x 1400 x 3 ) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609 . b )"
Answer: b
Question (general): if 5 < x < 11 and y = x + 6 , what is the greatest possible integer value of x + y ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "x + y = x + x + 6 = 2 x + 6 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 10.5 then x + y = 10.5 + 16.5 = 27 . the answer is c ."
Answer: c
Question (physics): pipe p can fill a tank in 8 hours , pipe q in 12 hours and pipe r in 20 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.4 hours , c ) 3.8 hours , d ) 3.5 hours , e ) 4.5 hours
Rationale: explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 8 + 1 / 12 + 1 / 20 ) = 31 / 120 all the three pipes together will fill the tank = 120 / 31 = 3.8 hours answer c
Answer: c
Question (general): a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 2 / 11 , b ) 3 / 14 , c ) 5 / 17 , d ) 7 / 20 , e ) 11 / 30
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 5 ( 1 - x ) p 12 xp = 5 p - 5 xp 17 xp = 5 p x = 5 / 17 the answer is c ."
Answer: c
Question (gain): a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 35 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 21.6 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 35 ) / 100 × 16 = 21.6 answer b"
Answer: b
Question (general): if the sum of two numbers is 55 and the h . c . f and l . c . m of these numbers are 5 and 120 respectively , then the sum of the reciprocal of the numbers is equal to :
Options: a ) 55 / 601 , b ) 601 / 55 , c ) 11 / 120 , d ) 120 / 11 , e ) 120 / 13
Rationale: "let the numbers be a and b . then , a + b = 55 and ab = 5 * 120 = 600 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 55 / 600 = 11 / 120 . answer : c"
Answer: c
Question (gain): a person bought 129 glass bowls at a rate of rs . 11 per bowl . he sold 118 of them at rs . 15 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 2900 / 129 , c ) 2430 / 70 , d ) 2791 / 11 , e ) 2719 / 8
Rationale: "cp = 129 * 11 = 1419 and sp = 118 * 15 = 1770 gain % = 100 * ( 1770 - 1419 ) / 1419 = 2900 / 129 answer : b"
Answer: b
Question (geometry): a cube of edge 12 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 5.76 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 12 * 12 * 12 cm ^ 3 rise in water level = volume / area = 12 * 12 * 12 / 20 * 15 = 5.76 cm answer is a"
Answer: a
Question (physics): two cars are driving toward each other . the first car is traveling at a speed of 100 km / h , which is 20 % slower than the second car ' s speed . if the distance between the cars is 1125 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 4.8 , d ) 5 , e ) 5.5
Rationale: "the speed of the first car is 100 km / h . the speed of the second car is 100 / 0.8 = 125 km / h . the two cars complete a total of 225 km each hour . the time it takes the cars to meet is 1125 / 225 = 5 hours . the answer is d ."
Answer: d
Question (physics): a train 140 m long running at 84 kmph crosses a platform in 16 sec . what is the length of the platform ?
Options: a ) 287 , b ) 298 , c ) 233 , d ) 726 , e ) 267
Rationale: "d = 84 * 5 / 18 = 16 = 373 â € “ 140 = 233 answer : c"
Answer: c
Question (physics): by travelling at 70 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 ) 25 kmph , b ) 20 kmph , c ) 28 kmph , d ) 35 kmph , e ) 32 kmph
Rationale: let the time taken to reach the destination be 3 x hours . total distance = 70 * 3 x = 210 x km he covered 2 / 3 * 210 x = 140 x km in 1 / 3 * 3 x = x hours so , the remaining 70 x km , he has to cover in 2 x hours . required speed = 70 x / 2 x = 35 kmph . answer : d
Answer: d
Question (general): the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 50 more than the number who did not , and if receipts for registration and lunch totaled $ 82,900 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 650 , c ) 1,300 , d ) 1,500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 50 more than the number who did not . that means , total number of people who registered and paid for lunch = 50 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 50 + x ) = 3600 + 72 x now , total amount received was 82900 . thus , from the above data , 50 x + 3600 + 72 x = 82900 122 x = 82900 - 3600 122 x = 79300 x = 650 hence the correct ans is b"
Answer: b
Question (general): the unit digit in the product ( 594 * 897 * 929 * 462 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 4 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 7 * 9 * 2 ) = 4 answer : d"
Answer: d
Question (general): how many times will the digit 8 be written when listing the integers from 1 to 1000 ?
Options: a ) 164 , b ) 297 , c ) 300 , d ) 345 , e ) 482
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 8 ) 3000 / 10 = 300 times . answer : c ."
Answer: c
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 63 km / hr . what is the length of the platform ?
Options: a ) 240 , b ) 288 , c ) 277 , d ) 226 , e ) 280
Rationale: "speed = 63 * 5 / 18 = 17.5 m / sec . length of the train = 17.5 * 20 = 350 m . let the length of the platform be x m . then , ( x + 350 ) / 36 = 17.5 = > x = 280 m . answer : e"
Answer: e
Question (gain): machine a and machine b are each used to manufacture 330 sprockets . it takes machine a 10 hours longer to produce 330 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 3
Rationale: "machine b : takes x hours to produce 330 sprockets machine a : takes ( x + 10 ) hours to produce 330 sprockets machine b : in 1 hour , b makes 330 / x sprockets machine a : in 1 hour , a makes 330 / ( x + 10 ) sprockets equating : 1.1 ( 330 / ( x + 10 ) ) = 330 / x 484 / ( x + 10 ) = 330 / x 363 x = 330 x + 3300 33 x = 3300 x = 100 a makes 330 / ( 110 ) = 3 sprockets per hour answer : e"
Answer: e
Question (other): if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 217 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 6 , e ) 1 / 6
Rationale: "217 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 217 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 217 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 216 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 216 = r ^ 3 r = 6 d"
Answer: d
Question (general): on dividing 136 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 18
Rationale: "d = ( d - r ) / q = ( 136 - 1 ) / 9 = 135 / 9 = 15 b )"
Answer: b
Question (general): a 72 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 14 , e ) 16
Rationale: "amount of salt = 7.2 assume x gallons of water are added . 7.2 / 72 + x = 8 / 100 720 = 8 x + 576 8 x = 144 x = 18 correct option : c"
Answer: c
Question (geometry): the radius of a cylindrical vessel is 9 cm and height is 3 cm . find the whole surface of the cylinder ?
Options: a ) 308 sq cm , b ) 220 sq cm , c ) 440 sq cm , d ) 132 sq cm , e ) 678.8 sq cm
Rationale: "r = 9 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 9 ( 12 ) = 678.8 answer : e"
Answer: e