Cheukting/mathqa huggingface dataset:
Question (general): what is the smallest number which when diminished by 10 , is divisible 2 , 6 , 12 and 24 ?
Options: a ) 35 , b ) 34 , c ) 20 , d ) 35 , e ) 342
Rationale: "required number = ( lcm of 2 , 6 , 12 and 24 ) + 12 = 24 + 10 = 34 option b"
Answer: b
Question (general): the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 108 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c"
Answer: c
Question (other): if n is the greatest positive integer for which 4 ^ n is a factor of 8 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "8 ! = 40320 e . 4 ^ 10 = 1048576 ( 40320 / 1048576 ) - this is not a factor of 8 ! d . 4 ^ 8 = 65536 ( 40320 / 65536 ) - this is not a factor of 8 ! c . 4 ^ 6 = 4096 ( 40320 / 4096 ) - this is not a factor of 8 ! b . 4 ^ 4 = 256 ( 40320 / 256 ) - this is not a factor of 8 ! a . 4 ^ 2 = 16 ( 40320 / 16 ) - this is a factor of 8 !"
Answer: a
Question (general): if the average ( arithmetic mean ) of a and b is 215 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 110 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 215 = = = > a + b = 430 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 430 - 320 = = = > a + b - b - c = 110 = = = > a - c = 110 answer : d"
Answer: d
Question (general): 3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is w , what is the difference between the probability that w is even and the probability that w is odd ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2
Rationale: age of boys w : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 1311 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 1714 9 combinations of sum between sets ( 10 , 1211 ) ( 13 , 1714 ) = 23 , 2724 - 16 , 3017 - 24 , 2825 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9
Answer: a
Question (physics): a can do a job in 30 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 26 days , c ) 30 days , d ) 31 days , e ) 39 days
Rationale: "c 1 / 30 + 1 / 30 = 1 / 15 15 * 2 = 30 days"
Answer: c
Question (general): 8 x 2.25 - 5 x 0.85 / 2.5 = ?
Options: a ) 3.8 , b ) 10 , c ) 5 , d ) 5.5 , e ) 7.5
Rationale: "given expression = ( 18 - 4.25 / 2.5 = 13.75 / 2.5 = 137.5 / 25 = 5.5 answer is d ."
Answer: d
Question (gain): a is a working partner and b is a sleeping partner in the business . a puts in rs . 20000 and b rs . 25000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4800 , e ) 7291
Rationale: 20 : 25 = > 4 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 4 / 9 = 3840 + 960 = 4800 answer : d
Answer: d
Question (gain): if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 170 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 170 and so k = 170 - l l + 10 = 1.5 k = 1.5 ( 170 - l ) 2.5 l = 245 l = 98 the answer is d ."
Answer: d
Question (geometry): 12 * 18 * 6 is the volume of some material . how many cubes of edge 3 can be insert into it ?
Options: a ) 48
b ) 49
c ) 50
d ) 51
e ) 52
Rationale: no . of such cubes = volume of material / volume of one cube ( 12 * 18 * 6 ) / ( 3 * 3 * 3 ) = 48 answer : a
Answer: a
Question (gain): john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.63 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.63 - - > 15 p - 13.5 p = 63 - - > p = 42 . answer : d ."
Answer: d
Question (general): 1904 x 1904 = ?
Options: a ) 3623216 , b ) 3624216 , c ) 3624316 , d ) 3625116 , e ) 3625216
Rationale: "1904 x 1904 = ( 1904 ) 2 = ( 1900 + 4 ) 2 = ( 1900 ) 2 + ( 4 ) 2 + ( 2 x 1900 x 4 ) = 3610000 + 16 + 15200 . = 3625216 . e )"
Answer: e
Question (gain): at what rate percent per annum will sum of money double in 20 years ?
Options: a ) 1.2 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) none of these
Rationale: "explanation : hint : if sum of money becomes ( z times ) in ( t ) years at simple interest , then rate of interest ( r ) can be calculated using the formula : rate of interest ( r ) % = 100 ( z – 1 ) / t here , principal amount is not given . hence , we can directly use the trick to calculate the rate of interest . rate of interest ( r ) % = 100 ( 2 – 1 ) / 20 rate of interest ( r ) % = 5 % p . a . answer is d"
Answer: d
Question (general): n is a positive integer . when n + 1 is divided by 3 , the remainder is 2 . what is the remainder when n is divided by 3 ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "n + 1 = 3 a + 2 i . e . n + 1 = 5 , 8 , 11 , 14 , . . . etc . i . e . n = 4 , 7 , 10 , 13 , . . . etc . when n is divided by 3 remainder is always 1 answer : a"
Answer: a
Question (gain): i bought two books ; for rs . 490 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337.83 , b ) 285.83 , c ) 284.83 , d ) 266.83 , e ) 299.83
Rationale: "x * ( 85 / 100 ) = ( 490 - x ) 119 / 100 x = 285.83 answer : b"
Answer: b
Question (physics): if 13 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 52 days
Rationale: "13 * 80 = 20 * x x = 52 days answer : e"
Answer: e
Question (general): 9773 + x = 13200 , then x is ?
Options: a ) 3427 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9773 = 3427 option : a"
Answer: a
Question (general): when 5 + 6 = 305 , 6 + 7 = 425 , 7 + 8 = 565 , then 8 + 9 = ?
Options: a ) 705 , b ) 735 , c ) 685 , d ) 665 , e ) 725
Rationale: 5 + 6 = > 5 ã — 6 = 30 = > 30 ã — 10 + 5 = 305 6 + 7 = > 6 ã — 7 = 42 = > 42 ã — 10 + 5 = 425 7 + 8 = > 7 ã — 8 = 56 = > 56 ã — 10 + 5 = 565 then 8 + 9 = > 8 ã — 9 = 72 = > 72 ã — 10 + 5 = 725 answer : e
Answer: e
Question (gain): the population of a town is 7800 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9600 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7800 ã — 100 / 90 ã — 100 / 90 = 9629 a )"
Answer: a
Question (geometry): a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls , the volume of hall is ?
Options: a ) 1100
b ) 1200
c ) 1300
d ) 1400
e ) 1500
Rationale: area of 4 wall = sum of area of floor and celling 2 ( l + b ) * h = 2 ( l * b ) ( 15 + 12 ) * h = 2 ( 12 * 15 ) on solving h = 20 / 3 m volume = l * b * h = 12 * 15 * 20 / 3 = 1200 m ^ 3 answer : b
Answer: b
Question (general): when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 4 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: "i tried plugging in numbers x = 9 q + 5 x = 14 4 x = 56 4 x / 9 = 9 * 6 + 2 remainder is 2 . answer is c"
Answer: c
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat weavers in 8 days ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "explanation : please always remember , that what exactly we need to calculate before applying chain formula . as in this question we need to find how many mats , right ! so we will compare everything with ` ` number of mats ' ' as , more men , more number of mats ( direct proportion ) more days , more number of mats ( direct proportion ) so , it can be solved as , [ weavers 4 4 days 8 8 ] : : 4 : x = > x ∗ 4 ∗ 4 = 8 ∗ 8 ∗ 4 = > x = 16 option c"
Answer: c
Question (geometry): the floor of a rectangular room is 21 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 128 m 2 , c ) 138 m 2 , d ) 148 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 25 ã — 16 = 400 m 2 area of the inner rectangle = 21 ã — 12 = 252 m 2 required area = ( 400 â € “ 252 ) = 148 m 2 answer d"
Answer: d
Question (physics): two bullet trains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 11 sec . , b ) 15 sec . , c ) 13.3 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 20 m / sec = 6 m / sec . relative speed = ( 12 + 6 ) = 18 m / sec . required time = ( 120 + 120 ) / 18 sec = 13.3 sec . c"
Answer: c
Question (general): in a tree , 3 / 7 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 3 / 5 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 11 / 35 , b ) 14 / 35 , c ) 18 / 35 , d ) 31 / 70 , e ) 37 / 70
Rationale: "the fraction of birds that are male robins is ( 2 / 3 ) ( 3 / 7 ) = 2 / 7 . the fraction of birds that are male bluejays is ( 2 / 5 ) ( 4 / 7 ) = 8 / 35 . the total fraction of male birds is 2 / 7 + 8 / 35 = 18 / 35 . the answer is c ."
Answer: c
Question (geometry): the length of a rectangular landscape is 8 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 6 rd of the total landscape . what is the length of the landscape ?
Options: a ) 180 , b ) 270 , c ) 340 , d ) 140 , e ) 240
Rationale: "sol . x * 8 x = 6 * 1200 x = 30 length = 8 * 30 = 240 e"
Answer: e
Question (other): ratio and proportion 215 : 474 : : 537 : ?
Options: a ) 26 , b ) 27 , c ) 25 , d ) 22 , e ) 23
Rationale: 2 + 1 + 5 + 4 + 7 + 4 = 23 5 + 3 + 7 + x = 23 = > x = 8 combination that match 8 is 26 since 2 + 6 = 8 answer : a
Answer: a
Question (physics): sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 288 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 288 per week 36 x = 288 x = 8 correct option : d"
Answer: d
Question (gain): a statue is being carved by a sculptor . the original piece of marble weighed 200 kg . in the first week 20 percent is cut away . in the second week 25 percent of the remainder is cut away . in the third week the statue is completed when 35 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 97.5 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "a 97.5 kg 250 ã — 0.8 ã — 0.75 ã — 0.65 = 97.5 kg ."
Answer: a
Question (general): an offshore company sells two products , l and m . last year , seventy percent of the units sold were product l , and the price of product l was 25 percent greater than the price of product m . approximately what percent of the total revenue the company received last year was from the sale of product l ?
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 65 % , e ) 74 %
Rationale: percentage of total units that is product l = 70 % price of product l = 25 percent greater than price of product m . now , we can consider this as a weighted average scenario . if the price of both the products l and m was equal , then contribution of product l to total sales would be = 70 % but since , price of product l is greater than m , then contribution of product l to total sales will be greater than 70 % the only option is 74 % answer e
Answer: e
Question (general): if x , y , and z are positive integers , and 4 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 23 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 4,5 and 8 = 40 now 4 x = 40 = > x = 10 5 y = 40 = > y = 8 8 z = 40 = > z = 5 10 + 8 + 5 = 23 . option b ."
Answer: b
Question (gain): find the principal which yields a simple interest of rs . 20 and compound interest of rs . 28 in two years , at the same percent rate per annum ?
Options: a ) s . 25 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 28 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 28 – 20 ) / 20 ] * 100 = 40 % p . a . let the principal be rs . x time = t = 2 years % rate = 40 % p . a . si = ( prt / 100 ) 20 = ( x * 40 * 2 ) / 100 x = rs . 25 answer : a"
Answer: a
Question (physics): joshua and jose work at an auto repair center with 2 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 4 probability of chosing jose second = 1 / 3 total = 1 / 12 probability of chosing jose first = 1 / 4 probability of chosing josh second = 1 / 3 total = 1 / 12 final = 1 / 12 + 1 / 12 = 1 / 6 d"
Answer: d
Question (general): in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 90 % , what was the average score for the entire class ?
Options: a ) 65 % , b ) 67 % , c ) 69 % , d ) 72 % , e ) 75 %
Rationale: "70 % of the class scored 60 % and 30 % of the class scored 90 % . the difference between 60 % and 90 % is 30 % . the average will be 60 % + 0.3 ( 30 % ) = 69 % . the answer is c ."
Answer: c
Question (general): of 90 applicants for a job , 42 had at least 4 years ' experience , 54 had degrees , and 8 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 8 , c ) 14 , d ) 16 , e ) 12
Rationale: "90 - 8 = 82 82 - 42 - 54 = - 14 then 14 are in the intersection between 4 years experience and degree . answer : c"
Answer: c
Question (gain): a shopkeeper sold an article at $ 1110 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 850 , b ) $ 875 , c ) $ 900 , d ) $ 925 , e ) $ 950
Rationale: "let x be the cost price . 1.2 x = 1110 x = 1110 / 1.2 = 925 the answer is d ."
Answer: d
Question (physics): two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively . if they cross each other in 33 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 7 , b ) 8 : 7 , c ) 6 : 7 , d ) 6 : 5 , e ) 4 : 7
Rationale: explanation : let the speed of the trains be x and y respectively length of train 1 = 47 x length of train 2 = 31 y relative speed = x + y time taken to cross each other = 33 s = > = 33 = > ( 47 x + 31 y ) = 33 ( x + y ) = > 14 x = 2 y = > x / y = 2 / 14 = 1 / 7 = 1 : 7 answer : a
Answer: a
Question (general): if 25 % of a class averages 80 % on a test , 50 % of the class averages 65 % on the test , and the remainder of the class averages 90 % on the test , what is the overall class average ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 25 % - 50 % = 25 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.25 x 80 + 0.50 x 65 + 0.25 x 90 = 75 the class average is 75 % final answer d ) 75 %"
Answer: d
Question (general): a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord s , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . s = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Question (general): if xy > 0 , 1 / x + 1 / y = 6 , and 1 / xy = 12 , then ( x + y ) / 6 = ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 6 canbe solved as { ( x + y ) / xy } = 12 . substituting for 1 / xy = 12 , we get x + y = 6 / 12 = = > ( x + y ) / 6 = 6 / ( 12 * 6 ) = 1 / 12 . a"
Answer: a
Question (general): how many 4 digit numbers have no repeat digits , do not contain zero , and have a sum of digits d equal to 28 ?
Options: a ) 14 , b ) 24 , c ) 28 , d ) 48 , e ) 96
Rationale: first , look for all 4 digits without repeat that add up to 28 . to avoid repetition , start with the highest numbers first . start from the largest number possible 9874 . then the next largest number possible is 9865 . after this , you ' ll realize no other solution . clearly the solution needs to start with a 9 ( cuz otherwise 8765 is the largest possible , but only equals 26 ) . with a 9 , you also need an 8 ( cuz otherwise 9765 is the largest possible , but only equals 27 ) . with 98 __ only 74 and 65 work . so you have two solutions . each can be rearranged in 4 ! = 24 ways . so d = 24 + 24 = 48 . d
Answer: d
Question (probability): a basket contains 8 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "the total number of ways to choose 2 apples is 8 c 2 = 28 the number of ways that include the spoiled apple is 7 c 1 = 7 p ( the spoiled apple is included ) = 7 / 28 = 1 / 4 the answer is c ."
Answer: c
Question (physics): a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 48 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 ∗ 2 / 25 = 48 seconds option d"
Answer: d
Question (general): of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout , the number of males is 45 more than twice the number of females . if the ratio of female speckled trout to male rainbow trout is 4 : 3 and the ratio of male rainbow trout to all trout is 3 : 20 , how many female rainbow trout are there ?
Options: a ) 192 , b ) 195 , c ) 200 , d ) 205 , e ) 208
Rationale: it will be easier if you draw a table for this one . let t be the total trout . total speckled trout ( st ) = 645 if female speckled trout = fst then male speckled trout = 45 + 2 fst therefore 45 + 2 fst + fst = 645 we solve and get fst = 200 and mst = 445 ratio of fst to mrt = 4 : 3 we have fst = 200 solve ratio to get mrt = 150 now ratio of mrt to t = 3 : 20 we have mrt = 150 solve ratio to get t = 1000 now unless youve drawn the table it might get a little complex . from above we have mst and mrt mst + mrt = 445 + 150 = 595 so t - 595 = total female trouts 1000 - 595 = 405 female trouts we have from above that fst = 200 so ( whew ! ) frt = 405 - 200 = 205 answer is d
Answer: d
Question (gain): find compound interest on rs . 8000 at 15 % per annum for 2 years 4 months , compounded annually
Options: a ) 3109 , b ) 3115 , c ) 3250 , d ) 3500 , e ) 4000
Rationale: "time = 2 yrs 4 mos = 2 ( 4 / 12 ) yrs = 2 ( 1 / 3 ) yrs . amount = rs . [ 8000 x ( 1 + ( 15 / 100 ) ) ^ 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = rs . 11109 . : . c . i . = rs . ( 11109 - 8000 ) = rs . 3109 . answer a"
Answer: a
Question (physics): it costs $ 3 for the first 1 / 3 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 2 hours and 35 minutes , how much will it cost him ?
Options: a ) $ 30 . , b ) $ 31 , c ) $ 32 . , d ) $ 33 . , e ) $ 34 .
Rationale: "2 hrs 35 min = 155 min first 20 min - - - - - - > $ 3 time left is 135 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 155 min costs $ 12 / 60 * 155 = > $ 31 so , total cost will be $ 31 + $ 3 = > $ 34 hence answer will be c"
Answer: c
Question (general): which number should replace both the asterisks in ( * / 21 ) x ( * / 84 ) = 1 ?
Options: a ) 21 , b ) 42 , c ) 63 , d ) 72 , e ) 168
Rationale: "let ( y / 21 ) x ( y / 84 ) = 1 y ^ 2 = 21 x 84 = 21 x 21 x 4 y = ( 21 x 2 ) = 42 the answer is b ."
Answer: b
Question (physics): a train 140 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 30.5 kmph , b ) 31.5 kmph , c ) 32.5 kmph , d ) 33.5 kmph , e ) 21.5 kmph
Rationale: "s = 140 / 16 * 18 / 5 = 31.5 kmph answer : b"
Answer: b
Question (general): how much water must be added to 52 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 13 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 52 litres of milk = ( 1 ⁄ 4 × 52 ) litres = 13 litres . answer b
Answer: b
Question (physics): a train 500 m long takes 10 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 175 kmph , b ) 150 kmph , c ) 162 kmph , d ) 145 kmph , e ) 100 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 500 / [ ( x + 5 ) * 5 / 18 ] = 10 10 ( x + 5 ) = 1800 x = 175 kmph answer is a"
Answer: a
Question (probability): a card is drawn from a pack of 52 cards . the probability of getting a face card ?
Options: a ) 2 / 15 , b ) 2 / 13 , c ) 1 / 15 , d ) 4 / 13 , e ) 5 / 7
Rationale: "clearly in the 52 cards out of which there are 16 face cards . probability of getting a face card = 16 / 52 = 4 / 13 correct option is d"
Answer: d
Question (physics): in what time will a railway train 90 m long moving at the rate of 44 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5 , c ) 4.3 , d ) 6.5 , e ) 7.4
Rationale: "t = 90 / 44 * 18 / 5 = 7.4 sec answer : e"
Answer: e
Question (other): in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 72 per kg ?
Options: a ) 6 : 1 , b ) 4 : 7 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8
Rationale: "( 96 - 72 ) / ( 72 - 68 ) = 24 / 4 = 6 / 1 answer : a"
Answer: a