Cheukting/mathqa huggingface dataset:
Question (general): how many odd 3 - digit integers greater than 800 are there such that all their digits are different ?
Options: a ) 40 , b ) 56 , c ) 72 , d ) 81 , e ) 104
Rationale: in the range 800 - 900 : 1 choice for the first digit : 8 ; 5 choices for the third digit : 1 , 3 , 5 , 7 , 9 ( as the number is odd ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 5 * 8 = 40 . in the range 900 - 999 : 1 choice for the first digit : 9 ; 4 choices for the third digit : 1 , 3 , 5 , 7 ( 9 is out as it ' s the first digit ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 4 * 8 = 32 . total : 40 + 32 = 72 . answer : c
Answer: c
Question (other): the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 40 x = 8 and the number of spinsters is 2 ( 8 ) = 16 . the answer is b ."
Answer: b
Question (gain): 33 1 / 3 % of 240 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 240 = 80 a )"
Answer: a
Question (gain): tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 60 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 980 , e ) $ 1,240
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 30 tickets = 30 * 26 = 780 revenue generated from sales of 60 tickets = 120 + 340 + 780 = 1240 $ answer e"
Answer: e
Question (general): if x is a number such that x ^ 2 + 5 x - 6 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =
Options: a ) - 1 , b ) 1 , c ) 4 , d ) - 6 , e ) 6
Rationale: "x ^ 2 + 5 x - 6 = ( x + 6 ) ( x - 1 ) = 0 then x = - 6 or x = 1 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 1 . the answer is b ."
Answer: b
Question (physics): one pump drains one - half of a pond in 7 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 7 hours so 14 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 14 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 14 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 14 + 1 / a ) = 1 / 2 solving u get a = 14 / 13 = 1.1 hence answer is b"
Answer: b
Question (geometry): what is the area of square field whose side of length 18 m ?
Options: a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 324 sq m , e ) 296 sq m
Rationale: "18 * 18 = 324 sq m answer : d"
Answer: d
Question (general): how much is 80 % of 40 is greater than 4 / 5 of 30 ?
Options: a ) 12 , b ) 27 , c ) 8 , d ) 12 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 32 - 24 = 8 answer : c"
Answer: c
Question (general): how many unique positive odd integers less than 60 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15
Rationale: "the odd numbers less than 60 are 1 , 3,5 , . . . 59 some of them are equal to product of 5 and odd number hence odd multiples of 5 which are less than 60 are 5,15 , 25,35 , 45,55 ( total = 6 ) ; answer : b"
Answer: b
Question (other): in a sports club with 30 members , 17 play badminton and 18 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 18 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a"
Answer: a
Question (general): a line that passes through ( – 3 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 3 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !"
Answer: c
Question (physics): the length of a train and that of a platform are equal . if with a speed of 90 kmph the train crosses the platform in one minute , then the length of the train in metres is
Options: a ) 500 , b ) 600 , c ) 750 , d ) 900 , e ) 950
Rationale: "2 x will be the distance travelled by the train if the length of the train = the length of the platform = x as distance = speed * time distance = 2 x speed in kmph = 90 speed in mps = 90 * 5 / 18 as dist = speed * time 2 x = ( 90 * 5 / 18 ) * ( 60 sec ) on solving x = 900 mts answer : d"
Answer: d
Question (general): a group of n students can be divided into equal groups of 4 with 2 student left over or equal groups of 5 with 2 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 46 , c ) 49 , d ) 53 , e ) 86
Rationale: "4 x + 2 = 5 y + 2 . . . . . . . . . . . ie : 4 x - 5 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x is fraction if y = 4 thus x = 5 n = 22 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 42 summation 22 + 42 = 64 c"
Answer: c
Question (general): in a forest 140 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,400 , e ) 2,500
Rationale: the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 140 tagged deers comprise 10 % of total # of deers - - > total # of deers = 140 * 10 = 1,400 . answer : d .
Answer: d
Question (physics): working at their respective constant rates , machine a makes 100 copies in 15 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 650 , d ) 700 , e ) 750
Rationale: "machine a can produce 100 * 30 / 15 = 200 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 650 copies . c is the answer"
Answer: c
Question (general): the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ?
Options: a ) 11 years , b ) 17 years , c ) 26 years , d ) 14 years , e ) 12 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 240 - 214 ) = 26 years . answer : c"
Answer: c
Question (gain): company a imported 10,500 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported ?
Options: a ) 480 , b ) 840 , c ) 1050 , d ) 420 , e ) 2100
Rationale: "answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are red and 40 % are blue . since we know that there are only three colors , the remaining 40 % must be green . 40 % blue of 10 % brass widgets leads to 4 % green brass widgets out of the total 10,550 widgets . 10,500 / 100 * 4 = 420 . answer d ."
Answer: d
Question (physics): a train 250 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is :
Options: a ) 100 , b ) 60 , c ) 55 , d ) 50 , e ) 45
Rationale: "speed of the train relative to man = 250 / 20 m / sec = 25 / 2 m / sec . = 25 / 2 x 18 / 5 km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 10 ) km / hr . x - 10 = 45 = 55 km / hr . answer : c"
Answer: c
Question (general): you collect baseball cards . suppose you start out with 17 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 17 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 17 + 1 which is 9 , so you ' re left with 17 - 9 = 8 . peter takes 1 baseball card from you : 8 - 1 = 7 baseball cards . paul triples the number of baseball cards you have : 7 ã — 3 = 21 baseball cards . so you have 21 at the end . correct answer : e"
Answer: e
Question (general): a bakery has 6 employees . it pays annual salaries of $ 19000 to each of 2 employees , $ 21000 to 1 employee , and $ 22000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 20,200 , b ) $ 20,500 , c ) $ 20,800 , d ) $ 21,000 , e ) $ 21,400
Rationale: average = 2 ( 19000 ) + ( 21000 ) + 3 ( 22000 ) / 6 = $ 20,833 the answer is c .
Answer: c
Question (general): if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 15.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 336 , 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 ) * 15 = 16 * 15 = 240 $ total charge = 126 + 240 = 366 $ answer a"
Answer: a
Question (geometry): one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .
Options: a ) 120 , b ) 147 , c ) 251 , d ) 451 , e ) 258
Rationale: "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a"
Answer: a
Question (general): a rainstorm increased the amount of water stored in state j reservoirs from 50 billion gallons to 75 billion gallons . if the storm increased the amount of water in the reservoirs to 37.5 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 90 , b ) 114 , c ) 124 , d ) 120 , e ) 127
Rationale: after the reservoir is filled to 75 gallons the amount of water is at 37.5 % - which means that 62.5 % of the reservoir is empty . to figure out what that 62.5 % is approximate : 75 gallons / 37.5 percent = x gallons / 62.5 percent , therefore , x = 125 gallons , answer choices a , b , c , d are below 125 . we know that the reservoir must be short more than 125 gallons , therefore , the only possible choice is e .
Answer: e
Question (general): a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scale ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
Rationale: first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c
Answer: c
Question (general): the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number .
Options: a ) 72 , b ) 64 , c ) 84 , d ) 12 , e ) 92
Rationale: let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 .
Answer: a
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : q = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Question (gain): how many litres of pure acid are there in 15 litres of a 20 % solution
Options: a ) 4 , b ) 5 , c ) 2 , d ) 3 , e ) 1
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 15 * 20 / 100 = 3 answer : option d
Answer: d
Question (general): rs . 385 were divided among x , y , z in such a way that x had rs . 20 more than y and z had rs 15 more than x . how much was y ’ s share ?
Options: a ) rs . 130 , b ) rs . 145 , c ) rs . 154 , d ) rs . 160 , e ) rs . 164
Rationale: let y gets rs x . then we can say x gets rs ( x + 20 ) and y gets rs ( x + 35 ) . x + 20 + x + x + 35 = 385 3 x = 330 x = 110 . r ’ s share = rs ( 110 + 35 ) = rs . 145 b
Answer: b
Question (general): when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a
Answer: a
Question (physics): a group of men decided to do a work in 20 days , but 8 of them became absent . if the rest of the group did the work in 28 days , find the original number of men ?
Options: a ) 60 , b ) 28 , c ) 40 , d ) 50 , e ) 25
Rationale: "original number of men = 8 * 28 / ( 28 - 20 ) = 28 answer is b"
Answer: b
Question (geometry): three walls have wallpaper covering a combined area of 280 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 36 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 32 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters
Rationale: "280 - 180 = 100 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 100 - 36 = 64 sq m of the wallpaper overlaps in three layers . 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m . answer ( b ) ."
Answer: b
Question (general): mr . x , a mathematician , defines a number as ' connected with 6 if it is divisible by 6 or if the sum of its digits is 6 , or if 6 is one of the digits of the number . other numbers are all ' not connected with 6 ' . as per this definition , the number of integers from 1 to 60 ( both inclusive ) which are not connected with 6 is
Options: a ) 18 , b ) 22 , c ) 42 , d ) 43 , e ) 45
Rationale: explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 48 , 54 , 60 . there are 10 such numbers . numbers from 1 to 60 , the sum of whose digits is 6 are : 6 , 15 , 24 , 33 , 42 , 51 , 60 . there are 7 such numbers of which 4 are common to the above ones . so , there are 3 such uncommon numbers . numbers from 1 to 60 , which have 6 as one of the digits are 6 , 16 , 26 , 36 , 46 , 56 , 60 . clearly , there are 4 such uncommon numbers . so , numbers ' not connected with 6 ' = 60 - ( 10 + 3 + 4 ) = 43 . answer : d
Answer: d
Question (general): a camera lens filter kit containing 5 filters sells for $ 67.50 . if the filters are purchased individually , 2 of them are priced at $ 7.45 each , 2 at $ 10.05 each , 1 at $ 14.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 25.66 % , b ) 26.66 % , c ) 27.66 % , d ) 28.66 % , e ) 29.66 %
Rationale: "cost of kit = $ 67.50 if filters are purchased individually - $ 7.45 * 2 + $ 10.05 * 2 + $ 14.50 = $ 49.50 amount saved = $ 67.50 - $ 49.50 = $ 18 required % age = ( $ 18 / $ 67.50 ) * 100 = 26.66 % so , the correct answer is b ."
Answer: b
Question (general): the largest 4 digit number exactly divisible by 90 is ?
Options: a ) 9935 , b ) 9939 , c ) 9944 , d ) 9954 , e ) 9990
Rationale: "largest 4 - digit number = 9999 90 ) 9999 ( 111 9990 - - - - - - - - - - - - largest number divisible by 90 is 9990 answer : e"
Answer: e
Question (general): if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ? .
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: 20 ! = 1 * 2 * 3 * 4 * 5 . . . * 19 * 20 ( this is 20 factorial written as 20 ! ) n = 1 * 2 * 3 * 4 * 5 * 6 * 7 . . . . . * 19 * 20 how many 2 s are there in n ? one 2 from 2 two 2 s from 4 one two from 6 three 2 s from 8 and so on . . . when you count them all , you get 18 . answer : d
Answer: d
Question (general): a man performs 1 / 2 of the total journey by rail , 1 / 4 by bus and the remaining 4 km on foot . his total journey is
Options: a ) 18 km , b ) 16 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 4 + 4 = x 3 x + 16 = 4 x x = 16 km answer : option b"
Answer: b
Question (probability): what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ?
Options: a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 7 / 15 , e ) none of these
Rationale: "explanation : since every third number starting from 10 will be divisible by 3 , so total number of numbers divisible by 3 are 90 / 3 = 30 numbers which are divisible by 3 and 5 both are numbers which are multiple of 15 . for the range 10 to 99 , 15 is the first number divisible by 15 and 90 is the last number . so total number of numbers divisible by 15 are : ( 90 - 15 ) / 15 + 1 = 5 + 1 = 6 number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6 . so number of numbers divisible by 3 and not by 5 are : 30 - 6 = 24 so total probability = 24 / 90 = 4 / 15 answer : c"
Answer: c
Question (gain): bhanu spends 30 % of his income on petrol on scooter 21 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 797 , e ) 147
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 21 % ( 700 ) = rs . 147 answer : e"
Answer: e
Question (physics): 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 35 meters deep by working for 6 hours ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 35 x = 70 total workers 70 - 45 = 30 new workers the answer is c ."
Answer: c
Question (general): one - third less than 25 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 25 % of 180 = 45 1 / 3 of 45 = 15 so , 1 / 3 less than 45 is equal to 45 - 15 = 30 answer : b"
Answer: b
Question (physics): if an object travels at 8 feet per second , how many feet does it travel in forty five minutes ?
Options: a ) 18000 , b ) 24000 , c ) 21600 , d ) 18000 , e ) 22000
Rationale: "if an object travels at 8 feet per second it covers 8 x 60 feet in one minute , and 8 x 60 x 45 feet in forty five minutes . answer = 21600 answer : c"
Answer: c
Question (general): in arun ’ s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun ’ s weight is greater than 60 kg but less than 70 kg . his mother ’ s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what is the average of different probable weights of arun ?
Options: a ) 66 kg , b ) 67 kg , c ) 68 kg , d ) 69 kg , e ) none of these
Rationale: explanation : let arun ’ s weight by x kg . according to arun , 65 < x < 72 according to arun ’ s brother , 60 < x < 70 . according to arun ’ s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b
Answer: b
Question (probability): there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 65
Rationale: approach 1 at - least 1 paper back = total - no paper back 8 c 4 - 5 c 4 = 65 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 3 c 1 * 5 c 3 + 3 c 2 * 5 c 2 + 3 c 3 * 5 c 1 = 65 answer is e
Answer: e
Question (gain): rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 500 . then his monthly salary is
Options: a ) rs . 2500 , b ) rs . 3500 , c ) rs . 1500 , d ) rs . 500 , e ) rs . 2000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 500 â ‡ ” 20 / 100 x = 500 â ‡ ” x = 500 ã — 5 = 2500 . answer a"
Answer: a
Question (other): there are 418 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 242 , d ) 171 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 418 = 242 answer : c"
Answer: c
Question (general): robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert borrowed rs . 7280 / - from company . but robert forget that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the incentive amount given to robert ?
Options: a ) 9500 , b ) 12500 , c ) 10780 , d ) 10500 , e ) 8600
Rationale: "total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c"
Answer: c
Question (other): what number has a 3 : 4 ratio to the number 400 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 300 , e ) 120
Rationale: "3 : 4 = x : 200 4 x = 3 * 400 x = 300 answer : d"
Answer: d
Question (physics): the food in a camp lasts for 40 men for 20 days . if 10 more men join , how many days will the food last ?
Options: a ) 22 days , b ) 30 days , c ) 23 days , d ) 16 days , e ) 17 days
Rationale: one man can consume the same food in 40 * 20 = 800 days . 10 more men join , the total number of men = 50 the number of days the food will last = 800 / 50 = 16 days . answer : d
Answer: d