regisss/math_qa huggingface dataset:
Problem: without stoppages , a train travels certain distance with an average speed of 80 km / h , and with stoppages , it covers the same distance with an average speed of 60 km / h . how many minutes per hour the train stops ?
Options: a ) 15 , b ) 18 , c ) 10 , d ) 16 , e ) none of these
Rationale: "due to stoppages , it covers 20 km less . time taken to cover 20 km = 20 ⁄ 80 h = 1 ⁄ 4 h = 1 ⁄ 4 × 60 min = 15 min answer a"
Answer: a
Problem: if 5 / ( 4 + 1 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 5 / ( 4 + 1 / x ) = 1 should have been equal to something . if 5 / ( 4 + 1 / x ) = 1 = > 5 x / ( 4 x + 1 ) = 1 = > 5 x = 4 x + 1 = > x = 1 correct option : b"
Answer: b
Problem: the average age of a class of 22 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 44 , b ) 48 , c ) 45 , d ) 43 , e ) 50
Rationale: "total age = 22 * 21 tot age of all stu + age of the teacher = 23 * 22 age of the teacher = 23 * 22 - 22 * 21 = 44 answer a"
Answer: a
Problem: by selling 88 pens , a trader gains the cost of 22 pens . find his gain percentage ?
Options: a ) 25 % , b ) 26 % , c ) 27 % , d ) 28 % , e ) 29 %
Rationale: let the cp of each pen be rs . 1 . cp of 88 pens = rs . 88 profit = cost of 22 pens = rs . 22 profit % = 22 / 88 * 100 = 25 % answer : a
Answer: a
Problem: the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 13 days , how large is the colony today ?
Options: a ) 512 , b ) 1024 , c ) 768 , d ) 2048 , e ) 4096
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 ans : b"
Answer: b
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 24
Rationale: "9 / 35 - 9 / 55 = 9 / 5 * ( 11 - 7 ) / 77 = 9 / 5 * 4 / 77 * 60 min = 9 * 12 * 4 / 77 = 432 / 77 ~ 5.6 answer - b"
Answer: b
Problem: if k is a non - negative integer and 18 ^ k is a divisor of 624,938 then 6 ^ k - k ^ 6 =
Options: a ) 0 , b ) 1 , c ) 36 , d ) 118 , e ) 420
Rationale: "6 + 2 + 4 + 9 + 3 + 8 = 32 , so this number is not divisible by 3 and thus not divisible by 18 . therefore , k = 0 6 ^ k - k ^ 6 = 1 - 0 = 1 the answer is b ."
Answer: b
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 3 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 18 , b ) 3 : 7 , c ) 1 : 2 , d ) 2 : 5 , e ) 4 : 9
Rationale: m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 4 * 4 / 9 + 2 / 5 * 5 / 9 = 1 / 9 + 2 / 9 = 1 / 3 losses = 1 - 1 / 3 = 2 / 3 the ratio of wins to losses is 1 : 2 . the answer is c .
Answer: c
Problem: two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 55 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 495 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 55 km more than the other , 25 x â € “ 20 x = 55 5 x = 55 x = 11 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 11 = 495 km . answer : b"
Answer: b
Problem: the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 2 , d ) 1 : 1 , e ) 1 : 7
Rationale: "5 / 6 * 3 / 2 * 4 / 5 = 1 / 1 1 : 1 answer : d"
Answer: d
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 146 , c ) 86 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 17 = 35 5 * quotient = 35 quotient = 7 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 7 ) + 6 = 146 . b )"
Answer: b
Problem: if albert ’ s monthly earnings rise by 36 % , he would earn $ 495 . if , instead , his earnings rise by only 25 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 454 , d ) 460 , e ) 490
Rationale: "= 495 / 1.36 ∗ 1.25 = 454 = 454 answer is c"
Answer: c
Problem: lilly has 10 fish and rosy has 9 fish . in total , how many fish do they have in all ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "10 + 9 = 19 the answer is d ."
Answer: d
Problem: after giving a discount of rs . 100 the shopkeeper still gets a profit of 30 % , if the cost price is rs . 1000 . find the markup % ?
Options: a ) . 50 , b ) . 45 , c ) . 40 , d ) . 48 , e ) . 52
Rationale: "cost price = 1000 s . p = 1000 * 130 / 100 = 1300 disc = 100 so . . . mark price = 1300 + 100 = 1400 . . . . . . mark up % = 1400 - 1000 / 1000 = 400 / 1000 = . 40 ( or ) 40 % answer : c"
Answer: c
Problem: of the goose eggs laid at a certain pond , 1 / 3 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1025 , b ) 1075 , c ) 1125 , d ) 1175 , e ) 1225
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 3 ) x = 120 ( 8 / 75 ) x = 120 x = 1125 the answer is c ."
Answer: c
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 20 miles per gallon , and from town b to town c , the car averaged 24 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 40 , b ) 30 , c ) 42 , d ) 33 , e ) 35
Rationale: "step 1 ) took lcm of 20 and 24 . . came as 120 . step 2 ) 120 distance between b to c . . . do 120 / 24 hence 5 gallons used step 3 ) twice distance . . hence 120 * 2 = 240 . . . do as above . . 240 / 20 = 7 gallons used step 4 ) total gallons . . 5 + 7 = 12 gallons step ) total miles = 120 + 240 = 360 miles hence . . average of whole journey = 360 / 12 which comes to 30 answer : b"
Answer: b
Problem: a bowl of fruit contains 10 apples and 23 oranges . how many oranges must be removed so that 50 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 13 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 10 number of oranges = 23 let number of oranges that must be removed so that 50 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 10 + ( 23 - x ) = 33 - x 10 / ( 33 - x ) = 5 / 10 = > 20 = 33 - x = > x = 13 answer b"
Answer: b
Problem: given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 5 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 5 is 6 + 5 = 11 . answer : e ."
Answer: e
Problem: if a / x = 1 / 3 and a / y = 1 / 4 , then ( x + y ) =
Options: a ) 2 a , b ) a / 2 , c ) 6 a , d ) 7 a , e ) 9 a
Rationale: ratio 1 : 3 a = x ratio 2 : 4 a = y x + y = 7 a answer is d
Answer: d
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 70 units . if today ' s production of 90 units raises the average to 75 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 3
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 70 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 70 n + 90 = 75 * ( n + 1 ) - - > n = 3 . answer : e ."
Answer: e
Problem: a is twice as good a work man as b and together they finish the work in 6 days . in how many days a alone can finish the work ?
Options: a ) 3 , b ) 9 , c ) 7 , d ) 2 , e ) 6
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 = > x = 1 / 18 2 x = 1 / 9 a can do the work in 9 days . answer : b"
Answer: b
Problem: three cubes of metal whose edges are 9 , 12 and 21 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 28 , b ) 22.7 , c ) 66 , d ) 18 , e ) 99
Rationale: "93 + 123 + 213 = a 3 = > a = 22.7 answer : b"
Answer: b
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 45 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 15 : 2 = > for 15 soap , salt = 2 = > for 2 soap , salt = ( 2 / 15 ) * 2 = 4 / 15 so , water : soap : salt = 3 : 2 : 4 / 15 = 45 : 30 : 4 after open container , water : soap : salt = 22.5 : 30 : 4 so , water : salt = 22.5 : 4 = 45 : 8 e"
Answer: e
Problem: if a @ b = a * b ^ ( 1 / 2 ) then 4 @ 9 = ? self made
Options: a ) 2 , b ) 12 , c ) 3 , d ) 8 , e ) 4
Rationale: 4 * ( 9 ) ^ 1 / 2 = 4 * 3 = 12 b is the answer
Answer: b
Problem: population of a city in 20004 was 1000000 . if in 2005 there isan increment of 25 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 980241 , d ) 1178125 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 25 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1178125 d"
Answer: d
Problem: the difference between simple interest and compound interest of a certain sum of money at 20 % per annum for 2 years is $ 48 . then the sum is
Options: a ) $ 600 , b ) $ 1000 , c ) $ 1200 , d ) $ 1500 , e ) $ 2000
Rationale: "20 % of ( year 1 interest ) = 20 % of ( 20 % of principal ) = 48 principal = $ 1200 answer ( c )"
Answer: c
Problem: the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 5 years respectively . if the difference between their interests is rs . 144 , find the each sum ?
Options: a ) 640 , b ) 500 , c ) 3000 , d ) 1000 , e ) 2000
Rationale: ( p * 5 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 75 p / 100 â € “ 52.5 p / 100 = 144 22.5 p = 144 * 100 = > p = rs . 640 answer a
Answer: a
Problem: the number of stamps that p and q had were in the ratio of 5 : 3 respectively . after p gave q 10 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 9 : 7 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 90
Rationale: "p started with 5 k stamps and q started with 3 k stamps . ( 5 k - 10 ) / ( 3 k + 10 ) = 9 / 7 35 k - 27 k = 160 k = 20 p has 5 ( 20 ) - 10 = 90 stamps and q has 3 ( 20 ) + 10 = 70 stamps . the answer is a ."
Answer: a
Problem: if y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer , then y must be
Options: a ) 21 , b ) 10 , c ) 61 , d ) 72 , e ) 14
Rationale: "31360 = 8 * 8 * 7 * 7 * 5 * 2 , so we need one 5 and one 2 to make it a square of a number . so 5 * 2 = 10 ans : b"
Answer: b
Problem: solution y is 30 percent liquid x and 70 percent water . if 3 kilograms of water evaporate from 8 kilograms of solution y and 3 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 35 % , b ) 37 % , c ) 41.3 % , d ) 42 % , e ) 45 %
Rationale: in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 3 kilograms of water are replaced by 3 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 3 = 0.9 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 0.9 = 3.3 kilograms of solution x , which is 3.3 / 8 * 100 = 41.3 % of this new solution . answer : c .
Answer: c
Problem: a train 480 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 108 kmph , c ) 54 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 480 / 16 * 18 / 5 = 108 kmph answer : b"
Answer: b
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 80 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 80 km downstream = ( 80 / 17 ) hrs = 4 hrs 42 minutes . answer e"
Answer: e
Problem: a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 187 , b ) 279 , c ) 280 , d ) 285 , e ) 262
Rationale: "since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d"
Answer: d
Problem: the sum of present age of abe and the age before 7 years is 35 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 35 2 x - 7 = 35 2 x = 35 + 7 x = 42 / 2 x = 21 z = x + 7 = 21 + 7 = 28 answer : d
Answer: d
Problem: the two lines y = x and x = - 6 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the point of intersection is ( - 6 , - 6 ) . the triangle has a base of length 6 and a height of 6 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 6 * 6 = 18 the answer is d ."
Answer: d
Problem: what distance will be covered by a bus moving at 36 kmph in 30 seconds ?
Options: a ) 287 , b ) 600 , c ) 289 , d ) 300 , e ) 207
Rationale: "36 kmph = 36 * 5 / 18 = 10 mps d = speed * time = 10 * 30 = 300 m . answer : d"
Answer: d
Problem: if 2.5 of a number is equal to 0.75 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 10 , d ) 20 : 3 , e ) 30 : 7
Rationale: "2.5 a = 0.75 b - > a / b = 0.75 / 2.5 = 75 / 250 = 3 / 10 : . a : b = 3 : 10 answer : c"
Answer: c
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.5 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 13 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.5 weight of the new student = ( 30 * 27.5 – 29 * 28 ) = 825 - 812 = 13 answer : d"
Answer: d
Problem: if 4 tic equals 3 tacs and 6 tacs equal 4 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 3 / 10 , e ) 2 / 1
Rationale: "4 tic = 3 * tac and 6 * tac = 4 * toc ; 24 * tic = 18 * tac and 18 * tac = 12 * toc - - > 24 * tic = 12 * toc - - > tic / toc = 24 / 12 = 2 / 1 . answer : e ."
Answer: e
Problem: the speed of a boat in still water is 30 kmph . what is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time ?
Options: a ) 11 kmph , b ) 10 kmph , c ) 12 kmph , d ) 16 kmph , e ) 15 kmph
Rationale: x = the speed of the stream ( 30 + x ) / ( 30 - x ) = 2 / 1 30 + x = 60 - 2 x 3 x = 30 x = 10 km / hour if the speed of the stream is 10 km / hour , then the ' downstream ' speed of the boat is 30 + 10 = 40 km / hour and the ' upstream ' speed of the boat is 30 - 10 = 20 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 40 = 80 km downstream and 2 x 20 = 40 km / hour upstream . answer : b
Answer: b
Problem: after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount .
Options: a ) 22 % , b ) 18 % , c ) 24 % , d ) 17 % , e ) 20 %
Rationale: "let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 = 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % answer is e ."
Answer: e
Problem: a rectangular plot measuring 60 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 44 m
b ) 66 m
c ) 26 m
d ) 56 m
e ) 25 m
Rationale: perimeter of the plot = 2 ( 60 + 50 ) = 220 m no of poles = 220 / 5 = 44 m answer : a
Answer: a
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 15 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15 - 2 * 1.5 = 12 . answer : d .
Answer: d
Problem: in how many years will a sum of money doubles itself at 12 % per annum on simple interest ?
Options: a ) 15 % , b ) 20 % , c ) 10 % , d ) 8 % , e ) 22 %
Rationale: "p = ( p * 12 * r ) / 100 r = 8 % answer : d"
Answer: d
Problem: 20 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 1600 , e ) 121
Rationale: "( 20 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 5 x = 320 x = 1600 answer : d"
Answer: d
Problem: it will take 18 days for cameron to complete a certain task alone . he worked for 9 days before she was joined by sandra . both of them completed the remaining task in 3 and half days . how many days will it take both of them to complete the entire job ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: explanation : cameron and sandra completed half work in 3.5 days = > they can complete whole work in 7 days answer : option b
Answer: b
Problem: if greg buys 5 shirts , 4 trousers and 2 ties , the total cost is $ 80 . if greg buys 7 shirts , 4 trousers and 2 ties , the total cost is $ 70 . how much will it cost him to buy 2 trousers , 3 shirts and 1 ties ?
Options: a ) $ 37.5 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 5 x + 4 y + 2 z = 80 7 x + 4 y + 2 z = 70 adding both the equations = 12 x + 8 y + 4 z = 150 3 x + 2 y + 1 z = 37.5 ans a"
Answer: a
Problem: what is the sum of all the numbers between 1 and 16 , inclusive ?
Options: a ) 190 , b ) 200 , c ) 185 , d ) 166 , e ) 213
Rationale: "all you have to do is add 1 + 2 + 3 + 4 . . . + 14 + 15 + 16 , which is 190 . final answer : a"
Answer: a
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 20 % if no discount was offered ?
Options: a ) 19200 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 20 % if no discount was offered = 16000 * 120 / 100 = rs . 19200 . answer : a"
Answer: a
Problem: the distance between delhi and mathura is 100 kms . a starts from delhi with a speed of 50 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 45 kmph at 8 p . m . from delhi . when will they meet ?
Options: a ) 11 , b ) 77 , c ) 8 3 / 4 , d ) 8 1 / 2 , e ) 8
Rationale: "d = 100 – 50 = 50 rs = 45 + 50 = 95 t = 90 / 45 = 0.5 hours 8 a . m . + 0.5 = 8 1 / 2 a . m . . answer : d"
Answer: d
Problem: the length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively . find how many minimum number of square tiles would be required to cover it completely ?
Options: a ) 375
b ) 2570
c ) 2800
d ) 3315
e ) none of these
Rationale: explanation : since we require minimum number of square tiles , the size of the tile is given as the h . c . f . of two sides of the room . the h . c . f . of 1625 cm & 1275 cm . is 25 cm . hence , we get , required number = ( 1625 * 1275 ) / ( 25 * 25 ) = 3315 answer : d
Answer: d
Problem: a man can row upstream at 25 kmph and downstream at 37 kmph , and then find the speed of the man in still water ?
Options: a ) 86 , b ) 67 , c ) 31 , d ) 15 , e ) 17
Rationale: "us = 25 ds = 37 m = ( 37 + 25 ) / 2 = 31 answer : c"
Answer: c
Problem: walking at 50 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 24 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "speed is inversly proprtional to time walking at 50 % of speed meand 1 / 2 s takes 2 t . it takes 24 minutes extra to cover the distance . then 2 t = t + 24 t = 24 . option a is correct"
Answer: a
Problem: 80 % of the population of a village is 32000 . the total population of the village is ?
Options: a ) 40000 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312
Rationale: "x * ( 80 / 100 ) = 32000 x = 400 * 100 x = 40000 answer : a"
Answer: a
Problem: a number x is 4 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 75 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 4 . then y = 1 is less than x = 4 by ( 4 - 1 ) / 4 * 100 = 3 / 4 * 100 = 75 % . answer : b ."
Answer: b
Problem: a trader has 1600 kg of sugar . he sells a part at 8 % profit and the rest at 12 % profit . if he gains 11 % on the whole , find the quantity sold at 12 % ?
Options: a ) 1000 , b ) 1200 , c ) 1400 , d ) 1450 , e ) 1500
Rationale: by rule of alligation , % profit by selling part 1 % profit by selling part 2 8 12 net % profit 11 12 - 11 = 1 11 - 8 = 3 = > quantity of part 1 : quantity of part 2 = 1 : 3 given that total quantity = 1600 kg hence , quantity of part 2 ( quantity sold at 12 % profit ) = 1600 × 3 4 = 1200 b )
Answer: b
Problem: john spent 40 percent of his earning last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did john have left over ?
Options: a ) 30 % , b ) 32 % , c ) 45 % , d ) 68 % , e ) 70 %
Rationale: say john ' s earning last month was $ 100 . john spent 40 percent of his earning last month on rent - - > $ 40 on rent ; 30 percent less than what he spent on rent to purchase a new dishwasher - - > $ 40 * 0.7 = $ 28 on the dishwasher . left over amount 100 - ( 40 + 28 ) = $ 32 . answer : b .
Answer: b
Problem: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 4 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 5 women + 4 children ) ' s 1 day work = ( 5 / 10 + 4 / 140 ) = 1 / 10 5 women and 4 children will complete the work in 10 days . e"
Answer: e
Problem: lloyd normally works 7.5 hours per day and earns $ 4.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 2.0 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 60.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.5 + 3 * 4.5 * 2.0 = 60.75 answer c"
Answer: c
Problem: on a certain road , 20 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 20 % of them exceeded the speed limit and received the ticket , i . e . x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = x / 5 or y / x = 1 / 4 or y / x * 100 = 1 / 4 * 100 = 25 % d"
Answer: d
Problem: if the remainder is 16 when the integer n is divided by 30 , what is the remainder when 2 n is divided by 15 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: n = 30 k + 16 2 n = 2 ( 30 k + 16 ) = 4 k * 15 + 32 = 4 k * 15 + 2 * 15 + 2 = 15 j + 2 the answer is b .
Answer: b
Problem: to apply for the position of photographer at a local magazine , a photographer needs to include 4 or 5 photos in an envelope accompanying the application . if the photographer has pre - selected 7 photos representative of her work , how many choices does she have to provide the photos for the magazine ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: 7 c 4 + 7 c 5 = 35 + 21 = 56 the answer is e .
Answer: e
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 30 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 28 , d ) 66 , e ) 11
Rationale: explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 30 / 5 = 6 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 6 = 66 secs . answer : d
Answer: d
Problem: john purchased some shirts and trousers for $ 1100 . he paid $ 550 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11
Rationale: "given that the total purchase of two items cost 1100 . so the average purchase of one item will cost 1100 / 2 = 550 . its given as total shirt cost 100 $ less . hence total shirt cost = 550 - 275 and total trouser cost = 300 + 275 5 shirts = 275 $ = = > one shirt = 55 $ one trouser = 55 + 20 = 75 $ total trousers = 825 / 75 = 11 . e"
Answer: e
Problem: a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent t of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is t = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Problem: in a throw of a coin find the probability of getting a head ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5
Rationale: s = { h , t } e = { h } p ( e ) = 1 / 2 answer is a
Answer: a
Problem: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 12 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 9 days , e ) 18 days
Rationale: explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 12 x = 18 days answer : option e
Answer: e
Problem: evaluate : 460 - 12 * 3 * 2 = ?
Options: a ) 878 , b ) 545 , c ) 434 , d ) 442 , e ) 452
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 460 - 12 * 3 * 2 = 460 - 8 = 452 correct answer e"
Answer: e
Problem: in a km race , a beats bby 28 metres or 7 seconds . find a ' s timeoverthe course
Options: a ) 4 min , b ) 3 min 3 sec , c ) 4 min 4 sec , d ) 5 min 3 sec , e ) 4 min 3 sec
Rationale: clearly , b covers 28 m in 7 seconds . : . b ' s time over the course = ( 278 x 1000 ) sec = 250 seconds . : . a ' s time over the course = ( 250 - 7 - ) sec = 243 sec = 4 min . 3 sec . answer e 4 min 3 sec
Answer: e
Problem: a thief is spotted by a policeman from a distance of 200 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 800 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 200 m / 1000 ) x 1 / 2 hr = 1 / 10 hr . in 1 / 10 hrs , the thief covers a distance of 8 x 1 / 10 km = 4 / 5 km = 800 m answer is d ."
Answer: d
Problem: set x consists of 10 integers and has median of 30 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 50 this is possible . hence it is the greatest such number . answer ( e )
Answer: e
Problem: a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.25 hrs , e ) 11.25 hrs
Rationale: "net part filled in 1 hour = 1 / 5 - 1 / 9 = 4 / 45 therefore the cistern will be filled in 45 / 4 hours or 11.25 hours . answer : e"
Answer: e
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 650 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 400 , d ) 589 , e ) 171
Rationale: "explanation : 650 = p ( 21 / 20 ) 2 p = 589.56 answer : d"
Answer: d
Problem: there are 456 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 ) 264 , b ) 209 , c ) 57 , d ) 171 , e ) 181
Rationale: given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 456 = 264 answer : a
Answer: a
Problem: find the simple interest on rs . 70,400 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 8800 , e ) s . 6500
Rationale: "p = rs . 70400 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 70,400 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8800 answer is d ."
Answer: d
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 153 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1275 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 153 . ∴ x 16 x 9 / 12 x 1 / 100 } = 153 or x = 1275 . ∴ p . w . = rs . 1275 . answer c"
Answer: c
Problem: a voltage will influence current only if the circuit is :
Options: a ) 2
b ) 7
c ) 6
d ) 889
e ) 1
Rationale: answer : b
Answer: b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 2 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 1009 , c ) s . 1166.7 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 90 % 102 % - - - - - - - - 12 % - - - - 140 100 % - - - - ? = > rs . 1166.7 answer : c"
Answer: c
Problem: in the junior basketball league there are 15 teams , 2 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 9 . , e ) 5 .
Rationale: "total teams = 16 bad teams = ( 2 / 3 ) * 15 = 10 rich teams = 8 so maximum value that the both rich and bad can take will be 8 . so e = 9 can not be that value . ans d ."
Answer: d
Problem: a movie buff buys movies on dvd and on blu - ray in a ratio of 17 : 4 . if she returns 4 blu - ray movies , that ratio would change to 9 : 2 . if she buys movies on no other medium , what was the original number of movies purchased ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 378
Rationale: if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 17 x and b ( d ) = 4 x now from the next line the new eqn becomes 17 x / ( 4 x - 4 ) = 9 / 2 solving it 34 x = 36 x - 36 x = 18 which means m ( d ) = 306 and b ( d ) = 72 so total initially is m ( d ) + b ( d ) = 378 e
Answer: e
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 15 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "let ' s test : 1998 revenues = $ 100 profits = $ 10 next we ' re told that , in 1999 , revenue fell by 20 % , but profits were 15 % of revenues . using the numbers from 1998 ( above ) , we end up with . . . 1999 revenues = $ 80 profits = $ 12 we ' re asked to compare the profits in 1999 to the profits in 1998 ( as a percentage ) : $ 12 / $ 10 = 1.2 = 120 % answer : c"
Answer: c
Problem: a cube has two of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 5 , b ) 3 : 6 , c ) 1 : 2 , d ) 2 : 9 , e ) 1 : 3
Rationale: "let x be the area of each face of the cube . the area painted red is 2 ( x / 2 ) = x the area painted white is 2 ( x / 2 ) + 4 x = 5 x the ratio of red to white is x : 5 x which is 1 : 5 . the answer is a ."
Answer: a
Problem: if athul rows 16 km upstream and 24 km down steam taking 4 hours each , then the speed of the stream
Options: a ) 1 kmph , b ) 2 kmph , c ) 1.5 kmph , d ) 12 kmph , e ) 15 kmph
Rationale: speed upstream = 16 / 4 = 4 kmph speed down stream = 24 / 4 = 6 kmph speed of stream = ½ ( 6 - 4 ) = 1 kmph answer : a
Answer: a
Problem: the average age of 30 students in a class is 5 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 45 , e ) 36
Rationale: "total age of 50 students = 30 * 5 = 150 total age of 51 persons = 31 * 6 = 186 age of teacher = 186 - 150 = 36 years answer is e"
Answer: e
Problem: a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 11000 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3000 , c ) rs . 6750 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 11000 ] = rs . 3000 answer : option b"
Answer: b
Problem: a batsman scored 120 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 30 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b"
Answer: b
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job
Options: a ) 49 , b ) 249 , c ) 349 , d ) 449 , e ) none of these
Rationale: explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 449 answer : d
Answer: d
Problem: 4.036 divided by 0.04 gives :
Options: a ) 10.09 , b ) 1.06 , c ) 10.06 , d ) 100.9 , e ) 100.6
Rationale: "= 4.036 / 0.04 = 403.6 / 4 = 100.9 answer is d ."
Answer: d
Problem: find the constant k so that : - x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) - 11 , b ) - 12 , c ) - 13 , d ) - 14 , e ) - 15
Rationale: "- x 2 - ( k + 7 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 7 ) x - 8 = - x 2 + 6 x - 8 - ( k + 7 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 13 : solve the above for k correct answer c"
Answer: c
Problem: a car takes 4.5 hours to travel from a to b , which is 360 miles apart . what is the average speed of the car ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 85
Rationale: average speed = 360 / 4.5 hours = 360 / 270 = 1.33 miles per min = 80 miles per hour answer : d
Answer: d
Problem: there are 20 balls which are red , blue or green . if 7 balls are green and the sum of red balls and green balls is less than 13 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : given : red + green + blue = 20 green = 7 solution : r + g < 13 therefore r + 7 < 13 so r < 6 ans : at most 5 red balls b . 5 hence ( b ) is correct . answer : b"
Answer: b
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 1 / 2 % , then the amount invested at 11 % was ?
Options: a ) 23777 , b ) 25000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 19 / 2 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 950000 x = 75000 sum invested at 9 % = rs . 75000 sum invested at 11 % = rs . ( 100000 - 75000 ) = rs . 25000 . answer : b"
Answer: b
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 64.5 , c ) 62.5 , d ) 82.5 , e ) 60.5
Rationale: c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.5 b
Answer: b
Problem: exactly 36 % of the numbers in set s are even multiples of 3 . if 40 % of the even integers in set s are not multiples of 3 , what percent of the numbers in set s are not even integers ?
Options: a ) 76 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 24 %
Rationale: let s be the total number of elements in set s . we know that 0.36 * s is the number of even multiples of three . let n be the number of even numbers . we know 0.40 * n are even numbers not multiple of three . this also means , 0.60 * n are even numbers that are multiples of three . therefore : 0.06 * n = 0.36 * s n = ( 0.36 / 0.60 ) * s = ( 36 / 60 ) * s = ( 6 / 10 ) * s = 0.60 * s = 60 % of s so even numbers are 60 % of s . that means , 40 % of s are not even integers . answer = d
Answer: d
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 48 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 48 + q = > q = 18 answer : a"
Answer: a
Problem: a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 3.00 , b ) 5.00 , c ) 4.50 , d ) 5.50 , e ) 6.75
Rationale: "we are given that a glucose solution contains 10 grams of glucose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution , we can set up a proportion . we can say : “ 10 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 45 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 10 / 100 = x / 45 when we cross multiply we obtain : ( 10 ) ( 45 ) = 100 x 450 = 100 x 4.50 = x there are 4.5 grams of glucose in the solution in the container . the answer is c ."
Answer: c
Problem: find the two digit number , such that the ratio is 7 / 4 of original number to the number formed by reversing the digits .
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: here ratio is 7 / 4 . so lets check one by one . for 1 : 7 * 1 / 4 * 1 = 7 / 4 for 2 : 7 * 2 / 4 * 2 = 14 / 8 , which does n ' t satisfy the conditions . for 3 : 7 * 3 / 4 * 3 = 21 / 12 answer : b
Answer: b
Problem: the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 7350 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6289 , b ) rs . 6298 , c ) rs . 6681 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 7350 ( 100 / 110 ) = rs . 6681 . answer : c"
Answer: c
Problem: a can do a piece of work in 4 days . b can do it in 5 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 16 days , d ) 19 days , e ) 36 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 5 = 1 / 20 = > 20 days answer : b"
Answer: b
Problem: what least no . must be subtracted from 10154 so that remaining no . is divisible by 30 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 10154 by 30 we get the remainder 14 , so 14 should be subtracted option c"
Answer: c
Problem: the length of the bridge , which a train 140 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 244 , c ) 245 , d ) 238 , e ) 235
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 = = > 2 ( 140 + x ) = 750 = = > x = 235 m . answer : option e"
Answer: e
Problem: the present population of a town is 240 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 264
Rationale: "p = 240 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 240 * ( 1 + 10 / 100 ) = 240 * ( 11 / 10 ) = 264 answer is e"
Answer: e
Problem: a batsman makes a score of 74 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 31 , c ) 26 , d ) 29 , e ) 39
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 74 = total runs scored in 17 innings = > 16 ( x - 3 ) + 74 = 17 x = > 16 x - 48 + 74 = 17 x = > x = 26 answer is c"
Answer: c
Problem: a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number q of ways this can be done is :
Options: a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225
Rationale: we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = { 1 , 2 , 3 , 4 , 5 } and 15 - 3 = { 0 , 1 , 2 , 4 , 5 } . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2 , 3 , 4 , 5 and 0 , 1 , 2 , 4 , 5 . how many 5 digit numbers can be formed using these two sets : 1 , 2 , 3 , 4 , 5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1 , 2 , 4 , 5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , desired # would be total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 4 ! ( 5 - 1 ) = 4 ! * 4 = 96 120 + 96 = 216 = q answer : c .
Answer: c
Problem: the red triangle is equilateral with a side of 23 centimetres . its perimeter is
Options: a ) 68 cm
b ) 69 cm
c ) 70 cm
d ) 71 cm
e ) none
Rationale: solution : all three sides of an equilateral triangle are equal . thus , its perimeter will be 23 × 3 = 69 cm answer b
Answer: b
Problem: the average height of 35 boys in a class was calculated as 180 cm . it has later found that the height of one of the boys in the class was wrongly written as 156 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) .
Options: a ) 168.58 cm , b ) 158.58 cm , c ) 179.29 cm , d ) 168.58 cm , e ) 178.58 cm
Rationale: "calculated average height of 35 boys = 180 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 156 cm . correct total height of 35 boys = 180 * 35 cm - 156 cm + 106 cm = 180 * 35 cm - 156 cm + 106 cm / 35 = 180 cm - 50 / 35 cm = 180 cm - 1.42 cm = 178.58 cm . answer : e"
Answer: e
Problem: in a group of 100 cars , 37 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 48 , d ) 49 , e ) 53
Rationale: "lets assume ac = 63 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 14 tocars with ac and racing stripes . hence ac = 63 - 14 = 49 . the answer is d"
Answer: d
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability r that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . r = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %
Answer: b