regisss/math_qa huggingface dataset:
Problem: 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
Problem: a trader bought a car at 30 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 7 % , b ) 62 % , c ) 12 % , d ) 19 % , e ) 5 %
Rationale: "original price = 100 cp = 70 s = 70 * ( 150 / 100 ) = 105 100 - 105 = 5 % answer : e"
Answer: e
Problem: how many cubes of 5 cm edge can be cut out of a cube of 20 cm edge
Options: a ) 36 , b ) 64 , c ) 216 , d ) 484 , e ) none of these
Rationale: "explanation : number of cubes = ( 20 x 20 x 20 ) / ( 5 x 5 x 5 ) = 64 answer : b"
Answer: b
Problem: in a weight - lifting competition , the total weight of joe ' s two lifts was 450 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 250 , b ) 275 , c ) 325 , d ) 350 , e ) 400
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 450 pounds . we sum the two variables to obtain : f + s = 450 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 450 3 f = 750 f = 250 answer is a ."
Answer: a
Problem: a particular library has 150 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 108 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the total number of books is 150 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 108 books , thus the number of un - returned books is 150 - 108 = 42 books . 0.35 x = 42 x = 120 the answer is e ."
Answer: e
Problem: ramu rides his bike at an average speed of 45 km / hr and reaches his desitination in 4 hours . somu covers the same distance in 6 hours . if ramu covered his journey at an average speed which was 9 km / hr less and somu covered his journey at an average speed which was 10 km / hr more , then the difference in their times taken to reach the destination would be ( in minutes ) .
Options: a ) 23 minutes , b ) 30 minutes , c ) 43 minutes , d ) 23 minutes , e ) 33 minutes
Rationale: distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b
Answer: b
Problem: if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 240 * 80 / 60 + 40 / 10 = ?
Options: a ) - 2305 , b ) - 2407 , c ) 2509 , d ) - 2101 , e ) none of these
Rationale: "explanation : given : 240 * 80 / 60 + 40 / 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = - 2407 answer : b"
Answer: b
Problem: elena purchased brand x pens for $ 5.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 6 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : c ."
Answer: c
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 2 : 3 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : c"
Answer: c
Problem: in order to fence a square manish fixed 48 poles . if the distance between two poles , is 2 metres then what will be the area of the square so formed ?
Options: a ) 133 cm 2
b ) 276 cm 2
c ) 2500 cm 2
d ) 576 cm 2
e ) none of these
Rationale: let the side of the square be x m . ∴ perimeter of the square = 48 × 2 = 4 x ∴ x = 24 m ∴ area = ( 24 ) 2 = 576 m 2 answer d
Answer: d
Problem: find the area of a parallelogram with base 20 cm and height 10 cm ?
Options: a ) 290 cm 2
b ) 380 cm 2
c ) 270 cm 2
d ) 280 cm 2
e ) 200 cm 2
Rationale: area of a parallelogram = base * height = 20 * 10 = 200 cm 2 answer : e
Answer: e
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 84 liters of drink a to convert it to drink b ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "in 84 liters of drink a , there are 48 liters of milk and 36 liters of juice . with 48 liters of milk , we need a total of 64 liters of juice to make drink b . we need to add 28 liters of juice . the answer is b ."
Answer: b
Problem: which greatest possible length can be used to measure exactly 12 meter 65 cm , 15 meter 25 cm and 10 meter 65 cm
Options: a ) 45 cm , b ) 5 cm , c ) 4 cm , d ) 15 cm , e ) 50 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1265 cm , 1525 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option b"
Answer: b
Problem: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b"
Answer: b
Problem: in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 200 , c ) 155 , d ) 350 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 620 - x ) . then , ( 11 3 / 4 × 620 ) ⇔ 11 x + 12 ( 620 - x ) ⇔ x = 7440 - 7285 ⇔ 155 . answer c"
Answer: c
Problem: two trains are moving in opposite directions with speed of 60 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "relative speed = 60 + 90 = 150 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 150 hr = 1 / / 75 hr = 3600 / 75 seconds = 1200 / 25 = 240 / 5 = 48 seconds answer is e ."
Answer: e
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 14 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 34 min , d ) 25 min , e ) 20 min
Rationale: clearly , the two will meet when they are 1000 m apart to be 20 + 14 = 34 km apart , they take 1 hour to be 1000 m apart , they take 34 * 1000 / 1000 = 34 min . answer is c
Answer: c
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 90 and rs . 80 respectively . the sum is :
Options: a ) 1360 , b ) 1450 , c ) 720 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 90 * 80 / ( 90 - 80 ) = rs . 720 . answer c"
Answer: c
Problem: find the l . c . m of 6 , 15 , 24 and 20 .
Options: a ) 140 , b ) 160 , c ) 120 , d ) 150 , e ) 250
Rationale: "explanation : 2 x 3 x 5 x 2 x 2 = 120 answer : option c"
Answer: c
Problem: if shreehari walks in the speed of 4.5 km / hr from his house , in what time will he reach his school which is 750 m long from his house ?
Options: a ) 5 , b ) 30 , c ) 10 , d ) 12 , e ) 15
Rationale: speed = 4.5 * 5 / 18 = 1.25 m / sec time taken = 750 / 1.25 = 600 sec ie . 10 mins . answer : c
Answer: c
Problem: if x is a number such that x ^ 2 + 2 x - 24 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =
Options: a ) 4 , b ) - 4 , c ) - 3 , d ) - 6 , e ) 1
Rationale: x ^ 2 + 2 x - 24 = ( x + 6 ) ( x - 4 ) = 0 then x = - 6 or x = 4 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 4 . the answer is a .
Answer: a
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 ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) none
Rationale: sol . since the month begins with a sunday , so there will be five sundays in the month . ∴ required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d
Answer: d
Problem: a horse chases a pony 8 hours after the pony runs . horse takes 12 hours to reach the pony . if the average speed of the horse is 320 kmph , what s the average speed of the pony ?
Options: a ) 182 kmph , b ) 192 kmph , c ) 193 kmph , d ) 196 kmph , e ) 190 kmph
Rationale: pony take 20 hours and horse take 12 hours . . . then distance chased by them is 320 * 12 . so speed of pony is ( 320 * 12 ) / 20 = 192 kmph . answer is b
Answer: b
Problem: a , b and c start a business each investing 10,000 . after 6 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 34,200 was recorded . find the share of b .
Options: a ) 9,600 , b ) 21,200 , c ) 28,200 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 10000 ã — 6 + 5000 ã — 6 : 10000 ã — 6 + 6000 ã — 6 : 10000 ã — 6 + 16000 ã — 6 = 90000 : 96000 : 156000 = 90 : 96 : 156 b â € ™ s share = ( 34200 ã — 96 â  „ 342 ) = 9600 answer a"
Answer: a
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 10 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 39.52 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 41.15 $
Rationale: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.10 x = 50 x = 39.52 hence , the correct option is a"
Answer: a
Problem: an aeroplane covers a certain distance at a speed of 300 kmph in 6 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 1008 kmph , b ) 760 kmph , c ) 1080 kmph , d ) 1070 kmph , e ) none
Rationale: "explanation : distance = ( 300 x 6 ) = 1800 km . speed = distance / time speed = 1800 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 1800 x 3 / 5 km / hr = 1080 km / hr . answer : option c"
Answer: c
Problem: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150 ?
Options: a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 150 / 2 = 75 answer is d"
Answer: d
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 25 seconds . the ratio of their speeds is ?
Options: a ) 3 / 1 , b ) 4 / 1 , c ) 3 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 25 = = > 27 x + 17 y = 25 x + 25 y = = > 2 x = 8 y = = > x / y = 4 / 1 . answer : b"
Answer: b
Problem: a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 15 ) / ( 15 - 0 ) = 3 / 1 1 / x = 3 / 1 x = 1 / 3 answer : b"
Answer: b
Problem: a certain car uses one gallon of gasoline every 32 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 30 %
Rationale: "4 miles on the highway = 4 / 32 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 32 + 4 / 20 = 13 / 40 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 13 / 40 - 8 / 32 ) / ( 8 / 32 ) = 0.30 . answer : e ."
Answer: e
Problem: a retailer sold an appliance for $ 100 . if the retailer ' s gross profit on the appliance was 25 percent of the retailer ' s cost for the appliance , how many dollars was the retailer ' s gross profit ?
Options: a ) $ 10 , b ) $ 16 , c ) $ 20 , d ) $ 24 , e ) $ 25
Rationale: let p be the original price paid by the retailer . 1.25 * p = 100 p = 80 the profit is $ 20 . the answer is c .
Answer: c
Problem: 24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to t ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice t will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice t = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice v = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d
Answer: d
Problem: if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 75 percent of the test takers answered the second question correctly , and 15 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: { total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 75 - { both correctly } + 15 { both correctly } = 75 . answer : d .
Answer: d
Problem: the grade point average of one third of the classroom is 69 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ?
Options: a ) 61 . , b ) 63 . , c ) 65 , d ) 67 , e ) it depends how many people are there in the class .
Rationale: "let the number of students in class a be = x 1 + x 2 + . . . . . . + a 1 ( where a 1 = remaining students ) now the remaining avg of the students be a 1 / t = 60 a 1 = 60 t ( we are not sure on the number of students , assuming it as t ) . a = x 1 + x 2 + . . . . . . + a 1 ( first set of students + remaining students ) . one third of a students avg is 60 . a / 3 = 69 = > a = 207 . now x 1 + x 2 + . . . . . . + a 1 = 207 . x 1 + x 2 + . . . . . . = 207 - 60 t . we are not sure about the number of students in the remaining class + whole class and without that we ca n ' t solve this . answer : e is correct option ."
Answer: e
Problem: find the least number of complete years in which a sum of money put out at 25 % compound interest will be more than double of itself ?
Options: a ) 6 years , b ) 9 years , c ) 5 years , d ) 4 years , e ) 6 years
Rationale: "4 years answer : d"
Answer: d
Problem: mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 24 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
Options: a ) 18 , b ) 19 , c ) 22 , d ) 20 , e ) 19
Rationale: "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : c"
Answer: c
Problem: 7 m - 20 = 2 m , then m + 7 is equal to ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c
Answer: c
Problem: which is greater than 16
Options: a ) 1.6 , b ) 66 , c ) 6 , d ) - 6 , e ) 6.1
Rationale: "66 greater than 16 . answer : b"
Answer: b
Problem: the smallest value of n , for which 2 n + 1 is not a prime number is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "sol . = ( 2 × 1 + 1 ) = 3 , = ( 2 × 3 + 1 ) = 7 , = ( 2 × 4 + 1 ) = 9 , which is not prime . therefore n = 4 . answer b"
Answer: b
Problem: two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 50 % , e ) 80 %
Rationale: two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a
Answer: a
Problem: in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 1 / 4 of the way by bus , and the remaining 5 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 13 , b ) 17 , c ) 42 , d ) 15 , e ) 12
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 5 x - 1 / 2 x - 3 / 5 x = 5 x = 12 km option : e"
Answer: e
Problem: the sector of a circle has radius of 14 cm and central angle 108 o . find its perimeter ?
Options: a ) 52 cm , b ) 54.4 cm , c ) 60 cm , d ) 65 cm , e ) 70 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 108 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 26.4 + 28 = 54.4 cm answer : b"
Answer: b
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 10 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.5 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: ( 1 mph + 10 mph ) / 2 = 5.5 mph correct option is : b
Answer: b
Problem: j is 25 % less than p and 20 % less than t . t is x % less than p . what is the value of x ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d"
Answer: d
Problem: denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination .
Options: a ) 1 , b ) 159 / 160 , c ) 157 / 160 , d ) 4 3 / 160 , e ) 0
Rationale: when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 39263999 / 4000 ∗ 3998 / 3999 ∗ . . . ∗ 3925 / 3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well . we ' ll get 3925 / 4000 = 157 / 160 . answer : c .
Answer: c
Problem: what percent is 36 paisa ' s of 12 rupees ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "12 rupees = 1200 paisa ' s 36 / 1200 × 100 = 3 / 12 12 / 3 = 3 % b"
Answer: b
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d"
Answer: d
Problem: two spheres of their radios in the ratio 4 : 3 . find its volumes ratio ?
Options: a ) 64 : 13
b ) 13 : 64
c ) 27 : 64
d ) 64 : 27
e ) none of them
Rationale: sphere volume ( v ) = 4 / 3 π r ( power 3 ) : 4 / 3 π r ( power 3 ) = 4 ( power 3 ) : 3 ( power 3 ) = 64 : 27 answer is d .
Answer: d
Problem: a train which has 420 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 42 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 420 / ( ( 45 - 9 ) ( 5 / 18 ) = 420 / 36 * ( 5 / 18 ) = 420 / 10 = 42 sec answer : b"
Answer: b
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 1536 , what is the area of the side face of the box ?
Options: a ) 34 , b ) 65 , c ) 88 , d ) 90 , e ) 128
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 1536 l * 1.5 l * 2 l = 1536 l = 8 side face area = l * d = l * 2 l = 8 * 2 * 8 = 128 e is the answer"
Answer: e
Problem: sum of the squares of 3 no . is 276 and the sum of their products taken two at a time is 150 . find the sum ?
Options: a ) 22 , b ) 18 , c ) 26 , d ) 24 , e ) 32
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 276 + 2 * 150 a + b + c = â ˆ š 576 = 24 answer d"
Answer: d
Problem: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 14 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 14 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: i got two equations : 3 x - 2 y = 25 x + y = 14 3 x - 2 ( 14 - x ) = 25 3 x - 28 + 2 x = 25 5 x = 53 x = 10.6 or between 10 and 11 . ( ans e )
Answer: e
Problem: bhaman travelled for 15 hours . he covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph . find the distance travelled by bhaman ?
Options: a ) 240 , b ) 230 , c ) 260 , d ) 220 , e ) 340
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a
Answer: a
Problem: in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 20 % , b ) 23 % , c ) 15 % , d ) 18 % , e ) 16 %
Rationale: fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a .
Answer: a
Problem: three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in .
Options: a ) 11 hours , b ) 12 hours , c ) 15 hours , d ) 16 hours , e ) 17 hours
Rationale: the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b
Answer: b
Problem: each factor of 220 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 55 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "the # of factors 220 has is 12 ; so out of 12 factors only three are multiples of 55 : 55 , 110 and 220 , itself ; so , the probability is 3 / 12 = 1 / 4 . answer : e ."
Answer: e
Problem: john makes $ 40 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 76.69 % , d ) 76.98 % , e ) 75 %
Rationale: "increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e"
Answer: e
Problem: an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 72 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 30 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 72 percent of the votes cast number of votes for winning candidate = ( 72 / 100 ) * 525 = 378 percent of total membership that voted for winning candidate = ( 378 / 1260 ) * 100 = 30 % answer c"
Answer: c
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4551 , b ) 4771 , c ) 4991 , d ) 4881 , e ) 4661
Rationale: "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer is c ."
Answer: c
Problem: one half of a two digit number exceeds its one third by 4 . what is the sum of the digits of the number ?
Options: a ) 6 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "explanation : x / 2 – x / 3 = 4 = > x = 24 2 + 4 = 6 a"
Answer: a
Problem: calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10 % of its volume is occupied by mortar ?
Options: a ) 720 , b ) 600 , c ) 660 , d ) 6000 , e ) none of these
Rationale: explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a
Answer: a
Problem: if the side length of square b is three times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 9 , b ) 8 , c ) 6 , d ) 3 , e ) 2
Rationale: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 3 x ) ^ 2 = 9 x ^ 2 . the answer is a ."
Answer: a
Problem: the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 20
Rationale: hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d
Answer: d
Problem: one night a certain hotel rented 3 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 50 % , b ) 55 % , c ) 60 % , d ) 65 % , e ) 70 %
Rationale: the rooms which were not rented is 2 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 2 / 5 ) = 1 / 2 = 50 % the answer is a .
Answer: a
Problem: in what time will a train 180 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 4.5 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 180 / 40 = 4.5 sec . answer : d"
Answer: d
Problem: how many 7 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 1234321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 9000 , e ) 1000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the 7 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 6 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways stage 3 : select the 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 3 in 10 ways stage 4 : select the 5 th digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 4 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 5 : select the hundreds digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . stage 6 : select the tens digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . stage 7 : select the units digit this digit must be the same as the ten - thousands digit ( which we already chose in stage 1 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 7 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 9000 ways ) answer : d"
Answer: d
Problem: the average monthly salary of 25 employees in an organisation is rs . 2500 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?
Options: a ) rs . 7700 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a"
Answer: a
Problem: the sum of two consecutive number is 49 . which is the larger number ?
Options: a ) 42 , b ) 43 , c ) 25 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 49 2 x + 1 = 49 2 x = 48 x = 24 therefore larger number is x + 1 = 25 answer : c"
Answer: c
Problem: we had $ 1400 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 2000 , b ) $ 2100 , c ) $ 2200 , d ) $ 2300 , e ) $ 2400
Rationale: "let x be the amount of money we started with . 0.7 x = 1400 x = 2000 the answer is a ."
Answer: a
Problem: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 94 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 16 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 94 % water and 6 % of non - water , so now 1 pound of non - water composes 6 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.06 = 16 pounds . answer : b ."
Answer: b
Problem: the average of 5 numbers is 6.8 . if one of the numbers is multiplied by a factor of 4 , the average of the numbers increases to 9.2 . what number is multiplied by 4 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0
Rationale: "the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 4 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 4 be n then , 4 n = n + 12 or 3 n = 12 or n = 4 answer : - d"
Answer: d
Problem: in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party .
Options: a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d"
Answer: d
Problem: the angle between the minute hand and the hour hand of a clock when the time is 10.30 , is
Options: a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 135 ° , e ) 95 °
Rationale: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 10 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 10 − 30 / 5 ) + 30 / 2 = 30 ( 10 − 6 ) + 15 = 30 × 4 + 15 = 135 ° answer is d ."
Answer: d
Problem: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 20.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 5 x = 20.5 minutes answer : a"
Answer: a
Problem: what is the last digit of 13 ^ 35 ?
Options: a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let ’ s begin by looking for a pattern as we increase the exponent . 13 ^ 1 = 13 ( units digit is 3 ) 13 ^ 2 = 169 ( units digit is 9 ) 13 ^ 3 = 2197 ( units digit is 7 ) notice that a nice pattern emerges . we get : 3 - 9 - 7 - 1 - 3 - 9 - 7 - 1 - 3 - 9 - 7 - 1 - … whenever n is a multiple of 4 , the units digit of 13 ^ n is 1 the units digit of 13 ^ 35 is 7 answer is b"
Answer: b
Problem: x is the product of each integer from 1 to 25 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 6 , e ) 7
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 25 = 25 ! no . of trailing zeros in 25 ! = 25 / 5 + 25 / 5 ^ 2 = 6 100 ^ k = 10 ^ 2 k → k = 6 / 2 = 3 c"
Answer: c
Problem: a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .
Options: a ) 50
b ) 30
c ) 20
d ) 40
e ) 10
Rationale: let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a
Answer: a
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 10 hours a day , the number of men required ?
Options: a ) 10 days , b ) 12 days , c ) 13 days , d ) 11 days , e ) 9 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 10 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 10 × 8 = 12 days b )"
Answer: b
Problem: there are 240 doctors and nurses at a hospital . if the ratio of doctors to nurses is 3 to 7 , how many nurses are at the hospital ?
Options: a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184
Rationale: "the number of nurses at the hospital is ( 7 / 10 ) * 240 = 168 . the answer is a ."
Answer: a
Problem: what annual payment will discharge a debt of rs . 1125 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 534.33 , d ) 605.03 , e ) 646.33
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1125 820 x + 1125 * 441 x = 605.03 so , value of each installment = rs . 605.03 answer : option d"
Answer: d
Problem: abel can complete a work in 8 days , ben in 12 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 3 days before the completion of the work . how long did the work last ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 4 of the job = 3 / 4 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 3 / 20 3 / 20 ( t ) = 3 / 20 - - - > t = 1 therefore , these 1 day worked plus the 3 days that carla had to work by herself add to 4 days answer : a"
Answer: a
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 2 ¤ √ 2 =
Options: a ) 0 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: "x = √ 2 and y also = √ 2 applying the function ( √ 2 + √ 2 ) ^ 2 - ( √ 2 - √ 2 ) ^ 2 = ( 2 √ 2 ) ^ 2 - 0 = 4 x 2 = 8 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 2 and y = √ 2 you get the answer 8 . answer b"
Answer: b
Problem: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 4 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 12 hours , d ) 24 hours , e ) 32 hours
Rationale: i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 4 = > 1 / 12 working alone taimour can do the job in 1 = 1 / 12 * hours = > 12 answer c
Answer: c
Problem: in the faculty of reverse - engineering , 100 second year students study numeric methods , 300 second year students study automatic control of airborne vehicles and 200 second year students study them both . how many students are there in the faculty if the second year students are approximately 40 % of the total ?
Options: a ) 550 , b ) 500 , c ) 600 , d ) 650 , e ) 700
Rationale: "total number of students studying both are 100 + 300 - 200 = 200 ( subtracting the 200 since they were included in the both the other numbers already ) . so 40 % of total is 200 , so 100 % is 500 answer is b"
Answer: b
Problem: if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 9 inclusive ?
Options: a ) 3 / 16 , b ) 5 / 16 , c ) 7 / 32 , d ) 11 / 32 , e ) 17 / 64
Rationale: "one possible case is : rainy - rainy - rainy - not rainy - not rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 6 = 1 / 64 the number of possible cases is 6 c 3 = 20 . p ( exactly 3 rainy days ) = 20 * 1 / 64 = 5 / 16 the answer is b ."
Answer: b
Problem: find √ ? / 20 = 4 ?
Options: a ) 76 , b ) 6400 , c ) 304 , d ) 1296 , e ) none
Rationale: "answer let √ n / 20 = 4 then √ n = 20 x 4 = 80 ∴ n = 80 x 80 = 6400 . correct option : b"
Answer: b
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 45 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 45 / 3 = 15 kmph answer : d"
Answer: d
Problem: a box contains 14 pairs of shoes ( 28 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 27 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 28 but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 27 ( as after taking one at random there are 27 shoes left and only one is the pair of the first one ) = 1 / 27 answer : d"
Answer: d
Problem: find the value of x from the below equation ? : x ^ 2 + 5 x + 4 = 0
Options: a ) 1 , b ) - 3 , c ) 3 , d ) 2 , e ) 0
Rationale: a = 1 , b = 5 , c = 4 x 1,2 = ( - 5 â ± â ˆ š ( 5 ^ 2 - 4 ã — 1 ã — 4 ) ) / ( 2 ã — 1 ) = ( - 5 â ± â ˆ š ( 25 - 16 ) ) / 2 = ( - 5 â ± 3 ) / 2 x 1 = ( - 5 + 3 ) / 2 = - 2 / 2 = - 1 x 2 = ( - 5 - 1 ) / 2 = - 6 / 2 = - 3 b
Answer: b
Problem: there are 1000 students in a school and among them 10 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "10 % of 1000 gives 100 . so 100 attends chess and 10 % of 100 gives 10 . so 10 enrolled for swimming answer : b"
Answer: b
Problem: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 20 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
Rationale: anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 20 % of $ 150 but instead , 20 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 20 % of s = s s = 150 / 0.8 profit = 150 / 0.8 - 150 = which is calculated on cost price in % terms . so 37.5 / 150 * 100 = 25 % is profit . e
Answer: e
Problem: a and b start walking towards each other at 4 pm at speed of 2 kmph and 3 kmph . they were initially 15 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 7 pm , d ) 10 pm , e ) 5 pm
Rationale: time of meeting = distance / relative speed = 15 / 3 + 2 = 15 / 5 = 3 hrs after 4 pm = 7 pm answer is c
Answer: c
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 3 and the 24 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 72 , c ) 76 , d ) 78 , e ) 90
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 3 and 4 are adjacent - consider 3 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 3 and 2 can be arranged as 32 or 23 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : b"
Answer: b
Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 20 ) = 180 - - > x = 80 . answer : b ."
Answer: b
Problem: 3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a ’ s present age is :
Options: a ) 22 , b ) 88 , c ) 40 , d ) 87 , e ) 17
Rationale: explanation : sum of the present ages of a , b and c = ( 27 × 3 + 3 × 3 ) years = 90 years . sum of the present ages of b and c = ( 20 × 2 + 5 × 2 ) years = 50 years . a ' s present age = 90 – 50 = 40 years . answer : c
Answer: c
Problem: a is thrice as good as workman as b and therefore is able to finish a job in 60 days less than b . working together , they can do it in :
Options: a ) 20 days , b ) 22 1 / 2 days , c ) 24 days , d ) 25 days , e ) 30 days
Rationale: ratio of times taken by a and b = 1 : 3 . the time difference is ( 3 - 1 ) 2 days while b take 3 days and a takes 1 day . if difference of time is 2 days , b takes 3 days . if difference of time is 60 days , b takes ( 3 / 2 * 60 ) = 90 days so , a takes 30 days to do the work . a ' s 1 day ' s work = 1 / 30 b ' s 1 day ' s work = 1 / 90 ( a + b ) ' s 1 day ' s work = ( 1 / 30 + 1 / 90 ) = 4 / 90 = 2 / 45 a and b together can do the work in 45 / 2 = 22 1 / 2 days answer = b
Answer: b
Problem: what is the difference between the largest number and the least number written with the figures 3 , 4 , 7 , 0 , 3 ?
Options: a ) 70983 , b ) 43893 , c ) 43983 , d ) 43883 , e ) 43823
Rationale: "74330 largest 30347 smallest - - - - - - - - - - - - - 43983 answer : c"
Answer: c
Problem: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 120 m is ?
Options: a ) 286 m , b ) 180 m , c ) 200 m , d ) 166 m , e ) 187 m
Rationale: "2 ( l + 120 ) = 600 = > l = 180 m answer : b"
Answer: b