regisss/math_qa huggingface dataset:
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 9 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 6440 , d ) 7200 , e ) 6800
Rationale: "number of bricks = volume of wall / volume of bricks = 900 x 600 x 22.5 / 25 x 11.25 x 6 = = 7200 answer : d"
Answer: d
Problem: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 65 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?
Options: a ) 1 , b ) 5 , c ) 9 , d ) 15 , e ) 30
Rationale: withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 60 customers per day . 30 / 30 = 1 day . choice ( a ) . withthe formula , we can set up the following : 90 = ( 60 x + 120 ) / ( x + 1 ) 90 x + 90 = 60 x + 120 30 x = 30 x = 1 answer choice ( a )
Answer: a
Problem: stacy has a 63 page history paper due in 7 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 8.5 , e ) 6
Rationale: "63 / 7 = 9 a . 9"
Answer: a
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Problem: you collect baseball cards . suppose you start out with 15 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: solution start with 15 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 15 + 1 which is 8 , so you ' re left with 15 - 8 = 7 . peter takes 1 baseball card from you : 7 - 1 = 6 baseball cards . paul triples the number of baseball cards you have : 6 × 3 = 18 baseball cards . so you have 18 at the end . correct answer : b
Answer: b
Problem: if the cost price of 18 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 28 % loss , c ) 40 % gain , d ) 40 % loss , e ) 50 % loss
Rationale: "explanation : 18 cp = 25 sp cost price cp = 25 selling price sp = 18 formula = ( sp - cp ) / cp * 100 = ( 18 - 25 ) / 25 * 100 = 28 % loss answer : option b"
Answer: b
Problem: evaluate 28 % of 450 + 45 % of 280
Options: a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 272
Rationale: "explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 280 = 126 + 126 = 252 option c"
Answer: c
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 2 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 16 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 2 / 3 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 2 / 3 ) * ( 3 / 8 ) = 1 / 16 . ans . a .
Answer: a
Problem: in a certain lottery , the probability that a number between 1 and 15 , inclusive , is drawn is 1 / 3 . if the probability that a number 1 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 15 is drawn ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 2 / 5
Rationale: you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 1 or larger set 2 : number 15 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or less or both ) 2 / 3 + p ( set 2 ) - 1 / 3 = 1 p ( set 2 ) = 2 / 3 answer a
Answer: a
Problem: the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 120 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 44 , c ) 60 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 2 hours for the trip . dan needs to exceed a constant speed of 120 / 2 = 60 miles per hour . the answer is c ."
Answer: c
Problem: a student travels from his house to school at 12 km / hr and reaches school 2 hours late . the next day he travels 20 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "let x be the distance from his house to the school . x / 12 = x / 20 + 3 5 x = 3 x + 180 2 x = 180 x = 90 km the answer is a ."
Answer: a
Problem: if x is less than y by 25 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 25 ( 100 - 25 ) * 100 = 33.33 % answer : a"
Answer: a
Problem: a pharmaceutical company received $ 8 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 79 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 8 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 8 / 20 ) x 60 = 24 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 24 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 24 ) / 24 ] x 100 - 475 / 6 x 100 at this point we can stop and consider the answer choices . since we know that 475 / 6 is just a bit less than ½ , we know that - 475 / 6 x 100 is about a 79 % decrease . answer e ."
Answer: e
Problem: a square with sides of 15 units each . what would be the area of the square . consider a square as a combination of two right angled triangles .
Options: a ) 100
b ) 256
c ) 225
d ) 81
e ) 144
Rationale: a square can be considered as a set of two right angled triangles joined from the hypotenuse . since the sides are 10 units each . the height and base of both the triangles is 10 each . area of a right angled triangle is 1 / 2 * base * height area of both the triangles is 2 * 1 / 2 * base * height . since both triangles are similar . = base * height = 15 * 15 = 225 ans : c
Answer: c
Problem: a man is standing on a railway bridge which is 180 m long . he finds that a train crosses the bridge in 20 seconds but himself in 8 seconds . find the length of the train and its speed
Options: a ) 50 km , b ) 52 km , c ) 54 km , d ) 56 km , e ) 58 km
Rationale: "explanation : let the length of the train be x meters , then , the train covers x meters in 8 seconds and ( x + 180 ) meters in 20 sec x / 8 = ( x + 180 ) / 20 ⇔ 20 x = 8 ( x + 180 ) < = > x = 120 length of the train = 120 m . speed of the train = ( 120 / 8 ) m / sec = m / sec = ( 15 × 18 / 5 ) kmph = 54 km answer : option c"
Answer: c
Problem: how many digits are required to number a book containing 240 pages ?
Options: a ) 756 , b ) 612 , c ) 492 , d ) 372 , e ) 250
Rationale: 9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 240 - ( 90 + 9 ) = 141 pages will require 141 * 3 = 423 digits . the total number of digits is 9 + 180 + 423 = 612 . the answer is b .
Answer: b
Problem: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many e applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) e = 20 - 15 = 5 answer : a"
Answer: a
Problem: george does 3 / 5 th of a piece of work in 9 days . he then calls in paul and they finish the work in 4 days . how long would paul take to do the work by himself ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "9 day 3 / 5 1 day 1 / 15 remaing 1 - 3 / 5 = 2 / 5 both can do 2 / 5 work in 4 day one day work of both = 1 / 10 therfor paul would take 1 / 10 - 1 / 15 = 1 / 30 or 30 days answer : c"
Answer: c
Problem: in august , a cricket team that played 120 matches won 24 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 68 , d ) 70 , e ) 98
Rationale: let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 28.8 + x by solving we get x = 70 answer : d
Answer: d
Problem: in a survey of 340 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 7 / 12 , b ) 8 / 41 , c ) 39 / 68 , d ) 1 / 8 , e ) 41 / 91
Rationale: - - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 286 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 340 we have to find not part time and not uninsured . in other words not part time and insured = x / 340 = ( 286 - 104 + 13 ) / 340 = 39 / 68 answer is c .
Answer: c
Problem: a ( 3 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 - 1 . what is the value of w ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: y = x ^ 2 - 1 w ^ 3 = 3 ^ 2 - 1 w ^ 3 = 8 w = 2 answer a
Answer: a
Problem: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 120 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 120 = ( 120 * 30 ) / 40 = 90 . in x game of 100 points , y gives ( 120 - 90 ) = 30 points to c . a
Answer: a
Problem: a house wife saved $ 2.50 in buying an item on sale . if she spent $ 25 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: actual price = 25 + 2.50 = $ 27.50 saving = 2.50 / 27.50 * 100 = 100 / 11 = 9 % approximately answer is b
Answer: b
Problem: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6700 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9795 , e ) s . 9980
Rationale: let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6700 1 = 6700 / 68.4 100 = ( 6700 * 100 ) / 68.4 = rs . 9795 . answer : option d
Answer: d
Problem: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 25 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 5 : 42 pm . the correct answer is c ."
Answer: c
Problem: in a factory , an average of 60 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 59
Rationale: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 60 = 240 ∴ average for last 5 days = 240 / 5 = 48 c
Answer: c
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 4.25 each . if none of the 30 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 260 , b ) $ 255 , c ) $ 285 , d ) $ 290 , e ) $ 275
Rationale: "if 30 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 60 books amount received for sold books = 60 * 4.25 = $ 255 answer : b"
Answer: b
Problem: the ratio between the present ages of a and b is 5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 9 , b ) 3 : 6 , c ) 3 : 1 , d ) 3 : 4 , e ) 3 : 2
Rationale: "let the present ages of a and b be 5 x and 3 x years respectively . then , ( 5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 2 x = 8 = > x = 4 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 24 : 8 = 3 : 1 answer : c"
Answer: c
Problem: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 2 / 3 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 2 / 3 of 300 = 200 total amount in her account = 500 answer d"
Answer: d
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors s ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have s = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm
b ) 220 cm
c ) 240 cm
d ) 270 cm
e ) 300 cm
Rationale: we have 40 for first triangle , when we join mid - points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues . so we have 40 , 20,10 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 40 / 1 - ( 1 / 2 ) = 80 equilateral triangle perimeter is 3 a = 3 * 80 = 240 . so option c .
Answer: c
Problem: two pipes a and b can fill a tank in 10 hours and 20 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 10 / 3 , b ) 20 / 3 , c ) 15 / 7 , d ) 11 / 17 , e ) 1 / 4
Rationale: "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 20 part filled by ( a + b ) in 1 hour = 1 / 10 + 1 / 20 = 3 / 20 both the pipes together fill the tank in 20 / 3 hours answer is b"
Answer: b
Problem: the number obtained by interchanging the digits of a two - digit number is less than the original number by 36 . the sum of the digits of the number is 8 . what is the original number ?
Options: a ) 71 , b ) 62 , c ) 53 , d ) 35 , e ) 45
Rationale: explanation : let the number be 10 x + y . ∴ x + y = 8 . . . . . ( i ) 10 x + y - ( 10 y + x ) = 36 ∴ 9 ( x - y ) = 3 ∴ x - y = 4 . . . . . . . ( ii ) from equation ( i ) and ( ii ) : x = 6 , y = 2 ∴ number = 62 answer : option b
Answer: b
Problem: in one alloy there is 10 % chromium while in another alloy it is 6 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 7.2 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.10 * 15 + 0.06 * 35 = 3.6 kg , so the percentage is 3.6 / 50 * 100 = 7.2 % . answer : a ."
Answer: a
Problem: the food in a camp lasts for 10 men for 20 days . if 30 more men join , how many days will the food last ?
Options: a ) 8 days , b ) 4 days , c ) 5 days , d ) 10 days , e ) 17 days
Rationale: "one man can consume the same food in 10 * 20 = 200 days . 30 more men join , the total number of men = 40 the number of days the food will last = 200 / 40 = 5 days . answer : c"
Answer: c
Problem: surface area of a sphere is 2464 cm 2 . if its radius is doubled , then the surface area of the new sphere will be
Options: a ) 4920 cm 2
b ) 4727 cm 2
c ) 9856 cm 2
d ) 19712 cm 2
e ) none
Rationale: sol . let the original radius be r . then , original surface area = 4 π r 2 = 2464 cm 2 ( given ) . new radius = 2 r . ∴ new surface area = 4 π ( 2 r ) 2 = 4 x 4 π r 2 = ( 4 x 2464 ) cm 2 = 9856 cm 2 answer c
Answer: c
Problem: how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 10.8 sec , e ) 11.8 sec
Rationale: "d 16.8 sec d = 100 + 80 = 180 m s = 60 * 5 / 18 = 50 / 3 t = 180 * 3 / 50 = 10.8 sec"
Answer: d
Problem: - 74 x 29 + 265 = ?
Options: a ) 2436 , b ) - 1881 , c ) - 2801 , d ) - 2071 , e ) none of them
Rationale: "given exp . = - 74 x ( 30 - 1 ) + 265 = - ( 74 x 30 ) + 74 + 265 = - 2220 + 339 = - 1881 answer is b"
Answer: b
Problem: the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ?
Options: a ) 1134 , b ) 1238 , c ) 1348 , d ) 1500 , e ) 1249
Rationale: population of seventh village = 7 * 1000 - ( 803 + 900 + 1100 + 1023 + 945 + 980 ) = 1249 answer is e
Answer: e
Problem: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 14 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d"
Answer: d
Problem: the radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 200 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 70 cm . then , circumference of wheel = 2 π r = 140 π = 440 cm distance covered by bus in 1 minute = 66 ⁄ 60 × 1000 × 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm ∴ revolutions per minute = 6600000 / 60 × 440 = 250 answer b"
Answer: b
Problem: harry started a 4 - mile hike with a full 6 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 4 , e ) 4 / 3
Rationale: no of cups leaked during the trip = 2 cups . no of cups harry drank = 3 cups . no of cups harry drank during the first 3 miles = 2 . drink / mile = 2 / 3 answer : b
Answer: b
Problem: in a room filled with 7 people , 2 people have exactly 1 sibling in the room and 5 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 5 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 5 - - 5 c 2 = 10 total = 1 + 1 + 10 = 12 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 12 / 21 ( 21 is 7 c 2 ) = 1 - 12 / 21 = 9 / 21 = 3 / 7 ans b"
Answer: b
Problem: two taps a and b can fill a cistern in 12 minutes and 18 minutes respectively . they are turned on at the same time . if the tap a is turned off after 4 minutes , how long will tap b take to fill the rest of the cistern ?
Options: a ) 8 min . , b ) 9 min . , c ) 10 min . , d ) 7 min . , e ) none of these
Rationale: in one min , ( a + b ) fill the cistern = 1 ⁄ 12 + 1 ⁄ 18 = 5 ⁄ 36 th in 4 min , ( a + b ) fill the cistern = 5 ⁄ 36 × 4 = 5 ⁄ 9 th rest part = 1 - 5 ⁄ 9 = 4 ⁄ 9 th ∵ 1 ⁄ 18 th part is filled by b in one min . ∴ 4 ⁄ 9 th part is filled by b in 18 × 4 ⁄ 9 = 8 min answer a
Answer: a
Problem: how many digits are in ( 8 × 10 ^ 18 ) ( 10 × 10 ^ 10 ) ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 30
Rationale: "the question simplfies to ( 8 × 10 ^ 18 ) ( 10 ^ 11 ) = > 8 * 10 ^ 29 = > will contain 29 zeros + 1 digit 8 = > 30 ans e"
Answer: e
Problem: jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 3 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 340 , b ) 360 , c ) 380 , d ) 400 , e ) 420
Rationale: "the relative speed of jack and christina is 3 + 3 = 6 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 6 = 40 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 40 = 400 feet . answer : d ."
Answer: d
Problem: the speed of a boat in still water is 60 kmph and the speed of the current is 17 kmph . find the speed downstream and upstream ?
Options: a ) 77,43 kmph , b ) 80,80 kmph , c ) 80,42 kmph , d ) 80,40 kmph , e ) 83,40 kmph
Rationale: speed downstream = 60 + 17 = 77 kmph speed upstream = 60 - 17 = 43 kmph . answer : a
Answer: a
Problem: a solution of 70 litres contains oil and water in the ratio 9 : x . if 6 litres of water is added to the solution , the ratio becomes 6 : 4 , find the value of x ?
Options: a ) 6 , b ) 8.5 , c ) 9 , d ) 6.5 , e ) 5
Rationale: exp . total new quantity = original sol + water = 70 + 6 = 76 new ratio = 6 : 4 , new quantity of oil = 6 / 10 * 76 = 45.6 lit , new quantity of water = 4 / 10 * 76 = 30.4 lit water present initially = ( 30.4 - 6 ) = 24.4 lit ratio = 45.6 / 24.4 = 9 / x there for x = 4.81 approx 5 answer : e
Answer: e
Problem: if an article is sold at 18 % profit instead of 11 % profit , then the profit would be $ 56 more . what is the cost price ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1000 , d ) $ 1200 , e ) $ 1400
Rationale: "7 % * cost price = $ 56 1 % * cost price = $ 56 / 7 = $ 8 the cost price is $ 800 . the answer is b ."
Answer: b
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number d of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see d = 5 or 1 will give you same equation . . ans d"
Answer: d
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 17 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 5 . hence , c is the correct answer ."
Answer: c
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 6 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 24 , b ) 32 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 6 * 6 = > a = 6 * 6 * 8 x * 2 x = 6 * 6 * 8 x = 12 = > 2 x = 24 answer : a"
Answer: a
Problem: the area of a triangle is with base 2 m and height 3 m ?
Options: a ) 11 , b ) 10 , c ) 787 , d ) 3 , e ) 12
Rationale: "1 / 2 * 2 * 3 = 3 m 2 answer : d"
Answer: d
Problem: if the price of a certain computer increased 30 percent from c dollars to 351 dollars , then 2 c =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = c after 30 % price increase price = c + ( 30 / 100 ) * c = 1.3 c = 351 ( given ) i . e . c = 351 / 1.3 = $ 270 i . e . 2 c = 2 * 270 = 540 answer : option a"
Answer: a
Problem: the purchase price of an article is $ 48 . in order to include 5 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 30 % , d ) 40 % , e ) 45 %
Rationale: "cost price of article = 48 $ % of overhead cost = 5 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 5 = 30 % answer c"
Answer: c
Problem: a store reduced the price of all items in the store by 12 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 79.2 , c ) 81.0 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 12 % price becomes = 0.88 * 100 = $ 88 after the final reduction of 10 % price becomes = 0.9 * 88 = $ 79.2 price of all items on second day is 79.2 % of price on first day correct answer option b"
Answer: b
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 10 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 ) 10.5 , b ) 15 , c ) 15.5 , 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 + 10 x = 15.5 minutes answer : c"
Answer: c
Problem: when the smallest of 3 consecutive odd integers is added to 4 times the largest , it produces a result 732 more than 4 times the middle integer . find the numbers ?
Options: a ) 732 , b ) 678 , c ) 698 , d ) 710 , e ) 729
Rationale: x + 4 ( x + 4 ) = 732 + 4 ( x + 2 ) solve for x and find all three numbers x + 4 x + 16 = 732 + 4 x + 8 x = 724 x + 2 = 726 x + 4 = 728 check : the smallest is added to four times the largest 724 + 4 * 728 = 3636 four times the middle 4 * 726 = 2904 3636 is more than 2904 by 3636 - 2904 = 732 a
Answer: a
Problem: in a particular city there are 100 homes numbered from 1 , 23 , . . , 100 . the city was build by a builder from chennai . there was 4 to 5 shops in the town which was build by a builder from mumbai . the 2 nd builder can build in 1 ½ times as compared to time by 1 st builder . the 2 nd builder builds in 15 days , then how many 2 ' s are used by the builder from chennai in numbering the 100 homes ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: in the last line it should be given the builder from chennai in numbering the 100 homes ? then ans is 20 answer : d
Answer: d
Problem: p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 20 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 8 days = 8 ã — ( 1 / 40 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 15 ) = 12 total days = 8 + 12 = 20 answer : option d"
Answer: d
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 2 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 225 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 2 ) * 270 = 135 gallons total paint used = 225 gallons . option b"
Answer: b
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 195
Rationale: by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me .
Answer: e
Problem: set s consists of integers { 7 , 8 , 10 , 12 , 13 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 10 % . what is the value of integer n ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 24
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 10 % , the new mean is 11 . thus , on average , 5 numbers increase by 1 . therefore n = 11 + 5 = 16 the answer is c ."
Answer: c
Problem: the average runs scored by a batsman in 30 matches is 50 . in the next 15 matches the batsman scored an average of 26 runs . find his average in all the 45 matches ?
Options: a ) 31 , b ) 42 , c ) 29 , d ) 97 , e ) 27
Rationale: total score of the batsman in 30 matches = 1500 . total score of the batsman in the next 15 matches = 390 . total score of the batsman in the 30 matches = 1890 . average score of the batsman = 1890 / 45 = 42 . answer : b
Answer: b
Problem: the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 2000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2789 , b ) 2772 , c ) 1250 , d ) 6725 , e ) 2099
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1250 ( 100 / 160 ) = rs . 1250 . answer : c"
Answer: c
Problem: a shipment of 240 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 9 / 74 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = ( 84 / 240 ) probability of chosing one defective phone from a lot of 239 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 239 ) combined probability of series of events = product of the probabilities = ( 84 / 240 ) * ( 83 / 239 ) 84 / 240 is close to ( 7 / 20 ) and ( 83 / 239 ) = ( 25 / 72 ) so answer is ( 7 / 20 ) * ( 25 / 72 ) ( 9 / 74 ) so , answer will be b"
Answer: b
Problem: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 8 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 600 per sq . metre .
Options: a ) $ 12375 , b ) $ 13575 , c ) $ 16575 , d ) $ 14575 , e ) $ 18575
Rationale: "a area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 600 hence , total cost = 5.5 × 3.75 × 600 = $ 12375 a"
Answer: a
Problem: if n = 10 ^ 100 and n ^ n = 10 k what is the value of k ?
Options: a ) 200 , b ) 10 ^ 100 , c ) 10 ^ 102 , d ) 100 ^ 100 , e ) 1000 ^ 10
Rationale: "there is a simple logic to this question . ( a ^ m ) ^ n = a ^ mn so , ( 10 ^ 100 ) ^ ( 10 ^ 100 ) = 10 ^ ( 100 * ( 10 ^ 100 ) ) = 10 ^ ( ( 10 ^ 2 ) * ( 10 ^ 100 ) ) = 10 ^ ( 10 ^ 102 ) and this equals 10 ^ k so , k = 10 ^ 102 answer : c"
Answer: c
Problem: a bag contains 30 red jellybeans and 30 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 1 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 1 / 20 answer : option d"
Answer: d
Problem: what is the sum of the multiples of 4 between 63 and 151 inclusive ?
Options: a ) 2240 , b ) 2250 , c ) 2310 , d ) 2330 , e ) 2332
Rationale: "the fastest way in an ap is to find the average and multiply with total integers . . between 63 and 151 , the smallest multiple of 4 is 64 and largest = 148 . . average = ( 64 + 148 ) / 2 = 106 . . total numbers = ( 148 - 64 ) / 4 + 1 = 21 + 1 = 22 . . sum = 22 * 106 = 2332 ans e"
Answer: e
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 60 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 25 %
Rationale: "0.1 m = 0.40 e = > e / m = 1 / 4 * 100 = 25 % so answer is e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Problem: if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 3 : 7 , d ) 2 : 5 , e ) 1 : 6
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9 . the ratio of apples to bananas to cucumbers is 4 to 3 to 9 . the answer is a ."
Answer: a
Problem: car dealership x , the total profit from sales increased by 12 percent over the previous years , while the number of cars sold decreased by 12 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 27.27 % , e ) 35 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.12 x / 0.88 y = 112 / 88 ( x / y ) increase in profit per car = ( ( 24 / 88 ) ( x / y ) ) / ( x / y ) * 100 = 27.27 % answer = d"
Answer: d
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 46.24 , the number of the member is the group is :
Options: a ) 57 , b ) 68 , c ) 77 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 46.24 x 100 ) paise = 4624 paise . ∴ number of members = √ ( 4624 ) = 68 . answer : b"
Answer: b
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 15 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 15 0 = a + d - 14 a + d = 14 a = d ( as they are twin brothers ) a = d = 7 d is the answer"
Answer: d
Problem: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 99 true ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "answer c ( a + b ) ( a - b ) = 99 3 cases for ( a + b ) , ( a - b ) 99 , 1 33 , 3 11 , 9 answer b"
Answer: b
Problem: how many positive integers less than 100 are there such that they are multiples of 8 or multiples of 7 but not both ?
Options: a ) 21 , b ) 22 , c ) 25 , d ) 24 , e ) 31
Rationale: "for 8 : 8 . . . 100 = 8 * 12 for 7 : 7 . . . 98 = 7 * 14 but there is one integer 8 * 7 . so n = ( 12 - 1 ) + ( 14 - 1 ) = 24 d"
Answer: d
Problem: when x is multiplied by 2 , the result is 19 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 15 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 2 x - 19 = 26 - x or , 3 x = 45 or , x = 15 . c answer ."
Answer: c
Problem: if - 3 x + 5 y = 48 and 3 x - 2 y = 6 , what is the product of x and y ?
Options: a ) 252 , b ) 428 , c ) 464 . , d ) 200 , e ) 642
Rationale: "given - 3 x + 5 y = 48 - - - eq 1 3 x - 2 y = 6 - - eq 2 sum both eqns we get 3 y = 54 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 6 . = > x = 14 now xy = 14 * 18 = 252 option a is correct answer ."
Answer: a
Problem: a can give b 60 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 148.94 , b ) 148.13 , c ) 148.22 , d ) 111.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 940 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 940 = 851.06 m . b can give c = 1000 - 851.06 = 148.94 m . answer : a"
Answer: a
Problem: kim finds a 6 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 7 / 5 , b ) 1 / 2 , c ) 8 / 15 , d ) 2 / 5 , e ) 3 / 5
Rationale: "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is e"
Answer: e
Problem: how many prime numbers between 1 and 100 are factors of 143 ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 2 , e ) 3
Rationale: "factor of 143 = 11 * 13 - - - 2 prime numbers d"
Answer: d
Problem: a jar contains a mixture of ab in the ratio 3 : 2 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 20 , e ) 36
Rationale: "20 litres of mixture that is replaced will contain 12 litres of a and 8 litres of b ( as a : b = 3 : 2 ) let the initial volume of the mixture be 3 k + 2 k = 5 k so by condition , [ 3 k - 12 ] / [ 2 k - 8 + 20 ] = 2 / 3 = > 9 k - 36 = 4 k - 16 + 40 = > 5 k = 60 solve for k which is k = 12 so initial volume of liquid a = 3 k = 36 litres answer : e"
Answer: e
Problem: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,600 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
Options: a ) 850 , b ) 1,100 , c ) 1,800 , d ) 2,550 , e ) 3,400
Rationale: "assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3600 therefore x = 2400 / 4 = 600 price of 28 inch + 30 inch = 800 + 1000 = 1800 option c"
Answer: c
Problem: the average of marks obtained by 120 boys was 38 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 115 , d ) 125 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 38 24 x = 4560 - 1800 = > x = 2760 / 24 x = 115 . hence , the number of boys passed = 115 . answer : c"
Answer: c
Problem: if x , y , and z are positive integers , and 2 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 28 , c ) 33 , d ) 42 , e ) 60
Rationale: "take lcm of 2,5 and 8 = 40 now 2 x = 40 = > x = 20 5 y = 40 = > y = 8 8 z = 40 = > z = 5 20 + 8 + 5 = 33 . option c ."
Answer: c
Problem: john and beth each drove from smallville to crown city by different routes . john drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than john to complete the trip . how many miles per hour was beth ' s average speed on this trip ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 54 , e ) 75
Rationale: speed = distance / time distance for john = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for john + 5 = 20 + 5 = 25 miles time taken by beth = time taken by john + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer .
Answer: b
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 100 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "prime factorization out is the way to go here ! 36 ^ 100 3 ^ 2 times 2 ^ 2 and both to the power of 100 [ ( 3 ^ 2 ) * ( 2 ^ 2 ) ] ^ 100 giving you the beautifully simplistic answer of 3 ^ 200 and 2 ^ 200 ans is 200 answer : b"
Answer: b