John spends one-fourth of his salary on rent and two-third less than he spent on rent for the utilities. What fraction of his earnings did he spend on the rent and utilities?

let x be the salary:
on rent he spent x/4
on utilities he spent x/4(1-2/3)
total x/6

answer:1/6
correct?

Book's answer is 5/12

I am getting 1/3

Explanation:

Rent = x/4
Utilities = x/4 - 2/3(x/4) => x/12

Add them up:
x/4 + x/12 = x/3


I don't think I should follow this book.
It's the EZ Solutions GMAT Math Strategy book and his method is to plug in random numbers and sometimes answers into the question to come up with solution while avoiding the direct algebraic method a lot of times. I think he has made up some of these questions to support his own theories and methods and these might not help in GMAT. I think I'll just study the Manhattam GMAT Books.

I got 1/3, as well. I started off with a smart number of 100 and worked from there. Would like to know how to get the answer 5/12...

he used "12" as the smart number. I do not trust random number plugging strategy. I'd rather have a solid direct algebraic method to work with.

I am also getting 1/3...

Answer could be 5/12 only if u consider rent expenses = x/4
and Utilities expenses = 2/3 (x/4) = x/6, according to the solution

If the question says, two thirds of...then this solution can be understood

two-third less than he spent on rent for the utilities

but according to me utilities expenses = (1-2/3)x/4 = x/12

Explanation from the book:

The problem involves two fractions: 1/4 and 2/3. Let us assume that the total earnings was $12. (12 is the least common denominator and is divisible by both the denominators 4 and 3).

Amount spent on Rent = 1/4 x 12 = 3
Amount spent on Utilities = 3 - 1/3 x 3 = 3 - 1 = 2
Amount spent on Rent + Utilities = 3 + 2 = 5
Fraction of th earnings spent on Rent & Utilities = 5 out of 12 = 5/12

Hence he's getting 5/12.

OK I just saw it. His calculation is flawed. He used 1/3 instead of 2/3 (perhaps in a hurry or by mistake). What a fool. And then he just forced that answer into one of the choices and made it the right answer! OMG!

Even before looking at the replies, here is what I calculated:

Assume the rent to be a a rounded number, where you can get a integer either splitting 1/4th or 2/3rd. I assumed 180 to be total earnings.

Rent = 1/4*180 = 45

Spends 2/3rd less of that on Utils 2/3*45 = 30

fraction of Rent+Utils to earnings (45+30)/180 = 5/12.

crackthetest wrote:Even before looking at the replies, here is what I calculated:

Assume the rent to be a a rounded number, where you can get a integer either splitting 1/4th or 2/3rd. I assumed 180 to be total earnings.

Rent = 1/4*180 = 45

Spends 2/3rd less of that on Utils 2/3*45 = 30

fraction of Rent+Utils to earnings (45+30)/180 = 5/12.

The answer is still 1/3 even if you use 180.

Explanation:

Rent = 1/4*180 = 45
Utilities = 45 - 2/3(45) = 15
Rent + Utilities = 60

Fraction => 60/180 => 1/3