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I do not understand the solution to this

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I do not understand the solution to this

by bfman » Sat Jun 20, 2009 1:29 pm
Hi Folks:

Here is the question...

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 me know what you guys get for this.
My answer doesn't agree with book's answer.

thanks!
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by vasbli » Sat Jun 20, 2009 1:58 pm
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?
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by bfman » Sat Jun 20, 2009 8:12 pm
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.
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by BlindVision » Sat Jun 20, 2009 8:23 pm
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...
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by bfman » Sat Jun 20, 2009 8:31 pm
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.
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by rahulg83 » Sun Jun 21, 2009 1:22 am
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
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by bfman » Sun Jun 21, 2009 10:30 am
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.
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by bfman » Sun Jun 21, 2009 10:32 am
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!
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by crackthetest » Sun Jun 21, 2009 11:13 am
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.
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by bfman » Sun Jun 21, 2009 11:49 am
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
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