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please help me attack this question

Problem Solving — algebra and arithmetic
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Source: — Quantitative Reasoning |

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by Brent@GMATPrepNow » Fri Dec 12, 2014 7:28 pm
Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save. If all money she saved lasr year was from her take-home pay, what fraction of her pay did she save each month?

a)1/2
b)1/3
c)1/4
d)1/5
e)1/6
Here's an algebraic approach.

Let M = Alice's monthly take home pay
Let f = the fraction we'll use to calculate monthly savings
The means that fM = the amount of $ Alice saves each month.
And this means that her annual savings = 12fM

Important: If f = the fraction used to calculate monthly savings, then 1-f = the fraction used to calculate amount not saved
The means that (1-f)M = the amount of $ Alice does not save each month.

Now we're ready to write an equation.

The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.
We get: 12fM = 3(1-f)M
Now solve for f
Expand to get: 12fM = 3M - 3fM
Simplify: 15fM = 3M
Divide both sides by 15M to get: f = 3M/15M = [spoiler]1/5 = D[/spoiler]

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Jun 17, 2015 9:27 am, edited 1 time in total.
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by [email protected] » Fri Dec 12, 2014 9:28 pm
Hi rodior,

This question shows up in this Forum every few months. Here was a discussion of the question (along with a variety of approaches to solving it):

https://www.beatthegmat.com/word-problems-t270244.html

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by regor60 » Wed Jun 17, 2015 8:39 am
Brent@GMATPrepNow wrote:
Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she saved at the end of the year was 3 times the amount of her take-home pay that she didn't save. If all money she saved lasr year was from her take-home pay, what fraction of her pay did she save each month?

a)1/2
b)1/3
c)1/4
d)1/5
e)1/6
The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.



Your interpretation adds the word "monthly" that doesn't exist in the original question. Without it and assuming annual take home pay not saved, I believe the answer would be 75%.
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by Brent@GMATPrepNow » Wed Jun 17, 2015 9:29 am
Hi regor60,

That was a bad transcription on my part. I've added the missing words.

The original question reads...

The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.

Cheers,
Brent
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