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Take-Home pay (word problem)

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by GMATGuruNY » Wed May 21, 2014 9:31 am
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 the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

a. 1/2
b. 1/3
c. 1/4
d. 1/5
e. 1/6
We can PLUG IN THE ANSWERS, which represent the fraction that must be saved each month.
When the correct answer choice is plugged in, the total amount saved at the end of the year will be 3 times the amount NOT saved each month.

Answer choice D: 1/5
Let the monthly pay = $5.
Since 1/5 is saved each month, the amount saved each month = 1/5 * 5 = $1.
Thus, the amount NOT saved each month = 5-1 = $4.
Since $1 is saved each month, the total amount saved at the end of the year = 12*1 = $12.
Success!
The total amount saved at the end of the year ($12) is 3 times the amount not saved each month ($4).

The correct answer is D.
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by Brent@GMATPrepNow » Wed May 21, 2014 9:34 am
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
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
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by gdshamain » Wed May 21, 2014 12:24 pm
Thank you. It is clear now!
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by GMATGuruNY » Thu May 22, 2014 2:38 am
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 the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

a. 1/2
b. 1/3
c. 1/4
d. 1/5
e. 1/6
Slightly different algebraic approach:

Let the monthly income = $1.
Let x = the fraction saved each month.
Fraction not saved each month = 1-x.
Total saved at the end of the year = 12x.
Since the total saved is equal to 3 times the fraction not saved each month, we get:
12x = 3(1-x)
12x = 3 - 3x
15x = 3
x = 3/15 = 1/5.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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