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by saidov.mikhail » Thu Oct 03, 2013 12:01 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
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by theCodeToGMAT » Thu Oct 03, 2013 12:15 am
Isn't the language of the question ambiguous.. The sentence
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"--> this highlighted text doesn't specify yearly or Monthly take home..


Case 1: Yearly take home

Monthly pay = X
Monthly Save = y

12Y = 3 ( 12(X-Y))
Y/X = 3/4

Case 2: Monthly take home

12Y = 3 ( X-Y)
Y/X = 1/5
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by theCodeToGMAT » Thu Oct 03, 2013 12:20 am
I searched on Web and Found:

Alice's take-home pay was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money 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?
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by [email protected] » Thu Oct 03, 2013 12:29 am
Hi saidov.mikhail,

We can solve this question with some algebra, but you have to be detailed with how you assign variables.

If...
X = the amount of money Alice earned per month
Y = the amount of money Alice saved per month
Y/X = the fraction of her paycheck she saved per month
then...
12Y = the amount of money Alice saved in one year

Since the TOTAL amount saved = 3 times (what she DIDN'T save), we have this...
12Y = 3(X - Y)

Now, we can simplify:
12Y = 3X - 3Y
15Y = 3X
5Y = X
Y/X = 1/5

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by GMATGuruNY » Thu Oct 03, 2013 2:54 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 saved each month.

Answer choice C: 1/4 saved each month
Let the total monthly pay = 4.
Amount saved each month = 1/4 * 4 = 1
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*3 = 9.
Since these last two values must be equal, too much money is being saved.
Eliminate A, B and C.

Answer choice D: 1/5 saved each month
Let the total monthly pay = 5.
Amount saved each month = 1/5 * 5 = 1.
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*4 = 12.
Success!

The correct answer is D.

Algebraically:
Let the fraction saved each month = x.
Amount saved for the whole year = 12x.
Fraction not saved each month = 1-x.
Since the amount saved for the whole year 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.
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by Brent@GMATPrepNow » Thu Oct 03, 2013 5:50 am
saidov.mikhail 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
Here's a different 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]

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