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Word problem

by rerika01 » Mon Mar 07, 2011 11:16 am
Need help approaching this problem efficiently.

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
3) 1/6

Thanks!
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by Night reader » Mon Mar 07, 2011 12:06 pm
P=pay, S=saving, S/P= C (constant), 12*C*P=3(P-S), S/P-?
12S=3P-3S, 15S=3P, S/P=1/5
rerika01 wrote:Need help approaching this problem efficiently.

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
3) 1/6

Thanks!
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by GMATGuruNY » Mon Mar 07, 2011 1:48 pm
rerika01 wrote:Need help approaching this problem efficiently.

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
3) 1/6

Thanks!
We can plug in the answers, which represent the fraction saved each month.

Answer choice C: 1/4 saved each month
Let monthly pay = 4.
1/4 * 4 = 1 saved each month, 3 not saved.
12*1 = 12 total saved for the whole year.
(Total saved)/(monthly not saved) = 12/3 = 4. We need Alice to save less.

Answer choice D: 1/5 saved each month
Let monthly pay = 5.
1/5 * 5 = 1 saved each month, 4 not saved.
12*1 = 12 total saved for the whole year.
(Total saved)/(monthly not saved) = 12/4 = 3. Success!

The correct answer is D.
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