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Alice's take-home pay last year was the same each month...

Expert replies
by BTGmoderatorLU » Mon Feb 26, 2018 11:38 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 money that she saved last year was from her take-home pay, what fraction of her take-home pay did she saved each month?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6

The OA is D.

I'm really confused by this PS question. Experts, any suggestion? I can't find the way to solve it. Thanks in advance.
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Source: — Problem Solving |

by Brent@GMATPrepNow » Mon Feb 26, 2018 11:44 am
LUANDATO 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 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 that she saved last year was from her take-home pay, what fraction of her take-home pay did she saved each month?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
Here's another 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 doesn't 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 =
1/5
= D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATGuruNY » Mon Feb 26, 2018 1:38 pm
LUANDATO 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 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 that she saved last year was from her take-home pay, what fraction of her take-home pay did she saved each month?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
Let the amount saved each month = $1.
Total saved for the entire year = 12*1 = $12.
Since the total saved for the entire year -- $12 -- is 3 times the amount not saved each month, the amount not saved each month = 12/3 = $4.
Thus, the total monthly pay = (amount saved each month) + (amount not saved each month) = 1+4 = $5.
Resulting fraction:
(amount saved each month)/(total monthly pay) = 1/5.

The correct answer is D.
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by Scott@TargetTestPrep » Wed Feb 28, 2018 10:36 am
LUANDATO 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 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 that she saved last year was from her take-home pay, what fraction of her take-home pay did she saved each month?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6
We are given 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.

To start we can let S = the amount of money Alice saved each month and N = the amount of money she did not save each month.

Since the 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 know that:

12S = 3N

4S = N

We need to determine what fraction of her take-home pay she saved each month. Setting this question up as an expression we have:

S/(S + N)= ?

Since 4S = N, we can substitute 4S in for for N in the expression S/(S + N).

S/(S + 4S) = S/5S = 1/5

Answer:D

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