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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

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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

by VJesus12 » Wed Jun 24, 2020 5:48 am

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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

[spoiler]OA=D[/spoiler]

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Re: Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each m

by Brent@GMATPrepNow » Wed Jun 24, 2020 7:11 am
VJesus12 wrote: ↑
Wed Jun 24, 2020 5:48 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

[spoiler]OA=D[/spoiler]

Source: GMAT Prep
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 = 1/5
Answer: D

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each m

by Scott@TargetTestPrep » Mon Jun 29, 2020 8:41 am
VJesus12 wrote: ↑
Wed Jun 24, 2020 5:48 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

[spoiler]OA=D[/spoiler]

Source: GMAT Prep
Solution:
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 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 for N in the expression S/(S + N).
S/(S + 4S) = S/5S = 1/5

Answer: D

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