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Alice’s take-home pay last year was the same each month, and

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Carcass
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Alice’s take-home pay last year was the same each month, and [#permalink] New post   09 Jun 2020, 09:15
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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
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D
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post   09 Jun 2020, 09:15
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post   09 Jun 2020, 09:45
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Carcass 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 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


Here's one 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 = 1/5
Answer: D

Cheers,
Brent
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post   02 Feb 2021, 20:08
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Let her total earnings be : x
Let the fraction that she saved every month be : y

Amount not saved every month : (x-y)

According to the question :

Total savings at year end = 3* amout not saved i.e.

12*y = 3* (x-y)
Which is

y = (1/5) x

So the correct option is D

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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post   02 Feb 2021, 23:18
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Carcass 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 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


OA is E?
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Re: Alice’s take-home pay last year was the same each month, and [#permalink] New post   02 Feb 2021, 23:23
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Fixed. It is D

I do not know why showed E

regards
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Re: Alices take-home pay last year was the same each month, and [#permalink] New post   05 Jun 2023, 01:04
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Alices take-home pay last year was the same each month, and [#permalink]
05 Jun 2023, 01:04
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