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

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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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New post 09 Feb 2018, 17:07
changhiskhan 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


pay per month = \(x\)
pay last year = \(12x\)

savings per month = \(\frac{1}{y}(x) = \frac{x}{y}\)
savings last year = \(\frac{12x}{y}\)

spending each month = \(x - \frac{x}{y} = \frac{(xy-x)}{y}\)
spending last year = \(\frac{12(xy-x)}{y}\)

\(\frac{12x}{y} = \frac{3[xy-x]}{y}\)
\(\frac{4x}{y} = \frac{xy-x}{y}\)
\(4x = xy-x\)
\(5x = xy\)
\(y = 5\).

Fraction = \(\frac{1}{5}\).
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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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New post 14 Feb 2018, 18:08
EMPOWERgmatRichC wrote:
Hi All,

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

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich


Hi Rich,

Can this be solved using smart numbers? For example, by using $120 for take-home pay to represent 12 months?
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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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New post 14 Feb 2018, 20:09
Hi OCDianaOC,

Yes, you could solve this question by TESTing VALUES. To use that approach efficiently though, you wouldn't start with Alice's take-home pay each month - you'd actually have to start with the information in the second sentence:

"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."

By TESTing VALUES that fit this information, you can then 'work backwards' and determine her take-home pay each month (and then answer the question).

GMAT assassins aren't born, they're made,
Rich
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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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New post 14 Feb 2018, 22:19
EMPOWERgmatRichC wrote:
Hi OCDianaOC,

Yes, you could solve this question by TESTing VALUES. To use that approach efficiently though, you wouldn't start with Alice's take-home pay each month - you'd actually have to start with the information in the second sentence:

"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."

By TESTing VALUES that fit this information, you can then 'work backwards' and determine her take-home pay each month (and then answer the question).

GMAT assassins aren't born, they're made,
Rich


Thanks Rich, but I'm not getting the correct answer by testing values.

I chose that she saved $10/month and had $120 by the end of the year. She did NOT save $40 (since $120 is 3 times bigger than $40).

Total take-home pay is $1,200/year.

My answer: I got 10/100 then reduced to 1/10. Wrong answer!

Help!
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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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New post 15 Feb 2018, 11:24
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Hi OCDianaOC,

The numbers you've chosen to TEST are perfect, but you made a small math mistake:

IF... $10 was saved each month and $40 was NOT saved each month, then the total for each month is $50 (not $100). Thus, the take-home pay for the year would be (12)($50) = $600.

Total saved for the year = (12)($10) = $120
Total take-home pay for the year = $600
$120/$600 = 1/5

GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.com

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Re: Alice’s take-home pay last year was the same each month, and   [#permalink] 15 Feb 2018, 11:24

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