Alice’s take-home pay last year was the same each month, and she saved : GMAT Problem Solving (PS)
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# Alice’s take-home pay last year was the same each month, and she saved

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

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20 Dec 2009, 05:58
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: alice-s-take-home-pay-last-year-was-the-same-each-month-and-91893.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Mar 2015, 07:21, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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20 Dec 2009, 06:54
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let monthly income is x; saving is y; expenditure is x-y

eqn 12y=3(x-y)
solving y=x/5
hence 1/5 i.e D
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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20 Dec 2009, 22:17
xcusemeplz2009 wrote:
let monthly income is x; saving is y; expenditure is x-y

eqn 12y=3(x-y)
solving y=x/5
hence 1/5 i.e D

wow! never thought that it cud be so easy
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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21 Dec 2009, 12:50
Same approach got 1/5.
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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21 Dec 2009, 15:14
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Saving: x
Income: p
Non saved p-x

12x=3(p-x)
15x=3p
x=p/5
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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18 Apr 2011, 11:31
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 she had saved at the end of the year was three 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?

Is it problem if I don't assume monthly payment [as saving is said in fraction so payment is one]
such as:
saving is x fraction
so, total saving of the year 12x
according to the condition 12x = 3(1-x)
12x = 3-3x
12x+3x= 3
15x = 3
x = 3/15 = 1/5 or D ans.
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Last edited by Baten80 on 01 May 2011, 03:10, edited 1 time in total.
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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18 Apr 2011, 11:34
Baten80 wrote:
Is it problem if I don't assume monthly payment [as saving is said in fraction so payment is one]
such as:
saving is x fraction
so, total saving of the year 12x
according to the condition 12x = 3(1-x)
12x = 3-3x
12x+3x= 3
15x = 3
x = 3/15 = 1/5 or D ans.

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

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18 Apr 2011, 11:53
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink]

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18 Apr 2011, 18:13
Let x = take home pay each month

Let y = Part of x saved each month

So y/x = constant

Part of monthly income not saved = x(1 - y/x)

So y/x = ?

12 * y/x * x = 3 * x(1 - y/x)

12y = 3x - 3y

=> 15y = 3x => y/x = 1/5

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

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

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07 Mar 2015, 07:22
Expert's post
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msunny 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

Let Alice's monthly take-home pay be $$p$$ and her monthly savings be $$s$$. Total savings will be $$12s$$ and we know that this is 3 times the amount she spends in month which is: $$p-s$$. So we have:

$$12s=3(p-s)$$ --> $$s=p\frac{1}{5}$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: alice-s-take-home-pay-last-year-was-the-same-each-month-and-91893.html
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Re: Alice’s take-home pay last year was the same each month, and she saved   [#permalink] 07 Mar 2015, 07:22
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