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Alice's take home package

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Alice's take home package

by prachich1987 » Sat Jan 01, 2011 11:27 pm
Alice's take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home 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


This is from the document "198 Level 700+ questions from GMAT Prep I which I downloaded from BTG.
But the answer given is D
Please explain
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by Anurag@Gurome » Sun Jan 02, 2011 12:28 am
prachich1987 wrote:Alice's take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home 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
Say, the fraction of monthly take home pay Alice saved each month = x
and the fraction of monthly take home pay Alice did not saved each month = y
Thus, (x + y) = 1

Now, the total amount she saved at the end of the year = 3 times the amount of that portion of her monthly take home that she did not save.

Thus, 12x = 3y => y = 4x

Replacing this in the first equation, (x + 4x) = 1 => x = 1/5

The correct answer is D.
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by ragz » Sun Jan 02, 2011 11:24 am
If you find it difficult to use two variables, we can assume a number value for her monthly salary since all we are worried about is the % of saving and not the actual saving.

So, let's assume that Alice's monthly take home pay = 100 -- (I)
Let's assume that her monthly savings = X -- (II)

From (I) and (II), Alice's monthly spending or the money not saved = 100-X -- (III)

From (II), her annual savings = 12X -- (IV)

Based on the information given in the question, 12X = 3(100 - X) ==> 15X = 300 ==> X = 20

Hence, the fraction of Alice's take home pay she saved each month = 20/100 = 1/5.

The answer is, therefore, D.

Hope this helps.[/b]
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by GMATGuruNY » Sun Jan 02, 2011 1:27 pm
prachich1987 wrote:Alice's take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home 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
This is a great question for plugging in the answers, which represent the fraction saved each month.

Plug in monthly pay = 60. (60 is a good number because it's divisible by all the denominators in the answer choices.)

Answer choice C: 1/4 saved each month
1/4 * 60 = 15 saved each month, 45 not saved.
12*15 = 180 total saved for the whole year.
(Total saved)/(monthly not saved) = 180/45 = 4. We need her to save less.

Answer choice D: 1/5 saved each month
1/5 * 60 = 12 saved each month, 48 not saved.
12*12 = 144 total saved for the whole year.
(Total saved)/(monthly not saved) = 144/48 = 3. Success!

The correct answer is D.
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