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Word Problem on Salary

Problem Solving — algebra and arithmetic
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Junior | Next Rank: 30 Posts
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by emiflo » Thu Jan 27, 2011 8:13 pm
Alice 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 saved at the end of the year was three times the amount of that portion of her monthly 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 last year?

a. 1/2
b. 1/3
c. 1/4
d. 1/5
e. 1/6

ANS. D

I saw this question in a question bank. Could someone please explain to me how to solve it and the principle behind solving the question.
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Source: — Quantitative Reasoning |
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by Target2009 » Thu Jan 27, 2011 9:16 pm
See Ron's reply

you can also do this problem by picking numbers, because you don't have a figure for the monthly pay (and, apparently, it doesn't matter, because the problem would be impossible to solve if it did matter).

so just let the monthly pay be '1'.
let the monthly savings be 'S', which is both a fraction and an actual amount of money. (it's both because the monthly pay is '1', so the fraction is the same as the dollar amount)
then she has saved 12S at the end of the year.
each month, she didn't save (1 - S)
so
12S = 3(1 - S)
12S = 3 - 3S
15S = 3
S = 3/15 = 1/5

faster, and probably less confusing, with only one variable
Regards
Abhishek
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MasterGmat Student
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