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

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

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26 Mar 2010, 16:21
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Mar 2012, 00:53, edited 1 time in total.
Edited the question
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26 Mar 2010, 16:39
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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

Thanks,

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:

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

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04 Jul 2010, 12:28
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ramana wrote:
I know i am terribly missing something, please elaborate

OA soon

Let's call the fraction of pay PER MONTH that Alice saved S, and the fraction of pay that she did not save N.
Therefore:
(% of pay saved) + (% of pay spent) = 100%
S + N = 1

The second sentence in the question states that Alice's total yearly savings is equal to three times the amount she would NOT save (a.k.a. the spending) in one month.
Therefore:
(yearly savings) = (3 * monthly spending)
(12 * monthly saving) = (3 * monthly spending)
12S = 3N
4S = N

Now plug this into the top equation to find a value for S:
4S = N
S + N = 1
S + (4S) = 1
5S = 1
S = 1/5

I'd be willing to bet that you didn't read carefully enough and you thought the second sentence in the question said, " The total amount of money at the end of the year that she had saved was 3 times the portion that she had spent." This is what I thought during my first read-through -- and I spent about 15 seconds working the problem incorrectly!
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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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11 Dec 2014, 07:13
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JackSparr0w wrote:
My apologies, I should have let this sit for a day and come back to it. I was subtracting 3s from 12s, instead of adding. Thanks again.

You should be very careful not to make such mistakes. Careless errors are the #1 cause of score drops on the GMAT! They cause you to miss easier questions, hurting your score a lot more than not know how to solve the harder ones. So, be more careful, before you submit your answer and double-check that it’s the answer to the proper question.
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Re: Alice’s take-home pay last year was the same each month, and [#permalink]

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06 Dec 2016, 09:22
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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

Responding to a pm:

Let monthly take home be 100 and the fraction she saves be x.

12*100*x = 3*100*(1-x)
4x = 1 - x
x = 1/5

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Alice's saving each month = $y Alice did not save each month =$x -$y Total Saving per year: 12y 12y = 3(x-y) ---1st y/x = ? 4y=x-y 4=x/y-1 x/y=5 y/x=1/5 Ans: "D" _________________ Manager Joined: 25 May 2011 Posts: 156 Followers: 2 Kudos [?]: 60 [0], given: 71 Re: please help me set up the equation for this problem [#permalink] ### Show Tags 18 Nov 2011, 05:51 Lets say that the total monthly revenue is R and she saved $$\frac{1}{x}$$ of this revenue every month. So based on the question: $$12 (\frac{1}{x}) R = 3 (1- \frac{1}{x}) R$$ $$x=5$$ So she saved $$\frac{1}{5}$$ of monthly revenue. VP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 1126 GMAT 1: 780 Q51 V48 GRE 1: 1540 Q800 V740 Followers: 124 Kudos [?]: 542 [0], given: 19 Re: Proportion of Take home pay saved [#permalink] ### Show Tags 18 Mar 2012, 21:04 Let her monthly take-home be x and her monthly savings be y. Then 12y = 3(x-y) => y/x = 1/5 Option (D) _________________ GyanOne | Top MBA Rankings and MBA Admissions Blog Top MBA Admissions Consulting | Top MiM Admissions Consulting Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738 Intern Joined: 06 Jan 2012 Posts: 32 Location: United States GMAT 1: Q48 V30 Followers: 0 Kudos [?]: 11 [0], given: 5 Re: Proportion of Take home pay saved [#permalink] ### Show Tags 18 Mar 2012, 22:25 GyanOne wrote: Let her monthly take-home be x and her monthly savings be y. Then 12y = 3(x-y) => y/x = 1/5 Option (D) Thank you. I initially did the equations as 12y = 3 x 12 (x-y) so didn't get it right. _________________ -If you like my post, consider giving KUDOS Senior Manager Joined: 12 Mar 2012 Posts: 369 Concentration: Operations, Strategy Followers: 2 Kudos [?]: 169 [0], given: 31 Re: Proportion of Take home pay saved [#permalink] ### Show Tags 18 Mar 2012, 22:58 D 12x=3(y-x) => x/y=1/5 _________________ Practice Practice and practice...!! If my reply /analysis is helpful-->please press KUDOS If there's a loophole in my analysis--> suggest measures to make it airtight. GMAT Club Legend Joined: 09 Sep 2013 Posts: 13550 Followers: 578 Kudos [?]: 163 [0], given: 0 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 07 Apr 2014, 10:57 Hello from the GMAT Club BumpBot! Thanks to another GMAT 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 19 Jan 2014 Posts: 31 Followers: 0 Kudos [?]: 16 [0], given: 51 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 03 Jul 2014, 17:36 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 I had a different approach to this question and I still don't understand why it doesn't work this way. Because the way people on this thread used, didn't come to my mind at all. So let x be the amount she earns each month. Then she earned total of 12x in a year. so I know that from this amount 3x was spent and 9x was saved. so 9x/12=3x/4 was her monthly save. (3x/4)/x= 3/4 and there isn't even an answer like that. I must be getting something completely wrong but I can't seem to understand where exactly i'm going wrong. SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1939 [0], given: 193 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 04 Jul 2014, 02:37 bytatia wrote: 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 I had a different approach to this question and I still don't understand why it doesn't work this way. Because the way people on this thread used, didn't come to my mind at all. So let x be the amount she earns each month. Then she earned total of 12x in a year. so I know that from this amount 3x was spent and 9x was saved. so 9x/12=3x/4 was her monthly save. (3x/4)/x= 3/4 and there isn't even an answer like that. I must be getting something completely wrong but I can't seem to understand where exactly i'm going wrong. The problem does not state that 1/4 th of the amount earned is spent OR 3/4 th of the amount earned in saved. We have to take another variable to compute the savings amount & draw relation between Total saved & Not Saved As always, Bunuel's method is the best to get along _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 30 Sep 2014 Posts: 7 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 02 Nov 2014, 12:00 Hi GMAT club members, I tried to solve this problem as follows. Asume her monthly take home pay is x, and she saves 1/2x. Then the portion she did not save is 1/2x. Setting up the equation: 1/2x x 12 = 3(1/2x) 6x = 3/2x Then I get a ratio of 1/4. Could someone please explain why my approach is wrong? Thank you Re: Alice’s take-home pay last year was the same each month, and [#permalink] 02 Nov 2014, 12:00 Go to page 1 2 Next [ 29 posts ] Similar topics Replies Last post Similar Topics: Average of money that group of 4 friends pay for rent each month is$8 2 15 Jun 2011, 07:52
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