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

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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, 01:53, edited 1 time in total.
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Re: please help me set up the equation for this problem [#permalink]

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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:

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

Answer: D.
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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

Therefore, the answer is D.


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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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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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

Answer (D)
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Re: please help me set up the equation for this problem [#permalink]

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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,

x - monthly take home
y - monthly save
x-y - monthly expenditure
given, 12y = 3(x-y) => x = 5y
to calculate, y/x = 1/5 hence D

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Re: please help me set up the equation for this problem [#permalink]

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

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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 total amount of money that she saved in a year was 3 times the amount of the money she spent per month.
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msharmita 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 saved at the end of the year was 3 times the amount of that portion of the 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


Please explain the same. Answer is D 1/5



Here lies the explanation -

Suppose fraction of her take home pay she did save each month \(= \frac{x}{y}\)
then fraction she did NOT save each month will be \(1- \frac{x}{y} = \frac{(y-x)}{y}\)

Now we are given that
whatever she saved in last year (in 12 months) =\(\frac{12*x}{Y}\) = 3 \(\frac{(y-x)}{y}\)
=> 12 x = 3 (y-x)
=> 15 x = 3 y
=>\(\frac{x}{y}= \frac{3}{15} = \frac{1}{5} = ANS D\)

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

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Re: please help me set up the equation for this problem [#permalink]

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New post 18 Nov 2011, 06:51
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.

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Re: Proportion of Take home pay saved [#permalink]

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New post 18 Mar 2012, 22:04
Let her monthly take-home be x and her monthly savings be y.
Then 12y = 3(x-y)
=> y/x = 1/5

Option (D)
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Re: Proportion of Take home pay saved [#permalink]

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New post 18 Mar 2012, 23:25
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.
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Re: Proportion of Take home pay saved [#permalink]

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New post 18 Mar 2012, 23:58
D
12x=3(y-x)
=> x/y=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 03 Jul 2014, 18:36
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.

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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 04 Jul 2014, 03:37
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 :)
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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 02 Nov 2014, 13:00
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

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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 03 Nov 2014, 02:42
sassy10 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?


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


Hi,

Notice that 6x does NOT equal to 3/2*x, so 6x = 3/2*x is not correct.

You cannot arbitrarily assume here that she saves half of her take home pay. The fraction of the savings is fixed so that 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.
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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 11 Dec 2014, 08:01
Bunuel wrote:

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

.


How do we solve this? I'm getting something different?

Thanks

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Re: Alice’s take-home pay last year was the same each month, and   [#permalink] 11 Dec 2014, 08:01

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