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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  [#permalink]

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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

Originally posted by changhiskhan on 26 Mar 2010, 17:21.
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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New post 26 Mar 2010, 17:39
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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:

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

Answer: D.
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Re: PS-gprep  [#permalink]

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New post 04 Jul 2010, 13:28
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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

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

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New post 27 Mar 2010, 04:17
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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: Alice’s take-home pay last year was the same each month, and  [#permalink]

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New post 27 Mar 2012, 18:30
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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
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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


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, 03:02
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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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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
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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 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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Alice’s take-home pay last year was the same each month, and  [#permalink]

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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, 08:09
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.
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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, 08:13
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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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New post 06 Dec 2016, 10:22
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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

Answer (D)
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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 09 Feb 2017, 17:31
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


We are given 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.
To start we can let S = the amount of money that Alice saved each month and N = the amount of money she did not save each month.
Since the 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 we know that:

12S = 3N

4S = N

We need to determine what fraction of her take-home pay she saved each month. Setting this question up as an expression we have:

S/(S + N)= ?

Since 4S = N, we can substitute 4S in for for N in the expression S/(S + N).

S/(S + 4S) = S/5S = 1/5

Answer: D
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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 14 Feb 2017, 11:41
Why isn't the equation 12y = (3(x-y))*12 since we are told that this is the amount by the end the year? So 12 months accumulated.
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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 14 Feb 2017, 12:21
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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


Here's another algebraic approach.

Let M = Alice's monthly take home pay
Let f = the fraction we'll use to calculate monthly savings
The means that fM = the amount of $ Alice saves each month.
And this means that her annual savings = 12fM

Important: If f = the fraction used to calculate monthly savings, then 1-f = the fraction used to calculate amount not saved
The means that (1-f)M = the amount of $ Alice does not save each month.

Now we're ready to write an equation.

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.
We get: 12fM = 3(1-f)M
Now solve for f
Expand to get: 12fM = 3M - 3fM
Simplify: 15fM = 3M
Divide both sides by 15M to get: f = 3M/15M = 1/5
Answer: D

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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 15 Feb 2017, 02:48
iliavko wrote:
Why isn't the equation 12y = (3(x-y))*12 since we are told that this is the amount by the end the year? So 12 months accumulated.



Note here what the question says:

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.

3 times the amount of the monthly pay fraction, not the total annual pay fraction. So you do not multiply by 12.
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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 09 Feb 2018, 12:21
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Hi All,

We can solve this question with some algebra, but you have to be detailed with how you assign variables.

If...
X = the amount of money Alice EARNED per month
Y = the amount of money Alice SAVED per month
Y/X = the FRACTION of her paycheck she saved per month
then...
12Y = the amount of money Alice saved in ONE YEAR

Since the TOTAL amount saved = 3 times (what she DIDN'T save), we have this...
12Y = 3(X - Y)

Now, we can simplify:
12Y = 3X - 3Y
15Y = 3X
5Y = X
Y/X = 1/5

Final Answer:

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Re: Alice’s take-home pay last year was the same each month, and   [#permalink] 09 Feb 2018, 12:21

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