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

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

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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

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

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14 Feb 2017, 12:21
Top Contributor
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

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

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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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09 Feb 2018, 18:07
1
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

pay per month = $$x$$
pay last year = $$12x$$

savings per month = $$\frac{1}{y}(x) = \frac{x}{y}$$
savings last year = $$\frac{12x}{y}$$

spending each month = $$x - \frac{x}{y} = \frac{(xy-x)}{y}$$
spending last year = $$\frac{12(xy-x)}{y}$$

$$\frac{12x}{y} = \frac{3[xy-x]}{y}$$
$$\frac{4x}{y} = \frac{xy-x}{y}$$
$$4x = xy-x$$
$$5x = xy$$
$$y = 5$$.

Fraction = $$\frac{1}{5}$$.
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Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

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14 Feb 2018, 19:08
EMPOWERgmatRichC wrote:
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

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Total take-home pay is $1,200/year. My answer: I got 10/100 then reduced to 1/10. Wrong answer! Help! VP Joined: 09 Mar 2016 Posts: 1229 Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 15 May 2018, 04:22 Bunuel 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 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. Hello Bunuel - founder of numerology hope you are well my solution is quite unusual but is super duper quck As per this sentence " Alice 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' So total amount she saved was 60 and total amount she didnt save was 20 So now question is "what fraction of her take-home pay did she save each month?" so i divide 60 by 12 (number of months ) 60/12 = 5 hence $$\frac{1}{5}$$ she saved each month. YAY is my correct approach ? thanks and have a good week in case Bunuel doesn't reply I will tag you friends too generis niks18 Senior SC Moderator Joined: 22 May 2016 Posts: 3670 Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 15 May 2018, 09:16 1 dave13 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 Hello Bunuel - founder of numerology hope you are well my solution is quite unusual but is super duper quck As per this sentence " Alice 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' So total amount she saved was 60 and total amount she didnt save was 20 So now question is "what fraction of her take-home pay did she save each month?" so i divide 60 by 12 (number of months ) 60/12 = 5 hence $$\frac{1}{5}$$ she saved each month. YAY is my correct approach ? thanks and have a good week in case Bunuel doesn't reply I will tag you friends too generis niks18 Hi dave13 , whether your approach is correct depends on whether you did some mental math and did not write down the steps. How did you calculate $$\frac{1}{5}$$? How did you go from 5 to $$\frac{1}{5}$$? (You have everything in place. You picked good numbers. How and whether you manipulated those numbers, I cannot discern.) _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead Manager Joined: 29 Sep 2017 Posts: 114 Location: United States Re: Alice’s take-home pay last year was the same each month, and [#permalink] ### Show Tags 15 May 2018, 11:28 1 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 Notice that the 60 is a good number to change fractions to whole numbers; hence, each choice becomes: A. 30 B. 20 C. 15 D. 12 E. 10 Simply plug and play: if her take home savings were$30, then she did not save $30. 12(30) = 360. Divide this by amount not saved ($30); hence, 12. We need this to be 3x, not 12x. Plugging in rest of numbers shows that D (12) fits.

12 (amount saved) * 12 (months in a year) = 144 (amount saved in year)
48 (amount not saved) * 3 (per stem) = 144. Both match; 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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15 May 2018, 12:01
generis wrote:
dave13 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

Hello Bunuel - founder of numerology hope you are well

my solution is quite unusual but is super duper quck

As per this sentence " Alice 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'

So total amount she saved was 60 and total amount she didnt save was 20

So now question is "what fraction of her take-home pay did she save each month?"

so i divide 60 by 12 (number of months ) 60/12 = 5

hence $$\frac{1}{5}$$ she saved each month. YAY

is my correct approach ?

thanks and have a good week

in case Bunuel doesn't reply I will tag you friends too generis niks18

Hi dave13 , whether your approach is correct depends on whether
you did some mental math and did not write down the steps.

How did you calculate $$\frac{1}{5}$$?
How did you go from 5 to $$\frac{1}{5}$$?
(You have everything in place. You picked good numbers.
How and whether you manipulated those numbers, I cannot discern.)

Greetings generis

i simply took number 60 because it is easy to work with (it can be divided by 2, 3, 4, 5, 6, 10 and 12) very practical number

so since her total amount saved for the whole year is 60 and we need to know how much she saved monthly i divided 60 by 12 = 5

optionally $$\frac{12}{60}$$= $$\frac{1}{5}$$

have a lovely jovely day
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Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

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16 Sep 2018, 11:12
In this problem we know that every payment across the year is the same, lets call those payments P.
Given this we know that we received at the end of the year 12P (p+p+p+p+p+....) 12 payments

Then we have 12P.

Ok, we also know that we save the same amount of money each month, lets call this S.
Given this we know that we save at the end of the year 12S (s+s+s+s+s+....) 12 "savings"

Then we have 12S.

Also the problem tell us 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"

Before this we know that if she receives P every month, and she saves S, then the portion that she didn't saved was P-S.
So, lets translate this:

The total amount of money that she had saved the end of the year (12S) was (=) 3 times the amount of that portion of her monthly take-home pay that she did NOT save (3*(P-S))

Translation:

---> 12S=3(P-S)
so...
---> 4S = P-S
---> 5S = P

S/P is the fraction of her monthly payment that she saved
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Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

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23 Dec 2018, 01:50
Let the total amount of money saved in a year = 900 (Money saved in a month = 900/12 =75)
and total amount of money spent in a year be = 300
Therefore, total amount of money saved in a year = 1200(Money saved in a month = 1200/12 = 100)

Therefore fraction of money saved in a month = 75/100 = 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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15 May 2019, 09:10
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.

Amount Saved per month= 1/X
Not Saved per month = (1 - 1/X)

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.

12* 1/X = 3*(1-1/X)
12*1/X = 3 * [(X-1)/X] /*X
12=3(X-1)
4=X-1
5=X

Amount Saved per month= 1/X =1/5
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Alice’s take-home pay last year was the same each month, and  [#permalink]

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23 May 2019, 03:32

Quote:
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?

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

May I know how your genius mind came up with figure of 100 (was it because of highlighted text?,
still we choose 100 as base figure in %tage problems not in fractions)

Quote:
12*100*x = 3*100*(1-x)

Should not above expression be:

12*x = 3*(100-x)

Bunuel chetan2u we choose p and s as separate variables in the first post since there is no co-relation
between two as evident from first sentence of the problem. Am I correct in my understanding?
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Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

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28 Jul 2019, 14:46
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

Let Monthly Saving = S
Monthly Spending = U

Need = S/(S + U) = ?

Transform the Word Problem into an equation

12S = 3U => S = U/4

S/(S + U) = U/4/(U/4 + U) = 1/5 => D
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Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

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04 Aug 2019, 00:41
Hello guys , could anyone verify if my approach is correct or I got extremely lucky?

Let's say k is the take-home pay and x/k the fraction she saves each month.

12*(k/x)=3 [ (k-x)/k ]
after calculations of the above we get 5x=k then x/5x=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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18 Oct 2019, 23:56
I would say this question is best solved with trial and error and by assuming a few numbers since the question does not give us any explicit values.

Let's assume her take home salary to be $100 Case 1: She saves$10
IS $10 x 12 months = 3($90) Note $90 is the amount that she did not save i.e Is 120 = 270? NO Case 2: She saves$20
IS $20 x 12 months = 3($80)?
i.e IS 240 = 240? YES

Therefore she saved 20% of her take-home money...option D
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Re: Alice’s take-home pay last year was the same each month, and  [#permalink]

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19 Oct 2019, 03:45
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

Let the amount saved each month = $1. Total saved for the entire year = 12*1 =$12.
Since the total saved for the entire year -- $12 -- is 3 times the amount not saved each month, the amount not saved each month $$= \frac{12}{3} = 4$$. Thus, the total monthly pay = (amount saved each month) + (amount not saved each month) = 1+4 =$5.

What fraction of her take-home pay did she save each month?
$$\frac{amount-saved-each-month}{total-monthly-pay} = \frac{1}{5}$$

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

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12 Nov 2019, 04:54
Take Home Pay = Saved (s) + Not Saved (ns)

T = S+NS

12S = 3NS; 4S = NS

Therefore, T = S+4S

hence T = 5S; S = T/5 or 1/5
Alice’s take-home pay last year was the same each month, and   [#permalink] 12 Nov 2019, 04:54

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