Alices take-home pay last year was the same each month, and she saved

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

Cheers,
Brent

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

Bunuel: A heart as pure as gold and a mind as sharp as a knife.

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.

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

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)

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

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.

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:

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

Hi Rich,

Can this be solved using smart numbers? For example, by using $120 for take-home pay to represent 12 months?

Hi OCDianaOC,

Yes, you could solve this question by TESTing VALUES. To use that approach efficiently though, you wouldn't start with Alice's take-home pay each month - you'd actually have to start with the information in the second sentence:

"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."

By TESTing VALUES that fit this information, you can then 'work backwards' and determine her take-home pay each month (and then answer the question).

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

Thanks Rich, but I'm not getting the correct answer by testing values.

I chose that she saved $10/month and had $120 by the end of the year. She did NOT save $40 (since $120 is 3 times bigger than $40).

Total take-home pay is $1,200/year.

My answer: I got 10/100 then reduced to 1/10. Wrong answer!

Help!

Hi OCDianaOC,

The numbers you've chosen to TEST are perfect, but you made a small math mistake:

IF... $10 was saved each month and $40 was NOT saved each month, then the total for each month is $50 (not $100). Thus, the take-home pay for the year would be (12)($50) = $600.

Total saved for the year = (12)($10) = $120
Total take-home pay for the year = $600
$120/$600 = 1/5

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

Can we use your technique of picking numbers here?

Hi GloryBoy92,

Yes - you can TEST VALUES here; since the variables in this question are related to one another though, you have to pay careful attention to what the prompt tells us (and make sure that the values you test match what we are told). We actually have to start off with the information in the 2nd sentence:

"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." Let's start with a nice, round number for the money that she did NOT save....

Money NOT saved each MONTH: $100

We're told that the total money saved for the YEAR was 3 times that amount....

TOTAL money saved for the YEAR: (3)($100) = $300

Since that total was for 12 months, we divide $300 by 12 to find the amount of money that she SAVED each MONTH...

$300/12 = $25

At this point, we know everything we need to now about her monthly pay:
-She saved $25 a month
-She did NOT save $100 a month (meaning she spent this money each month)

Total for the month = $25 + $100 = $125

Fraction of pay each month that is SAVED = $25/$125 = 1/5

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