ALICE'S TAKE-HOME PAY

[Guest]

WHAT IS THE BEST APPROACH TO SOLVING THIS PROBLEM:

[editor: i have posted a corrected version of the problem below this line.]

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

oa = d.

[Guest]

Alice's total take home per month = x
Alice's saving per month = y
Alice's saving for the entire yar = 12y
What Alice did not save = x-y
As per the stem , Alice's annual saving = 3 time what she did not save pre month
i.e. 12y = 3(x-y)
4y = x- y
y = x/5.

[RonPurewal]

you can also do this problem by picking numbers, because you don't have a figure for the monthly pay (and, apparently, it doesn't matter, because the problem would be impossible to solve if it did matter).

so just let the monthly pay be '1'.
let the monthly savings be 'S', which is both a fraction and an actual amount of money. (it's both because the monthly pay is '1', so the fraction is the same as the dollar amount)
then she has saved 12S at the end of the year.
each month, she didn't save (1 - S)
so
12S = 3(1 - S)
12S = 3 - 3S
15S = 3
S = 3/15 = 1/5

faster, and probably less confusing, with only one variable

[acmorcos]

The wording in this question is really confusing. The way I though of it, if she saved the same portion of her take home pay each month, then at the end of the year that ratio of save:not saved would be the same as the monthly ratio. In other words, if you assigned variable x as what she saved, the amount she did not save would be x/3 and the proportion she saved would be 3/4 after simplification.

Can someone point out how you would think that the proportions wouldn't be equal throughout? Is it because you're supposed to assume that there are other categories where she spent her money other than "saved" and "not saved?" That doesn't make very much sense if it's the case.

[arturocb86]

Help needed please!

X: payment per month
Total income= 12 X
expenses: Y
savings: (X-Y)

12 (X-Y) = 3Y --> 12X-12Y = 3Y -> X= 5Y/4

They are asking for the savings (X-_Y)--> (X-Y)= (5Y-4Y)/4 = Y/4

What I am doing wrong?

Thank you in advance for your help!

[stephen.p.webb]

The wording in this problem is confusing... i believe you are mis-representing the final part of the equation. It states 3 X (the amount of that portion of her MONTHLY (not annual) take home pay that she did not save. It does not mention anything about expenses, so I would not bring that into the equation.

To simplify.... Alice's take home pay/month= P
Savings/month= S

12S= 3 (P-S)
12S= 3P-3S
15S=3P (divide by 15 to solve for savings)
S= 3/15P or 1/5P equaling 1/5 of her take home pay

[mschwrtz]

The phrase that's causing you trouble is "3 TIMES THE AMOUNT OF THAT PORTION OF HER MONTHLY TAKE-HOME PAY THAT SHE DID NOT SAVE." This means the money that she saved each month, but you take this to mean the money that she saved [i]all year[i] from her monthly savings.

So, when the problem posits that,

Alice's yearly savings = 3(Alice's monthly spending)

you understand it as

Alice's yearly savings =3(Alice's yearly spending).

[aravind.deva]

this is a big TRAP .. Unfortunately i don't like the subtle differences in the wording...
this is neither a CR nor an RC..

the natural tendency of anyone is to account for 12 months the money she dint save . rather than counting the non-savings for 1 month

[mschwrtz]

Fair enough, you're not the only one thrown by the wording. But LOTS of quant questions require close reading.

Once again, in this case the critical phrase is "3 TIMES THE AMOUNT OF THAT PORTION OF HER MONTHLY TAKE-HOME PAY THAT SHE DID NOT SAVE." It has "monthly" right there.

[pushkalk]

Cant this be solved by picking numbers ?

Income = 6$
Expense every month = 4$,
Saving every month = 2$

therefore as per statement. total saving = 4*3 = 12$.

But this would contradict savings from the picked nos->2*12=24.

Please help. How to proceed ?

[RonPurewal]

Cant this be solved by picking numbers ?

Income = 6$
Expense every month = 4$,
Saving every month = 2$

you can't pick all of these numbers at random -- remember that the problem has a correct answer!
i.e., if you try to pick all of these numbers at random, without regard to the answer choices, then the problem will absolutely not work (unless you happen to be so lucky that you actually pick an amount of savings that equals 1/5 of her monthly take-home pay).

you *can* pick numbers, but you have to use the answer choices, too:
* pick a number for her TOTAL take-home pay
* select an answer choice
* using that answer choice, figure out how much she saves per month
* calculate through the rest of the problem and see whether all the numbers work out.

you should find that the numbers work out for the answer choice 1/5, but that they don't work out for any of the other answer choices.

[pushkalk]

Thanks Ron,
This is useful to cross check the answer here, but certainly not as a mode of attack :

Alice's monthly income = 10$.
From the answer choice, monthly saving = 1/5 of 10$ = 2$
Total saving = 8*3 = 24; which is also equal to 2$ saved for 12 months.


Hence the answer.

[RonPurewal]

Thanks Ron,
This is useful to cross check the answer here, but certainly not as a mode of attack :

Alice's monthly income = 10$.
From the answer choice, monthly saving = 1/5 of 10$ = 2$
Total saving = 8*3 = 24; which is also equal to 2$ saved for 12 months.


Hence the answer.

actually, this sort of thing *can* be used as a "mode of attack" (with some slight modifications). i.e., you can plug in the answer choices and work through the problem backward.

for more on working problems backward, see the FEBRUARY 4 lecture recording here:
http://www.manhattangmat.com/thursdays-with-ron.cfm

[krishnan.anju1987]

There is a problem with the last sentence of the question. It states IF ALL THE MONEY SHE SAVED LAST YEAR WAS HER TAKE-HOME PAY, WHAT FRACTION OF HER TAKE-HOME PAY DID SHE SAVE EACH MONTH? .

On the other hand, it should have been

IF ALL THE MONEY SHE SAVED LAST YEAR WAS FROM HER TAKE-HOME PAY, WHAT FRACTION OF HER TAKE-HOME PAY DID SHE SAVE EACH MONTH?

Had me confused for some time.

[RonPurewal]

you are right, the original post was mistranscribed.

it should say:

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?

i have edited the original accordingly (and added the answer choices).