tough word problem

[hpgmat]

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 ?

1/2
1/3
1/4
1/5
1/6

my approach :

X : monthly take home pay
12X : yearly take home pay
Y: portion of x saved

12XY( the total amount of money that she had saved at the end of the year)= 36X(1-Y)

dont know what to do

[Testluv]

Let S be money saved per month. Let U be money used (ie, spent) each month. Let P be her monthly pay. So, one equation is just S + U = P. The question is asking us to solve for the fraction S/P.

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"

"total amount of money saved at the end of the year" = 12S (12 months in the year, of course)

"was" means "="

"3 times the amount of that portion of her monthly take home pay that she did not save"

What is "that portion of her monthly take home pay that she did not save"? The portion of her monthly take home pay that she did not save is, of course, the same thing as that portion of her monthly take home pay that she spent or used up--"U".

So, 12S was 3 * U

12S = 3U

4S = U

And we also have S + U = P

Subbing in 4S for U:

S + 4S = P

5S = P

S/P = 1/5

Choose D.

You could have also fairly easily backsolved this one. When backsolving, the best (ie, score-maximizing) default strategy is to start with either choice B or choice D. On the GMAT, the answer choices are almost always ascending, arranged from smallest to largest. When the answer choices are in ascending order (small to large), then If B is too large, the answer is A, if B is too small check D. If D is too small, the answer is E, and if D is too large, check B. In this particular question, the answer choices are descending (one tip-off that this is probably not an official GMAC question!), so we would reverse this.

[AVRMBA]

Hi,

This problem can be solved in the following way:

Let the take home pay per month be x.
So by this yearly take home pay will be 12x.
Let us assume that saves nth fraction of her take home pay per month.So saving per month is x/n
As per this statement we can understand 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 "

12*(x/n) = 3*(x-x/n)

By solving this we can obtain value of n as 5.

Fraction of money she saved every month is x/n.

So we can conclude that: x/n = x*(1/5)[By substituting value of n]

Finally 1/5 will be the right choice.

Rgds,
AVR.

[hpgmat]

Thank you guys.

Interesting approach AVRMBA

[Testluv]

Hi,

This problem can be solved in the following way:

Let the take home pay per month be x.
So by this yearly take home pay will be 12x.
Let us assume that saves nth fraction of her take home pay per month.So saving per month is x/n
As per this statement we can understand 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 "

12*(x/n) = 3*(x-x/n)

By solving this we can obtain value of n as 5.

Fraction of money she saved every month is x/n.

So we can conclude that: x/n = x*(1/5)[By substituting value of n]

Finally 1/5 will be the right choice.

Rgds,
AVR.

If we let take home pay be x and money saved per month be n, then the fraction saved is n/x, and not x/n.

[AVRMBA]

Hi,
As per my solution i had not taken n as the "money saved per month be n". Here i had taken nth fraction as we dont know what fraction of take home she saves every month. So, nth fraction is taken i.e 1/n*(x) = x/n.For instance 1/4 th of x can be written as 1/4*(x) = x/4.


Rgds,
AVR.

[Testluv]

Hi,
As per my solution i had not taken n as the "money saved per month be n". Here i had taken nth fraction as we dont know what fraction of take home she saves every month. So, nth fraction is taken i.e 1/n*(x) = x/n.For instance 1/4 th of x can be written as 1/4*(x) = x/4.


Rgds,
AVR.

I see.

[gmatfailed]

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 ?

1/2
1/3
1/4
1/5
1/6

Let "t" be her take home pay every month.
Let "s" be her saving ever month.

At the end of the year she saves 12s
12s=3(t-s) Here (t-s) is the money she spends..imagine her earning 5 dollars...and saving 1 dollar...so 5-1 or t-s is what she'd spend...
4s=t-s
5s=t
s/t=1/5

[analyst218]

well
x=monthly pay
y=monthly savings
x-y= amount she did not save monthly
12y=3(x-y)
15y=3x
y/x = 1/5
simple as that.