tough word problem

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hpgmat: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Thu Aug 20, 2009 11:55 am; Location: vancouver, B.C; GMAT Score:640

by hpgmat » Tue Dec 08, 2009 10:08 pm

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

Will Win

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Source: Beat The GMAT — Problem Solving | Tue Dec 08, 2009 10:08 pm

Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Tue Dec 08, 2009 10:36 pm

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.

Kaplan Teacher in Toronto

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AVRMBA: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Dec 02, 2009 5:01 am

by AVRMBA » Wed Dec 09, 2009 3:54 am

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.

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hpgmat: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Thu Aug 20, 2009 11:55 am; Location: vancouver, B.C; GMAT Score:640

by hpgmat » Wed Dec 09, 2009 12:27 pm

Thank you guys.

Interesting approach AVRMBA

Will Win

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Wed Dec 09, 2009 4:27 pm

AVRMBA wrote: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.

Kaplan Teacher in Toronto

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AVRMBA: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Dec 02, 2009 5:01 am

by AVRMBA » Thu Dec 10, 2009 2:41 am

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.

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Thu Dec 10, 2009 10:54 am

AVRMBA wrote: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.

Kaplan Teacher in Toronto

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gmatfailed: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Feb 23, 2010 9:48 pm

by gmatfailed » Tue Feb 23, 2010 9:59 pm

hpgmat 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 ?

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

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analyst218: Master | Next Rank: 500 Posts; Posts: 140; Joined: Fri Feb 05, 2010 2:43 pm; Thanked: 3 times; GMAT Score:720

by analyst218 » Thu Feb 25, 2010 11:18 am

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.

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