GMAT Prep Problem 1

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RachelAL: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Wed Mar 07, 2007 5:57 am

by RachelAL » Tue Mar 27, 2007 6:05 am

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Some of these problems are driving me nuts. I am missing something for sure. Any help would be much appreciated. Thanks!

Alices take home pay 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 saved at the end of the year was 3 times the amount of that portion of her monthly take home pay she did not save. If all the money she saved last year was from take home pay, what fraction of her take home pay did she save each month?

Answer: 1/5

-Rachel

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Source: Beat The GMAT — Problem Solving | Tue Mar 27, 2007 6:05 am

gmatme: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Tue Mar 06, 2007 8:57 am

by gmatme » Tue Mar 27, 2007 7:44 am

Let x be the pay for each month
x/y is the fraction saved for each month
so for 12 months it is 12 * (x/y). This is equal to 3 times not saved which is 3(1-x/y)

12 * (x/y) = 3 (1 - x/y)
so,

x/y = 1/5

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RachelAL: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Wed Mar 07, 2007 5:57 am

by RachelAL » Tue Mar 27, 2007 8:41 am

Thanks, it was not clear to me that is was 12(x/y) = 3(1-x/y) rather than 12(x/y) = 12*3(1-x/y).

-Rachel

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Tue Mar 27, 2007 10:36 am

Alices take home pay 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 saved at the end of the year was 3 times the amount of that portion of her monthly take home pay she did not save. If all the money she saved last year was from take home pay, what fraction of her take home pay did she save each month?

Lets say she saves x every month

Thus total savings by end of the year = 12x

Lets say that she spent y every monnth

x + y is her salary

12x = 3y

x / x + y

y = 4x

x/x + 4x

= 1/5

thus she saved 1/5th every month

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Aug 26, 2018 6:45 pm

RachelAL wrote:Some of these problems are driving me nuts. I am missing something for sure. Any help would be much appreciated. Thanks!

Alices take home pay 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 saved at the end of the year was 3 times the amount of that portion of her monthly take home pay she did not save. If all the money she saved last year was from take home pay, what fraction of her take home pay did she save each month?

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 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 for N in the expression S/(S + N).

S/(S + 4S) = S/5S = 1/5

Answer: 1/5

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 27, 2018 9:08 am

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 money that she saved last year was from her take-home pay, what fraction of her take-home pay did she saved 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 doesn't 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
= D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Aug 27, 2018 1:01 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 saved at the end of the year was 3 times the amount of her take-home pay that she didn't save. If all money she saved lasr year was from her take-home pay, what fraction of her 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 total not saved each month, the total not saved each month = 12/3 = $4.
Thus, the total monthly pay = (total saved each month) + (total not saved each month) = 1+4 = $5.
Resulting fraction:
(total monthly savings)/(total monthly pay) = 1/5.

The correct answer is D.

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