Alice's take-home pay last year was the same each month...

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Alice's take-home pay last year was the same each month...

by BTGmoderatorLU » Mon Feb 26, 2018 11:38 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

The OA is D.

I'm really confused by this PS question. Experts, any suggestion? I can't find the way to solve it. Thanks in advance.

Quote

Source: Beat The GMAT — Problem Solving | Mon Feb 26, 2018 11:38 am

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Mon Feb 26, 2018 11:44 am

LUANDATO 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 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

Quote

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

by GMATGuruNY » Mon Feb 26, 2018 1:38 pm

LUANDATO 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 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

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 amount not saved each month, the amount not saved each month = 12/3 = $4.
Thus, the total monthly pay = (amount saved each month) + (amount not saved each month) = 1+4 = $5.
Resulting fraction:
(amount saved each month)/(total monthly pay) = 1/5.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 28, 2018 10:36 am

LUANDATO 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 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

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

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

Answer:D

Scott Woodbury-Stewart
Founder and CEO
[email protected]