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
We can plug in the answers, which represent the fraction saved each month.
Answer choice C: 1/4 saved each month
Let the total monthly pay = 4.
Amount saved each month = 1/4 * 4 = 1
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*3 = 9.
Since these last two values must be equal, too much money is being saved.
Eliminate A, B and C.
Answer choice D: 1/5 saved each month
Let the total monthly pay = 5.
Amount saved each month = 1/5 * 5 = 1.
Amount saved for the whole year = 12*1 = 12.
3 times the amount not saved each month = 3*4 = 12.
Success!
The correct answer is
D.
Algebraically:
Let the fraction saved each month = x.
Amount saved for the whole year = 12x.
Fraction not saved each month = 1-x.
Since the amount saved for the whole year is equal to 3 times the fraction not saved each month, we get:
12x = 3(1-x)
12x = 3 - 3x
15x = 3
x = 3/15 = 1/5.
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
