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

Redeem

Fractions Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Tue Jun 29, 2010 9:41 am
Thanked: 2 times

Fractions Problem

by taneja.niks » Sat Apr 16, 2011 4:57 am
This year Henry will save a certain amount of his income, and he will spend the rest. Next year
Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars
available to spend. In terms of r, what fraction of his income should Henry save this year so that
next year the amount he was available to spend will be equal to half the amount that he spends this
year?

A.1/r+2
B. 1/2r+2
c.1/3r+2
d. 1/r+3
e.1/2r+3
Top
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 am
Thanked: 72 times
Followed by:6 members

by manpsingh87 » Sat Apr 16, 2011 5:17 am
taneja.niks wrote:This year Henry will save a certain amount of his income, and he will spend the rest. Next year
Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars
available to spend. In terms of r, what fraction of his income should Henry save this year so that
next year the amount he was available to spend will be equal to half the amount that he spends this
year?

A.1/r+2
B. 1/2r+2
c.1/3r+2
d. 1/r+3
e.1/2r+3
let his income be i and the amount that he spends= s,
amount saved= i-s; next year's income=(i-s)(1+r);
as next year's income is equal to the half of the amount that he spends this year, therefore we have
(i-s)*(1+r)=s/2;
i-s+ir-sr=s/2;
i(1+r)=3s/2+sr;
i(1+r)=((3+2r)/2)s;
s={2(1+r)/(3+2r)}i
required fraction=i-s/i= i(1-{2+2r/3+2r})/i=3+2r-2r-2/3+2r=1/3+2r; hence E
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Apr 16, 2011 5:26 am
taneja.niks wrote:This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A. 1/r+2
B. 1/2r+2
c. 1/3r+2
d. 1/r+3
e. 1/2r+3
Let Henry spends $x and he saves $y. This implies total income = $(x + y)
Then, next year Henry spends $y(1 + r) = x/2 implies x = 2y(1 + r)

We have to find y/(x + y) = y/[2y(1 + r) + y] = y/(3y + 2yr) = 1/(3 + 2r)

The correct answer is E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
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 » Sat Apr 16, 2011 5:44 am
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he has available to spend will be equal to half the amount that he spends this year?
Since there is a variable in the answer choices, and the question is asking only for a fraction, we can plug in our own numbers for all of the unknowns in the problem.

Let r=2.

For each dollar that Henry saves this year, he will have 1+r = 1+2 = 3 dollars available to spend next year:
Saves this year = 1, spends next year = 3.

Next year the amount Henry has available to spend will be equal to half the amount that he spends this year:
Spends next year = 3, spends this year = 6.

What fraction of his income should Henry save this year?
Total this year = saves this year + spends this year = 1+6 = 7.
Saves/Total = 1/7. This is our target fraction.

Now we plug r=2 into the answers to see which yields our target of 1/7.

Only E works:
1/(2r+1) = 1/(2*2 + 3) = 1/7.

The correct answer is E.
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
Top
Post new topic Post Reply
• Page 1 of 1