Word Translation

Question

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.
B.
C.
D.
E.

Te phrase " for each dollar that he saves this year, he will have 1 + r dollars available to spend" is confusing. It is not letting me to phrase an equation. Can I have suggestions

Brent@GMATPrepNow · Answer

rintoo22 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?

Let us assume that this year Henry spends $x and he saves $y.
So, total income of Henry in this year = $(x + y)
Then, next year Henry will spend $y(1 + r)

So, y(1 + r) = x/2
--> x = 2y(1 + r)

Required fraction = y/(x + y) = y/[2y(1 + r) + y] = y/(3y + 2yr) = 1/(3 + 2r)

The correct answer is E.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §

Brent@GMATPrepNow · Answer

rintoo22 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?

Let us assume that this year Henry spends $x and he saves $y.
So, total income of Henry in this year = $(x + y)
Then, next year Henry will spend $y(1 + r)

So, y(1 + r) = x/2
--> x = 2y(1 + r)

Required fraction = y/(x + y) = y/[2y(1 + r) + y] = y/(3y + 2yr) = 1/(3 + 2r)

The correct answer is E.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §

Brent@GMATPrepNow · Answer

Last edited by Brent@GMATPrepNow on Wed Feb 18, 2015 8:36 am, edited 1 time in total.

Brent Hanneson - Creator of GMATPrepNow.com

Anju@Gurome · Answer

rintoo22 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?

Let us assume that this year Henry spends $x and he saves $y.
So, total income of Henry in this year = $(x + y)
Then, next year Henry will spend $y(1 + r)

So, y(1 + r) = x/2
--> x = 2y(1 + r)

Required fraction = y/(x + y) = y/[2y(1 + r) + y] = y/(3y + 2yr) = 1/(3 + 2r)

The correct answer is E.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §

GMATGuruNY · Answer

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?

A. 1/(r+2)
B. 1/(2r+2)
C. 1/(3r+2)
D. 1/(r+3)
E. 1/(2r+3)

Let r=2.
Now let's plug in values that follow the words in the problem, step by step.

For each dollar that Henry saves this year, he will have 1+r = 1+2 = 3 dollars available to spend [next year]:
If he saves $1 this year, he can spend $3 next year.

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

What fraction of his income should Henry save this year?
Since he saves $1 and spends $6, saved/total = 1/(1+6) = 1/7. This is our target.

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

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

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Word Translation

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER