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Word Translation

by rintoo22 » Thu Mar 21, 2013 8:28 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.
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
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by Brent@GMATPrepNow » Thu Mar 21, 2013 8:42 am
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?

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
Here's an algebraic solution:
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Cheers,
Brent
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by Brent@GMATPrepNow » Thu Mar 21, 2013 8:43 am
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?

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
Here's a "non-algebraic" (plug in) solution:
Image

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Mar 21, 2013 8:46 am
By the way, this question is known as a "Variables in the Answer Choices" question.
The good thing about these questions is that there are typically 2 approaches you can take:
1) Algebraic
2) Plug in numbers

Here are some more questions where both approaches are demonstrated (in case you'd like to practice):
- https://www.beatthegmat.com/rtw-nails-t116215.html
- https://www.beatthegmat.com/cost-of-p-pe ... 92958.html
- https://www.beatthegmat.com/plugging-in- ... 08985.html
- https://www.beatthegmat.com/wire-cut-int ... 64814.html
- https://www.beatthegmat.com/investment-o ... 55128.html
- https://www.beatthegmat.com/algebraic-tr ... 24969.html
- https://www.beatthegmat.com/ps-computing ... 22912.html
- https://www.beatthegmat.com/lunch-t105634.html

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Feb 18, 2015 8:36 am, edited 1 time in total.
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by Anju@Gurome » Thu Mar 21, 2013 9:00 am
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.
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by GMATGuruNY » Thu Mar 21, 2013 10:09 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?

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.
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