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Re: This year Henry will save a certain amount of his income [#permalink]

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07 Feb 2016, 09:34

Experts:

In this type of problems (long word problems with variables in the choices) I face 2 challenges: 1) Speed: It usually takes me more than 60 secs just to read and understand what is going in it. Is the reading speed lower than the normal for a guy who aims Q50/51 or maybe for anyone? Do i need more practice so that I can improve the speed? 2) choosing between algebra and vic(using numbers) method: how much time should one spend to decide which way one should go- algebra or vic? What indicators should we look for each approach i.e. algerbra or vic? I usually know that I have taken an inefficient approach only when I am well past half way around 3mins.

Re: This year Henry will save a certain amount of his income [#permalink]

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26 Jul 2017, 13:19

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?

Let the total income of Henry be H and let the amount he saves be s. ⇒ Amount he spends = H − s

Given that for each dollar that he saves this year, he will have 1 + r dollars available to spend. ⇒ Amount Henry will have next year = s(1 + r)

The amount Henry has available to spend next year should be half the amount that he spends this year. ⇒ s(1 + r) = ½ × (H − s) ⇒ 2s(1 + r) = H − s ⇒ H = 2s(1 + r) + s ⇒ H = s(3 + 2r)

We have to find the fraction of his income should Henry save this year, i.e. we have to find s/H. From above equation: s/H = 1/(3 + 2r)

Re: This year Henry will save a certain amount of his income [#permalink]

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01 Sep 2017, 06:41

udaymathapati 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. \(\frac{1}{(r+2)}\)

B. \(\frac{1}{2r+2}\)

C. \(\frac{1}{3r+2}\)

D. \(\frac{1}{r+3}\)

E. \(\frac{1}{2r+3}\)

income - save = spent

save*(1 + r) = (1/2)*spent

save*(1 + r) = (1/2)*(income - save)

save*(1 + r) + (1/2)*save = (1/2)*income

save (1 + r + 1/2) = 1/2*income

save*(3/2 + r) = 1/2*income

save*(3 + 2r) = income

save / income = 1/(2r + 3)
_________________

"Be challenged at EVERY MOMENT."

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"Each stage of the journey is crucial to attaining new heights of knowledge."

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. \(\frac{1}{(r+2)}\)

B. \(\frac{1}{2r+2}\)

C. \(\frac{1}{3r+2}\)

D. \(\frac{1}{r+3}\)

E. \(\frac{1}{2r+3}\)

We can let s = the amount of money, in dollars, Henry saves this year and t = his income, in dollars, this year; thus, the amount that he spends this year is (t - s). Since for each dollar that he saves this year he has 1 + r dollars available to spend next year, he has s(1 + r) dollars to spend next year. Furthermore, since this amount is half what he spends this year, we have:

s(1 + r) = (1/2)(t - s)

2s(1 + r) = t - s

2s + 2sr = t - s

2sr + 3s = t

s(2r + 3) = t

s = t/(2r + 3)

s = [1/(2r + 3)] * t

So, the amount he saves this year is 1/(2r + 3) of his income.

Answer: E
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: This year Henry will save a certain amount of his income [#permalink]

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19 Oct 2017, 10:32

Bunuel wrote:

udaymathapati 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. \(\frac{1}{(r+2)}\) B. \(\frac{1}{2r+2}\) C. \(\frac{1}{3r+2}\) D. \(\frac{1}{r+3}\) E. \(\frac{1}{2r+3}\)

Let \(x\) be the fraction of saving, and \(I\) be the income income.

Set the equation: \(x*I*(1+r)=\frac{(1-x)*I}{2}\), \(I\) cancels out.

Here LHS is "the amount he has available to spend next year", which according to the stem equals to RHS: "half the amount that he spends this year".

\(x=\frac{1}{3+2r}\)

Answer: E.

Hi Bunuel

I didnt understand the equation that u have formed..

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. \(\frac{1}{(r+2)}\) B. \(\frac{1}{2r+2}\) C. \(\frac{1}{3r+2}\) D. \(\frac{1}{r+3}\) E. \(\frac{1}{2r+3}\)

Let \(x\) be the fraction of saving, and \(I\) be the income income.

Set the equation: \(x*I*(1+r)=\frac{(1-x)*I}{2}\), \(I\) cancels out.

Here LHS is "the amount he has available to spend next year", which according to the stem equals to RHS: "half the amount that he spends this year".

\(x=\frac{1}{3+2r}\)

Answer: E.

Hi Bunuel

I didnt understand the equation that u have formed..