GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2019, 05:22 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # This year Henry will save a certain amount of his income

Author Message
TAGS:

### Hide Tags

Manager  B
Joined: 15 Dec 2015
Posts: 50
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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.

Intern  S
Joined: 07 May 2015
Posts: 43
Location: India
Schools: Darden '21
GPA: 4
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

Income = Save (X) + Spend (Y)

For $1 saved Henry gets$(1+r)
So, next year he will get $(X*(1+r)) by saving$X this year

We are given that Y/2 = X(1+r)
Y = 2X(1+r)

We need to find X/(X+Y)

X / (X + 2X(1+r))
1 / (1+2+2r)
1 / (2r + 3) [option E]
Manager  G
Joined: 15 Dec 2015
Posts: 114
GMAT 1: 680 Q49 V34 GPA: 4
WE: Information Technology (Computer Software)
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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?

1/(r + 2)
1/(2r + 2)
1/(3r + 2)
1/(r + 3)
1/(2r + 3)
Explanation:

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)

Senior SC Moderator V
Joined: 14 Nov 2016
Posts: 1347
Location: Malaysia
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

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

Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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. $$\frac{1}{2r+3}$$

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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  B
Joined: 19 Aug 2016
Posts: 73
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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".

$$x=\frac{1}{3+2r}$$

Hi Bunuel

I didnt understand the equation that u have formed..

How did u get (1-x)* I

Pls help..thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 59675
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

zanaik89 wrote:
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".

$$x=\frac{1}{3+2r}$$

Hi Bunuel

I didnt understand the equation that u have formed..

How did u get (1-x)* I

Pls help..thanks

I tried to explain this here: https://gmatclub.com/forum/this-year-he ... l#p1276031
_________________
Manager  B
Joined: 10 Sep 2014
Posts: 75
GPA: 3.5
WE: Project Management (Manufacturing)
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

Bunuel do you have anymore problem links like this to practice?

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 59675
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

1
Bunuel do you have anymore problem links like this to practice?

Posted from my mobile device

Somewhat similar questions:
https://gmatclub.com/forum/mary-decided ... 19290.html
https://gmatclub.com/forum/a-man-saves- ... 18796.html
https://gmatclub.com/forum/last-year-ca ... 67602.html
_________________
Manager  B
Joined: 17 Jul 2016
Posts: 54
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

Assume he makes 1 dollar this year. That way his income saved will equal the fraction of his income saved.

This year income:1
Saved: S
Spent: 1-S

Next Year:
Spent: (1+R)S

"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?"

1/2(1-S)=(1+R)(S)

.5-.5S=S+SR
.5=1.5S+SR
1=3S+2SR
1=S(3+2R)
S=(1)/(3+2R)
Manager  B
Joined: 03 May 2017
Posts: 85
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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. $$\frac{1}{2r+3}$$

1. Read and understand. We are looking for the fraction $$(\frac{x}{I})$$saved such that the amount available to spend $$(y)$$ this year would be half of the disposed income$$(I)$$ of yesteryear.

2. Note that the amount saved can be deducted from the amount disposed of and we can then find the amount required to be saved (x), i.e $$I-y$$

Now the best approach can be either algebraic or arithmetic, I will go for a combination of both. I will start with arithmetic, i.e plugging in numbers as this can allow for a quick backsolve if running out of time.

Now to choose numbers just a cursory look at the problem would suggest that multiples of 2 and 3 would make for straightforward (I). Why we are looking for three parts in two periods( I know this may be confusing, but it's not necessary to solve the problem), however, it does help to backsolve. Then I will choose 0 or 1 for $$r$$ (easy to manipulate).

Now onto the solution:

Say$$I = 6$$ and$$r=0$$

Then $$x= \frac{y}{2}= \frac{(6-x)}{2}$$

$$2x= 6-x; 3x= 6; x=2$$

Our fraction is $$\frac{2}{6}= \frac{1}{3}$$

Only option $$E$$ fulfills this when r= 0. Hence, $$E$$
Senior Manager  P
Joined: 02 Apr 2014
Posts: 462
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

current: income = x saving = y spending = x-y
next: income = 0, saving = 0, spending = y(1+r) (as every dollar saved, (1+r)\$ will be spent)

now to determine savings/income = y/x , such that y(1+r) = (x-y)/2
=> 2y(1+r) = x - y
=> y + 2y(1+r) = x
=> y(2r+3) = x => y/x = 1/(2r+3) => (E)
Manager  B
Joined: 17 Jul 2016
Posts: 54
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

Suppose he saves 50 dollars and spends 50 dollars the first year.

The next year he needs to spend 25 dollars. 50(1+r)=25

r=-.5

He spent 50 dollars and saved 50 dollars his first year so he saved 1/2 of his income. Only choice E gives 1/2 when]

we substitute r=-.5
Intern  B
Joined: 11 Nov 2013
Posts: 16
Location: Pakistan
Concentration: Finance, Nonprofit
GMAT 1: 480 Q34 V22 GMAT 2: 540 Q33 V31 GMAT 3: 620 Q42 V34 GPA: 3.6
WE: Other (Non-Profit and Government)
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

gmat1011 wrote:
Saving this year = S
Spending this year = E

Next year spend = S (1+r)

Given, S(1+r) = E/2

2 + 2r = E/S

2 + 2r + 1 = E/S + 1
3+2r = E+S/S

S/E+S = 1/(3+2r)

How did you we get to adding 1 in "2 + 2r + 1 = E/S + 1" ?
SVP  D
Joined: 03 Jun 2019
Posts: 1881
Location: India
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

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. $$\frac{1}{2r+3}$$

Given:
1. This year Henry will save a certain amount of his income, and he will spend the rest.
2. 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.

Asked: 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 the fraction of income saved be x

Income spent this year = I(1-x)
Income saved this year = Ix
Income available to spend next year = Ix(1+r) = I(1-x)/2
$$x(1+r) = \frac{(1-x)}{2}$$
$$\frac{x}{1-x} = \frac{1}{2(1+r)}$$
$$x = \frac{1}{1+2(1+r)} = \frac{1}{3+2r}$$

IMO E
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5470
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: This year Henry will save a certain amount of his income  [#permalink]

### Show Tags

good question:
Let total income ; I
Saving = S
Expenditure = I-S

given ; 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
find 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?

we can create an eqn;
(I-S)/2 = S(1+r)
so Income ; I = 3s+2sr
fraction of saving ; s/3s+2sr ; $$\frac{1}{2r+3}$$
IMO E

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. $$\frac{1}{2r+3}$$ Re: This year Henry will save a certain amount of his income   [#permalink] 19 Sep 2019, 12:18

Go to page   Previous    1   2   [ 36 posts ]

Display posts from previous: Sort by

# This year Henry will save a certain amount of his income  