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 Your Progress

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

12 Sep 2010, 07:21

4

This post received KUDOS

45

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

47% (03:28) correct
53% (02:28) wrong based on 618 sessions

HideShow timer Statictics

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?

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

Show Tags

12 Sep 2010, 09:01

9

This post received KUDOS

Expert's post

12

This post was BOOKMARKED

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".

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

Show Tags

12 Sep 2010, 10:40

18

This post received KUDOS

7

This post was BOOKMARKED

My approach:

Table

Total Income

Saving

Spends

X

a

X-a

Given: Amount available next year is 'a' times \((r+1)\) => \(a(r+1)\). Question: 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.

Setting up the equation => \((X-a)/2 = a(r+1)\) \(X - a = 2ar+ 2a\) \(X = 2ar +3a\) Fraction of the income that Henry should save this year is \((a/X)\) which is equal to \(1/(2r+3)\). _________________

Support GMAT Club by putting a GMAT Club badge on your blog

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

Show Tags

27 Dec 2010, 19:46

2

This post received KUDOS

Expert's post

tonebeeze wrote:

I'm having trouble charting this problem out. Can someone help? Thanks.

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?

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

Show Tags

25 Apr 2012, 11:13

4

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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

Responding to a pm:

There is no 'best' way to solve a problem, in my opinion. The best way for you depends on what you are comfortable with. You can follow Bunuel's algebraic approach here (by taking x as the fraction of saving) or you can plug in values for r and check (or do something else... I would like to plug in values for r as shown in my second method)

Say r = 0 Whatever he saves this year, he has only that next year so he must save 1/3 this year (so that he spends 2/3 this year) Only options D and E give 1/3 when r = 0.

Say r = 1 Whatever he saves this year, it becomes double. This double should be half of what he spends this year. So what he spends this year should be 4 times what he saves i.e. he should save 1/5 of his income this year. Out of D and E, only E gives you 1/5

Answer E

OR, preferably, look for a value of r which gives a different answer for each option right in the beginning. I would choose r = 2. Whatever he saves, it becomes 3 times. This 3 times amount must be half of what he spends this year. So what he spends this year must be 6 times of what he saves. Therefore, he saves 1/7 of his income. Only option E gives 1/7 _________________

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

Show Tags

27 Jun 2012, 14:27

Even I went for number picking. I chose slightly different numbers and approach. I am not sure if I chose the correct path but ended up getting the same answer. It took me about 3 minutes to get there finally so I do not think my approach was the optimum one. I am going over Karishma's approach again to see if I can apply it.

Let total income = 100.

This year Henry saved : 50 This year Henry spent : 50

Next Year amount available to spend = 50(1+r) ---> (I)

Per the last statement in the question stem, this amount is half of his amount spent this year. Hence, overall amount that we should get for a value of r is (1/2)

Also we get that, therefore 50(1+r)=25. Solving for r gives r= (-1/2)

Plug in r=(-1/2) in the answer choices to see which option gives answer as (1/2). Only E gives this answer.

----- Going over my response now, I realized that I might not follow my above approach again. _________________

My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blogspot.com

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

Show Tags

26 Sep 2012, 12:42

There is one more way to these kind of question :By using nbr.

Lets say u have saved 10$. The next year it will be lets saey y=10(1+1)=20 [r=1] As question suggest the spending is twice lets say Z=2*20=40 So the total income will be 40+10=50$ and 10/50=1/5=1/(2*1+3)=1/(2*r+3)..

It may looks lenghthy while explaining but the very simple..

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

Show Tags

09 Oct 2013, 00:03

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

\(x\) fraction of saving,\(I\) 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".

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

Answe: E.

How did you make the LHS equation, whats the logic behind it?

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

Show Tags

09 Oct 2013, 02:40

Expert's post

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

\(x\) fraction of saving,\(I\) 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".

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

Answe: E.

How did you make the LHS equation, whats the logic behind it?

We are told that "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". So, if he saves $10, then the amount available to spend next year is 10(1+r).

The amount saved this year = x*I, where x is the fraction of savings (say 1/2) and I is the income. The amount available to spend next year = x*I*(1+r).

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

Show Tags

09 Apr 2014, 14:23

You can pick smart numbers. Let's first set r = .1 (10%) Let's say he spent $110 this year. We want him to have $55 ($110/2) to spend next year. The amount he would have to save this year would be given by x(1 + .1) = $55, solving for x gives us x = $50 Therefore his income last year was $110 + $50 = $160 The fraction of his income he saved was 50/160 = 1 / 3.2 Plug in .1 for each of the answer choices and you get E.

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

Show Tags

10 Apr 2014, 13:16

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

\(x\) fraction of saving,\(I\) 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".

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

Answe: E.

How did you make the LHS equation, whats the logic behind it?

Hi - probably look at the question like this that every dollar you save, your bank gives you a return of r on every dollar, so your wealth increases by a factor of (1+r)

if you are saving x part of your income I, the money will increase to xI *(1+r)

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

Show Tags

24 Aug 2014, 10:58

Bunuel wrote:

We are told that "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". So, if he saves $10, then the amount available to spend next year is 10(1+r).

The amount saved this year = x*I, where x is the fraction of savings (say 1/2) and I is the income. The amount available to spend next year = x*I*(1+r).

Hope it's clear.

Hi Bunuel,

The statement "for each dollar that he saves this year, he will have 1 + r dollars available to spend." -- how does this imply that it's (savings)*(1+r) vs. just "1+ savings".

I tried to plug in numbers, or even algebra for that matter and I took 1+r to be a definite. For example:

Income = 100 Savings = 10 Spent = 90

Therefore, to get 45 next year, I did 1+r=45, therefore r=44. That was obviously wrong based on your explanation above but I fail to see why we multiply savings by (1+r)?

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

Show Tags

07 Sep 2014, 00:39

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

T.I = Sp+Sa..

but for each dollar that he saves this year, he will have 1 + r dollars available to spend --> so Sa(1+r).

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-->

(T.I-Sa)/2 = Sa(1+r) => T.I - Sa = 2Sa(1+r)

T.I = 2Sa(1+r)+Sa ==> Sa(2(1+r) +1)

T.I=Sa(2r+3)

since asked for fraction, Sa/T.I = 1/ (2r+3)..

first i have tried with number plug in with 150 - T.I & saving as 50 but got an wrong answer D later with the help of Bunuel's post got an idea on this.

could someone please share similar problems for practice?

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

Show Tags

06 Oct 2014, 22:53

Let the total income be \(x\) and the saved income be \(y\). That means the income spent=\(x-y\). The question asks us to find out \(y/x\) such that \(y(1+r)=(x-y)/2\). Solving this equation we can get \(y/x=1/(3+2r)\). Answer E.

PS OG 12 - Q163: This year henry will save a certain amount [#permalink]

Show Tags

28 Oct 2014, 04:43

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?

I need help understanding the math rules. Using the following to represent the amount he saved this year, say FI, why should next year's amount that he spends be represented as FI(1+r)? The OA and Quantum GMAT indicated.

I originally just jotted down 1+r.

I sort of understand why doing the problem a couple of times, and struggling, but can someone explain this to me please? Doing the problem so many times is resulting in memorization, I really want to understand why it should be done this way.

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

Show Tags

28 Oct 2014, 04:50

Expert's post

joaomario 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 has available to spend will be equal to half the amount that he spends this year?

I need help understanding the math rules. Using the following to represent the amount he saved this year, say FI, why should next year's amount that he spends be represented as FI(1+r)? The OA and Quantum GMAT indicated.

I originally just jotted down 1+r.

I sort of understand why doing the problem a couple of times, and struggling, but can someone explain this to me please? Doing the problem so many times is resulting in memorization, I really want to understand why it should be done this way.

Thank you all!

Merging similar topics. Please refer to the discussion above and ask if anything remains unclear.

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...