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

 It is currently 19 Oct 2019, 10:39

### 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

# Amy’s retirement portfolio contains only stocks and bonds. At the begi

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58445
Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

22 Nov 2016, 05:52
00:00

Difficulty:

15% (low)

Question Stats:

81% (02:03) correct 19% (02:19) wrong based on 154 sessions

### HideShow timer Statistics

Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%

_________________
Senior Manager
Joined: 06 Jun 2016
Posts: 254
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

22 Nov 2016, 06:43
1
1
Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%

B

Let the total value of her portfolio be $100,000 then the value of her stocks will be$60,000 and the value of her bonds will be $40,000 Her total portfolio value increased by 8% to$108,000
her stock holding value increased by 10% to $66,000 so her bond increased to$108,000-$66,000=$42000
required = $42,000-$40,000/$40,000 = 1/20 = 5% Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4773 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi [#permalink] ### Show Tags 22 Nov 2016, 08:14 Bunuel wrote: Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase? A. 4% B. 5% C. 6% D. 7% E. 7.5% As usual a tabular approach works best for me - Attachment: Capture.PNG [ 5.25 KiB | Viewed 1838 times ] Thus total value of Bond at the end of 2016 is 420 ( ie, 1080 - 660 ) So, Per unit value of Bond at the end of 2016 is $$\frac{420}{40} = 10.50$$ Hence, percentage increase is $$\frac{0.50}{10}*100 =5$$%, answer will be (B) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Senior SC Moderator Joined: 14 Nov 2016 Posts: 1348 Location: Malaysia Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi [#permalink] ### Show Tags 22 Feb 2017, 22:08 Bunuel wrote: Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase? A. 4% B. 5% C. 6% D. 7% E. 7.5% Official solution from Veritas Prep. If you recognize that this is a weighted average problem, you can employ the weighted average Mapping Strategy to solve. You know that the weighted average of growth is 8% and that the growth from stocks is 10%, so you can draw your map accordingly: x------------8%------10% You also know that the ratio of stocks to bonds is 3:2, meaning that the distances from x% to 8% and from 8% to 10% will follow a ratio of 3:2, with the more heavily-weighted stocks (10%) having the shorter distance. So since there are two places from 8 to 10 that means that x will be three places from 8, meaning that the answer is 5%, answer choice B. Alternatively, you can solve algebraically or by picking numbers. Since you're working with percent changes, if you want to pick numbers a good place to start is to pick a number like$1,000 for her total value. That would mean that she started with $600 in stocks, from which a 10% increase would mean that stocks gained her$60. Since her total value increased from $1000 to$1080, that means that bonds needed to account for the other 20% gain. Given a starting value of $400 in bonds, you can then ask what percent of$400 is \$20, and the answer is 5%.
_________________
"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."

Intern
Joined: 25 Aug 2007
Posts: 43
Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

16 Sep 2017, 11:35
Stupid question. Trying to solve this with weighted average formula, but for some reason it doesn't work. (x is bond return)
$$\frac{0.6*10+0.4*x}{10+x}$$= 8

6+0.4x=80+8x

-7.6x= 74
Senior SC Moderator
Joined: 22 May 2016
Posts: 3558
Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

16 Sep 2017, 12:45
1
Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%

inter , I ran into exactly the same problem.

I don't use the scale method or alligation.

I stayed with weighted average, but I used different numbers and got the answer.

I kept everything in decimals because x is a percent; x is really $$\frac{x}{100}$$.

This weighted average works, where x = percent return on bonds:

(.6)(.1) + (.4)(x) = .08

.06 + .4x = .08
.4x = .02

x = $$\frac{.02}{.4}$$

x = .05 = 5 percent

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Intern
Joined: 25 Aug 2007
Posts: 43
Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

16 Sep 2017, 13:09
Thanks - just realized everything is already in percents.
Senior SC Moderator
Joined: 22 May 2016
Posts: 3558
Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

16 Sep 2017, 13:51
inter wrote:
Thanks - just realized everything is already in percents.

inter - this question is really basic, but now I'm a little scrambled : when you say "everything is already in percents," what, in weighted average terms, do you mean?

I usually work with rounder numbers (I change decimal percentages to integers). I went wrong by multiplying the weights, instead of the percentages, by 100 to get rounder numbers.

I also know that I could multiply the percentages by 100 and it works (result is .4x = 2, x = 5, and I've included the "percent" already by multiplying all the percents by 100).

For the future: if "everything is already in percents," do you find that it is easier to just leave them that way? Or did you intend something else?
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

14 Dec 2017, 08:21
Bunuel wrote:
Amy’s retirement portfolio contains only stocks and bonds. At the beginning of 2016, her portfolio had an allocation of 60% stocks and 40% bonds. Over the course of 2016, the total value of her portfolio increased by 8%, with the value of her stock holdings increasing by 10%. By what percent did the value of her bond holdings increase?

A. 4%
B. 5%
C. 6%
D. 7%
E. 7.5%

We can let p = the value of Amy’s portfolio at the beginning of 2016.

We are given that she initially had 60% stocks or 0.6p and 40% bonds or 0.4p. Since the total value of her stock holdings increased by 10% and the total value of her portfolio increased by 8%, we can create the following equation in which n is the percentage increase of the bond holdings.

1.1(0.6p) + (1 + n/100)(0.4p) = 1.08p

0.66p + [(100 + n)/100)](0.4p) = 1.08p

0.66p + [(40p + 0.4pn)/100] = 1.08p

Multiplying the entire equation by 100, we have:

66p + 40p + 0.4pn = 108p

106p + 0.4pn = 108p

0.4pn = 2p

0.4n = 2

n = 2/0.4 = 5

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

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.

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi  [#permalink]

### Show Tags

12 Jan 2018, 14:10
Hi All,

This question can be solved in a number of different ways, including algebraically and by TESTing VALUES. It's ultimately a Weighted Average question though, so here's how you can approach it with that formula:

Since we have 60% stocks and 40% bonds, the ratio is 6/4 = 3/2... meaning that for every 3 stocks we have 2 bonds. We know that the value of the stocks increased by 10% and the TOTAL value of the portfolio increased by 8%. We're asked to find the increase in the value of the bonds....

X = increase in value of the bonds

[3(10) + 2(X)] / (5) = 8
30 + 2X = 40
2X = 10
X = 5

Thus, the value of the bonds increased by 5%

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: Amy’s retirement portfolio contains only stocks and bonds. At the begi   [#permalink] 12 Jan 2018, 14:10
Display posts from previous: Sort by