Problem Solving

ziyuenlau 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%

Source : Veritas
OA=B

Say Amy had 6 stocks and 4 bonds

Say each stock and each bond values $100

Thus, currently, the value of the stocks = 6*100 = $600 and the value of the bonds = 4*100 = $400 .

Thus, currently, the value of the portfolio = 600 + 400 = $1000.

Value of the portfolio after the increase = 1000 + 8% = $1080.

Value of the stocks after the increase = 600 + 10% = $660.

Thus, Value of the bonds after the increase = 1080 - 660 = 420

The percentage increase in the value of the bonds = [(420-400)/400] * 100% = 5%

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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Hi ziyuenlau,

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%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

ziyuenlau 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

Answer: B