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by akash singhal » Wed Nov 04, 2015 8:35 am
A certain portfolio consisted of 5 stocks, priced at $20, $35, $40, $45, and $70, respectively. On a given
day, the price of one stock increased by 15%, while the price of another stock decreased by 35% and the
prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by
approximately 2%, which of the following could be the prices of the shares that remained constant?


(A) $20, $35, and $70 (B) $20, $45, and $70 (C) $20, $35, and $40
(D) $35, $40, and $70 (E) $35, $40, and $45

OE E

I have no idea how to approach this question.
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by GMATGuruNY » Wed Nov 04, 2015 9:09 am
A certain portfolio consisted of 5 stocks, priced at $20, $35, $40, $45 and $70, respectively. On a given day, the price of one stock increased by 15%, while the price of another decreased by 35% and the prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by approximately 2%, which of the following could be the prices of the shares that remained constant?

A. 20, 35, 70
B. 20, 45, 70
C. 20, 35, 40
D. 35, 40, 70
E. 35, 40, 45

OA E
Use reason.
The increase in one price (15%) is LESS THAN HALF the decrease in another price (35%), yet the NET increase is 2%.
Thus, the price that increases must be MUCH HIGHER than the price that decreases.
Only $70 and $20 are sufficiently far apart, implying that the other 3 prices (35,40,45) do not change.

The correct answer is E.
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by GMATinsight » Sat Nov 07, 2015 3:24 am
akash singhal wrote:A certain portfolio consisted of 5 stocks, priced at $20, $35, $40, $45, and $70, respectively. On a given
day, the price of one stock increased by 15%, while the price of another stock decreased by 35% and the
prices of the remaining three remained constant. If the average price of a stock in the portfolio rose by
approximately 2%, which of the following could be the prices of the shares that remained constant?


(A) $20, $35, and $70 (B) $20, $45, and $70 (C) $20, $35, and $40
(D) $35, $40, and $70 (E) $35, $40, and $45

OE E

I have no idea how to approach this question.
Make the smallest decrease and the highest increase, and you have:

- for the smallest: 35% of $20 = $7 decrease
- for the highest: 15% of $70 = $10.5 increase

i.e. maximum increase of the portfolio = 10.5-7 = $3.5 total

Total value of the portfolio was $20+$35+$40+$45+$70 = $210

So the Maximum increase corresponds to 3.5/210 = 1.7%

You cannot be closer to 2%, thus it is $20 that decrease and $70 that increase

Answer: Option E
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