arjtryarjtry 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 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
If the average price of the stocks rose by approximately 2%, then a stock with a higher price (for example, $45 or $70) must have increased by 15%, while a stock with a lower price (for example, $20 or $35) must have decreased by 35%. So let’s guess that the stock with the highest price has increased by 15%, and the stock with the lowest price has decreased by 35%. We need to verify that this is indeed the case.
Old average price = (20 + 35 + 40 + 45 + 70)/5 = 210/5 = $42
New average price = (20 x 0.65 + 35 + 40 + 45 + 70 x 1.15) = 213.5/5 = $42.7
Now let’s calculate the percent change:
(42.7 - 42)/42 x 100 = 0.7/42 x 100 = 1.67% ≈ 2%
Therefore, we do see that the stock with the highest price has increased by 15%, and the stock with the lowest price has decreased by 35%. That is, the three stocks whose prices remain constant are $35, $40, and $45.
Answer: E
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