A certain portfolio consisted of 5 stocks, priced at $20, $3

BTGmoderatorDC 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

OA E

Source: Veritas Prep

The price of five stocks before change = $(20 + 35 + 40 + 45 + 70) = $210;
The change in the price of five stocks = ~$210*2% = ~$4.2

So, we have to find the two options such that when the price of one of them increases by 15% and the price of the other decreases by 35%, the net result should be $4.2.

Since the numeric value of 15% (increase) is less than the numeric value of 35% (decrease), and the net result is apppx $4.2, which is positive, the 15% change must be greater than the 35% change.

Let's consider that the 15% change occurred with $70 stock (highest among 5 stocks) and the 35% change occurred with $20 stock (lowest among 5 stocks).

Thus, the net result = 15% of 70 – 35% of 20 = 10.5 – 7 = $3.50

Note that $3.50 is the maximum possible net change, which is less than $4.2. If we take other combinations of two stocks, the net change would be less than $3.50, so the change in $20 and in $70 is the best scenario. Or, the prices of the shares that remained constant would be 35, 40, and 45.

The correct answer: E

Hope this helps!

-Jay
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