Question

A certain stock begins the week trading at $87\frac{1}{2}$ per share. If the average gain for the next four days is $\frac{1}{2}$, by how much should the price of the stock increase during Friday so that the total grain for the stock during the entire five days is $5$ percent?

• A. $1\frac{9}{4}$
• B. $1\frac{7}{8}$
• C. $2\frac{1}{8}$
• D. $2\frac{1}{4}$
• E. $2\frac{3}{8}$

Answer 1

The correct option is E $2\frac{3}{8}$

Since we require the total gain in the stock price in five days to be $5\%$, the price of the stock on Friday would be $87.5\times 1.05=91.875$

On the first four days of the week, the price increases by 0.5, thus increasing in all by 2.

Therefore the price should increase by $91.875-2-87.5=2.375=2\frac{3}{8}$ on friday.