Question

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

Answer 1

Answer:

Option E: 35, 40, 45

Step-by-step explanation:

To solve this problem we can test the options, checking if the calculations will match the result.

A.

20, 35 and 70 remained constant.

The average price of a stoc in the portfolio before the changings were:

(20+35+40+45+70)/5 = 42

With an increase of approximately 2%, the average value will be approximately 42*1.02 = 42.84

If the average price of a stock in the portfolio rose, and the rise of one stock in percentage was bigger than the fall of the other stock, we need to choose the stock that has the bigger price as the one that increased its value.

An increase of 15% is calculated multiplying the base value by 1.15, and a decrease of 35% is calculated multiplying the base value by (1-0.35)=0.65.

So, if the stocks affected were the $40 and 45$, we have that:

(20+35+40*0.65+45*1.15+70)/5 = 40.55

That's not the correct answer.

B.

20, 45 and 70 remained constant.

Affected: 35 and 40

(20+35*0.65+40+45*1.15+70)/5 = 40.9

That's not the correct answer.

C.

20, 35 and 40 remained constant.

Affected: 45 and 70

(20+35+40+45*0.65+70*1.15)/5 = 40.95

That's not the correct answer.

D.

35, 40 and 70 remained constant.

Affected: 20 and 45

(20*0.65+35+40+45*1.15+70)/5 = 41.95

That's not the correct answer.

E.

35, 40 and 45 remained constant.

Affected: 20 and 70

(20*0.65+35+40+45+70*1.15)/5 = 42.7

That's the correct answer, with an increase in the average value of 0.7/42 = 0.0167 = 1.67%