snaps 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
Sum of price of all stocks : $ 210
Avg price : $ 42
The average price of the stock goes up by 2% of Avg stock price which is $ 0.84-------> This indicates the total increase in the sum is 0.84*5 = $ + 4.20
from the Q we can say that since the avg stock price has gone up therefore 0.15A - 0.35B >0. A has to be greater than B and thus we have
or 0.15A- 0.35B ~ 4.2$
Now 35% of 20 = 7 and 15% of 70 = 10.5 Diff : 3.5
0.15*35 = ~ 5.25 and 15 % of 70 =10.5 Diff: ~ 5
0.15*35= 5.25. and 15% of 45 = 6.75, Diff~ 1.5
For any other combination
ex B = 35 and 0.35 B = 12.25 and A =0.15*70 = 10.5 and the difference between A and B is negative and as B increase the the difference of A and B will become more negative.
Hence Ans option E. The values which are constant
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