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Stock Portfolio

by harsh.champ » Tue Feb 09, 2010 5:00 am
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

The OA is E.
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by shashank.ism » Tue Feb 09, 2010 5:07 am
harsh.champ 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

The OA is E.
Add the 5 prices together:
20 + 35 + 40 + 45 + 70 = 210
2% of that is 210 x .02 = 4.20
Let x be the stock that rises and y be the stock that falls.
.15x -.35y = 4.20 ==> x = (7/3)y + 27
This tells us that the difference between x and y has to be at least 27. Since the answer
choices list the ones that DONT change, we need to look for an answer choice in which
the numbers NOT listed have a difference of at least 27.
Ans E
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by ajith » Tue Feb 09, 2010 6:52 am
harsh.champ 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

The OA is E.
Total value of portfolio = 210
2% of 210 = 4.2

If 70 increased by 15% value of portfolio increases by 10.5 and
20 decreased by 35 % value of portfolio decreases by 7

Net gain = 4.5 approx = 2%
{no other combination gives a +ve gain)
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