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Averages Problem

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Averages Problem

by MI3 » Sat Jul 16, 2011 12:51 am
Q. 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, and $70 (B) $20, $45, and $70 (C) $20, $35, and $40 (D) $35, $40, and $70 (E) $35, $40, and $45
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by goalevan » Sun Jul 17, 2011 3:48 am
20 + 35 + 40 + 45 + 70 = 210

If the average price of a stock in the portfolio increases by 2%, the total will also increase by 2%.

210 * 0.02 = 4.2

We need to find the combination of stock prices that increases the total by $4.20 when we increase one stock by 15% and decrease the other by 35%.

The difference between the two prices must be relatively large, since 35% is so much larger than 15%, so 70 and 20 make the most sense to check first.

70 * 0.15 = 10.5
20 * 0.35 = 7

10.5 - 7 = 3.5

The difference is only $3.50, but comes close to the $4.20 increase required. No other combination will increase this difference, so we can go with answer choice E.
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by amit2k9 » Mon Jul 18, 2011 10:32 pm
old average = 210/5 = 42
new average = 42*1.02 = 42.84
thus increase = 42.84-42 = 0.84
increased sum = 0.84*5 = 4.2

now, (A+B+constant)/5 = 42 and (1.15A+ 0.65B+constant)/5 = 42.84

thus, [(1.15A+ 0.65B+ constant)- (A+B+constant)]/5 = 0.84
hence,
0.15 A - 0.35 B = 4.2 (approx)

for A = 70 and B = 20 we have RHS = 3.5.(max difference possible)

hence constant = E = 35,40 and 45.
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