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NUMERICAL CHALLENGE

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NUMERICAL CHALLENGE

by sayanpaul » Tue May 07, 2013 8:39 am
A certain portfolio consisted of 5 stocks priced at $20, $35, $40, $45, $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
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by Jim@StratusPrep » Tue May 07, 2013 9:05 am
Just a warning... Stay clear of non-official questions so you don't pick up bad habits. There are a lot of holes in this question and any of these can be answers based on the weighting of the stocks in the portfolio.
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by Atekihcan » Tue May 07, 2013 9:18 am
Let us assume the price of that has increased by 15% was $x and price of the stock that has decreased by 35% was $y.

As the total price increased by approximately 2%, the increase in price is 2% of (20 + 35 + 40 + 45 + 70) = 2% of 210 = 4.2

So, 15% of x - 35% of y ≈ 4.2
--> 0.15x - 0.35y ≈ 4.2

Clearly, x must be greater than y.
Let us check two extreme values of x and y, i.e. x = 75 and y = 20

(0.15)*70 - (0.35)*20 = 10.50 - 7.00 = 3.50
Note that, this difference cannot be more than this.
So, the closes we can get to $4.2 increase only if prices of $20 and @70 stocks has changed.

Answer : E
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