The purpose of this problem is to check your understanding

Question

The purpose of this problem is to check your understanding of how the mean works intuitively  without  making any manual calculations. So set the timer for 2 minutes and put your pencil down!

Good luck! :m16 


A certain stock 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, 70
B. $20, 45, 70
C. $20, 35, 40
D. $35, 40, 70
E. $35, 40, 45

nero44 · Answer

pure intuition A) took 35 seconds...

laxieqv · Answer

Matt, I think this question tests logic and reasoning rather than sheer intuition :wink:

nakib77 · Answer

got C) took me 3 minutes.

first of all because portfolio value is increasing by 2% overall the new value will be (20+35+40+45+70) * 1.02 = 210 *1.02 = little higher than 214

so we can say 1.15x- .85y = 4.xx

now it is number plugging time, if you put 70 as y and 45 as x you get the difference. 51.75 -47.5 = 4.25

so the stock valued at 20, 35 and 40 will remain constant.

duttsit · Answer

My intuition says E. (1.5 min)

the avg stock portfolio price : 210/5 = 42

fi avg increased by 2% or by 0.84, the sum of all stock prices should increase by 0.84 * 5 or ~ $ 4.2

in oder to get this difference,

maximum price stock would have increase by 15%
minimum value stock would have decreased by 35%

gotoknow3 · Answer

Its E; Same explanation as duttsit

GMATT73 · Answer

If the overall average price of the portfolio increased, despite the larger percentage drop in one stock than the percentage increase in another , then the stock that went down in price must have been fairly cheap, while the stock that increased must have had a high price. $70 clearly stands out to balance off the price decline. Because the percentage value of a 35% drop is more than twice the percentage value of a 15% increase, in order to get a positive end result,  the initial price of the increased stock must have been more than twice that of the reduced security.   The only two stocks that are more than two times apart are $20 and $70. The best answer is E.

The purpose of this problem is to check your understanding

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