Problem Solving

Ques)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

Please assist with above problem.

alanforde800Maximus wrote:Ques)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

Please assist with above problem.

Use reason.
The increase in one price (15%) is LESS THAN HALF the decrease in another price (35%), yet the NET increase is 2%.
Thus, the price that increases must be MUCH HIGHER than the price that decreases.
Only $70 and $20 are sufficiently far apart, implying that the other 3 prices (35,40,45) do not change.

The correct answer is E.

While the method described by GMATGuruNY is the quickest way to do it, in case that logic doesn't strike, a slightly convoluted way to solve the problem is:
15% rise and 35% decline shows that the rise has to be on a higher value than the decline
The value of the stock portfolio increased by 2%. The total stocks have been purchased for $210. Thus, in absolute terms the increase is approximately $4.2.
Use the process of elimination and check as to in which option 15% of the higher missing stock value is greater than 35% of the smaller missing stock value.
Starting from the middle ie Option C, the constant shares are $20, $35 and $40. So, 15% of $70 should be $4.20 more than 35% of $45. Comparing $10.5 (15% of $70) and -$15.75 (35% of $45) shows that the value of the portfolio would have dropped.
Thus, we need a much smaller share for the one where the value has dropped while keep the $70 share constant for the 15% increase. The only other option where the $70 stock is one of the moving shares is Option E. Comparing $10.5 (15% of $70) and -$7 (35% of $20) shows that the value of the portfolio rose by $3.5 which is approximately the absolute value of 2% on the portfolio.
Thus, the answer to this question is E.