Problem Solving

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

Will share the OA once get some response...

Just realised that solving this one using options would be a better strategy...

Its easy, last and the first options are the only possibilities.
No need to try for answer options.
Avg price = 210/5 = 42
Appx rise = $42 x 2% = $.84 (or arond $.84)

70 x 15% = $10.50 rise
20 x 35% = $07.00 fall
Net rslt = $03.50 rise
Therefore, total avg increase = 3.5/5 = $.7(= around .84)
Hence, E.

I am not sure how to solve this question..
i could arrive by brute force but it may take forever to solve this unless you are lucky and u pick the right option in the first go.
Experts, can you please explain how to arrive at the correct ans without taking lifetime to arrive at the solution ??

winniethepooh wrote:Its easy, last and the first options are the only possibilities.
No need to try for answer options.
Avg price = 210/5 = 42
Appx rise = $42 x 2% = $.84 (or arond $.84)

70 x 15% = $10.50 rise
20 x 35% = $07.00 fall
Net rslt = $03.50 rise
Therefore, total avg increase = 3.5/5 = $.7(= around .84)
Hence, E.

how can you say that??
and can you please explain your ans in detail?

How much more detailed buddy?

Actually, the options don't really leave a great deal of options available with me. What I mean is that the question has vast differences only between $20 and $70. Though, the difference between $20 and $45 is great too(45 is 2.25 of 20) , but then seeing the difference between the increase % and decrease % and the usage of the words AVERAGE PRICE and ROSE BY 2% can create a good picture of the options to solve the questions!

Another alternative is to go with the answer options:
As you can see,In option A - there is no need to calculate further as difference between 40 and 45 is not really great, so the problem is surely not mentioning about this option. Similarly you can exclude option B.

Now, in between options C, D and E - The greatest distance is between 20 and 70 that is option E, so consider it first, then consider D and if both don't work you are left with option C which would be the answer(BUT NOT IN THIS CASE). As you get the answer by considering the first option here(Option E) there is no need for further calculation.