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?XXX
20, 35, 40
35, 40, 70
20, 45, 70
20, 35, 70
35, 40, 45


OA is E

I solved it this way,

in all total of all the stocks is 210$ its means total increase will be 4.2 $

15 % 35 %

$20, 3 7
$35, 5.25 12.25
$40, 6 14
$45 6.75 15.75
$70 10.5 24.5

we have to decrease one stock by 35 % and increase another by 15 %

it means 15 % value should be higher than 35 % value. because we want the overall increase of 2 %
70 is the only value whose 15% value is higher 35 % of other stock.
so 70 is out and 20 has the least value of 35 % to that is also out,

Answer will be 35, 40,45,

But i was not able to solve it in the test and i think there must be short way to deal with this kind of problem.

Guys please help me understand the missing link, or better to say the SHORT CUT