RULE:
If x+y = k, then the greatest possible value for xy occurs when x=y.
For example:
If x+y = 10, then the greatest possible value for xy occurs when x=y=5:
If x=1 and y=9, then xy = 9.
If x=2 and y=8, then xy = 16.
If x=3 and y=7, then xy = 21.
If x=4 and y=6, then xy = 24.
If x=5 and y=5, then xy = 25.
The case in blue yields the greatest product.

lheiannie07 wrote:Which of the following gives the highest overall percent increase, if in each case, the second percent increase is applied on the value obtained after application of the first percent Increase?

(A) 10 percent increase followed by 50 percent increase
(B) 25 percent increase followed by 35 percent increase
(C) 30 percent increase followed by 30 percent increase
(D) 40 percent increase followed by 20 percent increase
(E) 45 percent increase followed by 15 percent increase

Increasing a value by x% and then by y% implies multiplication first by x/100 and then by y/100, as follows:
(x/100)(y/100) = xy/10000.
The expression in red indicates the following:
Increasing a value by x% and then by y% implies MULTIPLICATION BY THE PRODUCT OF X AND Y.
Thus:
The answer choice with the GREATEST PRODUCT will yield the GREATEST PERCENT INCREASE.
Every answer choice is composed of two values with a sum of 60.
As noted above, the greatest possible product will be yielded when the two values are equal, as in C:
30*30 = 900.

The correct answer is C.