oss198 wrote:

If the side length of a square is reduced by p percent, what is the resulting percent reduction in the area of the square?

(A) \(\frac{p^2}{100}%\)

(B) \([1-\frac{p^2}{100}]^2%\)

(C) \([2p-\frac{p^2}{100}]%\)

(D) \(\frac{(100-p)^2}{100} %\)

(E) \(\frac{p^2-2p}{100}%\)

Two ways to solve this problem. My preferred option here is to determine the pattern (I always like to do that over memorizing complex formulas or rules).

I drew 3 squares with sides of 10, 9 and 8. The areas are 100, 81, 64.

Based on that, I was able to easily figure out the answer choice C fits that mold just by plugging in. It all took less than 90 seconds.

The second way to do this is algebraically.

Side of a square = s^2.

Side reduced by p% = s(1-(p/100))

Area after side reduced by p% = (s(1-(p/100)))^2

Difference = ((s^2) - (s(1-(p/100)))^2)/(s^2)

Simplify (and it's not easy to simplify this thing!), and you end up with answer choice C.

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