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I set the side length of a square is 1 ( just to simplify the calculation). Set x = p/100 ( since p is in percent, for instance, p = 50% , x = 0.5) Area = 1^2 = 1

New side length = 1*( 1-x) = 1-x , Area after the reduction = (1-x)^2

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.

Re: If the side length of a square is reduced by p percent, what [#permalink]

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10 Aug 2014, 12:25

The most effective way to solve this problem is to use smart numbers. Ex: s=10, p=50 A = 100 A_reduced = 25 % reduction = (100-25)/100*100% = 75% Only C gives the correct answer of 75.

Re: If the side length of a square is reduced by p percent, what [#permalink]

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01 Sep 2015, 06:38

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Re: If the side length of a square is reduced by p percent, what [#permalink]

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06 Sep 2016, 18:34

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Let’s let the side of the square be 100 units. After a p percent reduction, the side of the square becomes (100 - p) units. The area of the original square was 10,000 square units and the area of the reduced square is (100 - p)^2. Thus, the reduction is 10000 - (100 - p)^2 = 10000 - (10000 -200p + p)^2 = 200p - p^2 square units. Compared to the original area, this corresponds to a [(200p - p^2)/10000]x100 = (200p - p^2)/100 = 2p - (p^2/100) percent reduction.

Answer: C
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