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Which of the following is closest to (-3/4)^199？

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by Max@Math Revolution » Sat Sep 10, 2016 8:41 pm
Which of the following is closest to (-3/4)^199？
A. -1
B. -1/2
C. 0
D. 1
E. 2

*An answer will be posted in 2 days.
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by Brent@GMATPrepNow » Sun Sep 11, 2016 3:21 pm
Max@Math Revolution wrote:Which of the following is closest to (-3/4)^199?

A. -1
B. -1/2
C. 0
D. 1
E. 2

*An answer will be posted in 2 days.
Let's make a few observations and look for a pattern...

(-3/4)¹ = -3/4
(-3/4)² = (-3/4)(-3/4) = 9/16 ≈ a little more than 1/2
(-3/4)³ = (-3/4)(-3/4)(-3/4) = -27/64 ≈ a little more than -1/2
(-3/4)� = (-3/4)(-3/4)(-3/4)(-3/4) = 81/256 ≈ a little less than 1/3

As the exponent, n, increases, the MAGNITUDE of (-3/4)^n decreases
That is, as the exponent, n, increases, the value of (-3/4)^n approaches zero
So, 0 is the closest value to (-3/4)^199

Answer: C


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by Max@Math Revolution » Mon Sep 12, 2016 7:59 am
From -1<x<1, x^n approaches 0 as n increases. Hence, the correct answer is C.
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