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If -1<x<0, Which of the following is listed in ascendi

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If -1<x<0, Which of the following is listed in ascendi

by Max@Math Revolution » Thu Oct 18, 2018 11:57 pm

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[Math Revolution GMAT math practice question]

If -1<x<0, Which of the following is listed in ascending order?

A. x^-1, x, x^2, 1, x^-2
B. x^-1, x^2, x, 1, x^-2
C. x^-2, x, x^2, 1, x^-1
D. x, x^-1, x^2, 1, x^-2
E. x^-1, x, x^2, x^-2, 1
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by Brent@GMATPrepNow » Fri Oct 19, 2018 4:46 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If -1 < x < 0, Which of the following is listed in ascending order?

A. x^-1, x, x^2, 1, x^-2
B. x^-1, x^2, x, 1, x^-2
C. x^-2, x, x^2, 1, x^-1
D. x, x^-1, x^2, 1, x^-2
E. x^-1, x, x^2, x^-2, 1
Let's test a value of x.

If -1 < x < 0, then x COULD equal -1/2

So, x^(-1) = (-1/2)^(-1) = 1/(-1/2) = -2
And, x^(-2) = (-1/2)^(-2) = 1/(-1/2)^2 = 1/(1/4) = 4
And, x^2 = (-1/2)^2 = 1/4

Listed in ascending order, we get: -2, 1/4, 4
In other words, x^(-1), x^2, x^(-2)

Answer: A

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Brent
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by Max@Math Revolution » Sun Oct 21, 2018 5:44 pm
=>

We can find the correct order by plugging in a value for x.
Suppose x = -1/2. Then -1 < x < 0, and
x^2 = 1/4, x^-1 = -2 and x^-2 = 4.
Thus, x^-1 < x < x^2 < 1 < x^-2

Therefore, the answer is A.
Answer: A
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