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

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

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New post 19 Oct 2018, 01:06
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A
B
C
D
E

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Question Stats:

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

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New post 19 Oct 2018, 01:14
Lets's consider x as \(\frac{-1}{2}\)

And start by substituting the value of x in the options.

\(x^{-1}\) = \((\frac{-1}{2})^{-1}\) or \((\frac{-2}{1})^1\) = -2.

x = -0.5

\(x^2\) = 1/4 = 0.25

\(x^{-2}\) = 4.

Only option a is in ascending order.

A is the answer.
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Re: If -1<x<0, Which of the following is listed in ascending order?  [#permalink]

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New post 19 Oct 2018, 01:53
MathRevolution 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 compare \(x^2\) and \(x^{-2}\) as both are going to be positive...
But |X|<1, so x^2<1....
.. As x^2 is positive, divide both sides by x^2, so \(\frac{x^2}{x^2}\)<\(\frac{1}{x^2}\)........\(\frac{1}{x^2>1}\)........\(x^{-2}>1\)
So \(x^2,1,x^{-2}\)
, x is negative and reciprocal of x.......\(x^{-1}<x\)

A
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Re: If -1<x<0, Which of the following is listed in ascending order?  [#permalink]

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New post 21 Oct 2018, 18:57
=>

We can find the correct order by plugging in a value for \(x\).
Suppose \(x =\frac{-1}{2.}\) Then \(-1 < x < 0,\) and
\(x^2 = \frac{1}{4}\), \(x^{-1} = -2\) and \(x^{-2} = 4.\)
Thus, \(x^{-1} < x < x^2 < 1 < x^{-2}\)

Therefore, the answer is A.
Answer: A
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Re: If -1<x<0, Which of the following is listed in ascending order?   [#permalink] 21 Oct 2018, 18:57
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