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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If -1<x<0, Which of the following is listed in ascending order?  [#permalink]

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19 Oct 2018, 01:06
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Difficulty:

35% (medium)

Question Stats:

66% (01:31) correct 34% (01:40) wrong based on 71 sessions

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[Math Revolution GMAT math practice question]

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

$$A. x^{-1}, x, x^2, 1, x^{-2}$$
$$B. x^{-1}, x^2, x, 1, x^{-2}$$
$$C. x^{-2}, x, x^2, 1, x^{-1}$$
$$D. x, x^{-1}, x^2, 1, x^{-2}$$
$$E. x^{-1}, x, x^2, x^{-2}, 1$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1019 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) If -1<x<0, Which of the following is listed in ascending order? [#permalink] ### Show Tags 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. _________________ Press +1 Kudos If my post helps! Math Expert Joined: 02 Aug 2009 Posts: 7977 Re: If -1<x<0, Which of the following is listed in ascending order? [#permalink] ### Show Tags 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If -1<x<0, Which of the following is listed in ascending order? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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