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# If -1 < x < 0, which of the following is correct?

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
If -1 < x < 0, which of the following is correct?  [#permalink]

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07 Feb 2019, 01:36
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45% (medium)

Question Stats:

54% (01:19) correct 46% (01:18) wrong based on 70 sessions

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If -1 < x < 0, which of the following is correct?

A. $$x^{-3} < x^{-2} < x^{-1}$$

B. $$x^{-1} < x^{-2} < x^{-3}$$

C. $$x^{-1} < x^{-3} < x^{-2}$$

D. $$x^{-2} < x^{-3} < x^{-1}$$

E. $$x^{-3} < x^{-1} < x^{-2}$$

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Re: If -1 < x < 0, which of the following is correct?  [#permalink]

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07 Feb 2019, 02:11
Bunuel wrote:
If -1 < x < 0, which of the following is correct?

A. $$x^{-3} < x^{-2} < x^{-1}$$

B. $$x^{-1} < x^{-2} < x^{-3}$$

C. $$x^{-1} < x^{-3} < x^{-2}$$

D. $$x^{-2} < x^{-3} < x^{-1}$$

E. $$x^{-3} < x^{-1} < x^{-2}$$

$$x^{-2}$$ is always positive so greatest among $$x^{-3},x^{-1}$$ So A,B,D eliminated

by putting values we can tell $$x^{-3} < x^{-1}$$
So E
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Joined: 28 Sep 2018
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Re: If -1 < x < 0, which of the following is correct?  [#permalink]

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07 Feb 2019, 02:32
If -1 < x < 0, which of the following is correct?

Inference
X = (-0.1,-0.01...)
X = (-1/10, -1/100...)

From the above it clear that X is a proper fraction

Now for all proper fractions
X > X^2 > X^3...

I.e. X^small power > X^large power

We are given X^-1 which is the highest power and X^-3 which is the smallest power since -3<-1

Thus we can say that
X^-3 > X^-2 > X^-1 (B)

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Re: If -1 < x < 0, which of the following is correct?  [#permalink]

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07 Feb 2019, 02:46
kunalcvrce wrote:
Bunuel wrote:
If -1 < x < 0, which of the following is correct?

A. $$x^{-3} < x^{-2} < x^{-1}$$

B. $$x^{-1} < x^{-2} < x^{-3}$$

C. $$x^{-1} < x^{-3} < x^{-2}$$

D. $$x^{-2} < x^{-3} < x^{-1}$$

E. $$x^{-3} < x^{-1} < x^{-2}$$

$$x^{-2}$$ is always positive so greatest among $$x^{-3},x^{-1}$$ So A,B,D eliminated

by putting values we can tell $$x^{-3} < x^{-1}$$
So E

I get what you did

X^-1 = 1/X
X^-2 = 1/X^2
X^-3 = 1/X^3

If X = -0.1 then we get
X^-1 =-1/0.1
X^-2 = 1/0.01
X^-3 = -1/0.001

X^-2 > X^-1 > X^-3

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Posts: 8006
Re: If -1 < x < 0, which of the following is correct?  [#permalink]

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07 Feb 2019, 02:47
Bunuel wrote:
If -1 < x < 0, which of the following is correct?

A. $$x^{-3} < x^{-2} < x^{-1}$$

B. $$x^{-1} < x^{-2} < x^{-3}$$

C. $$x^{-1} < x^{-3} < x^{-2}$$

D. $$x^{-2} < x^{-3} < x^{-1}$$

E. $$x^{-3} < x^{-1} < x^{-2}$$

Simply take x as -0.1,that is -1/10..
. $$x^{-1} =(-1/10)^{-1}=-10.... x^{-2} =(-1/10)^{-2}=(-10)^2=100......x^{-3}=(-1/10)^{-3}=(-10)^{-3}=-1000$$..
So . $$x^{-3} < x^{-1} < x^{-2}$$

E
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Re: If -1 < x < 0, which of the following is correct?  [#permalink]

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07 Feb 2019, 03:15
Bunuel wrote:
If -1 < x < 0, which of the following is correct?

A. $$x^{-3} < x^{-2} < x^{-1}$$

B. $$x^{-1} < x^{-2} < x^{-3}$$

C. $$x^{-1} < x^{-3} < x^{-2}$$

D. $$x^{-2} < x^{-3} < x^{-1}$$

E. $$x^{-3} < x^{-1} < x^{-2}$$

Out of the above options bottom 2 will be C and E

Now just pick a value, x = -0.5

Only E satisfies the above value.

E
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Re: If -1 < x < 0, which of the following is correct?  [#permalink]

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10 Feb 2019, 08:49
Bunuel wrote:
If -1 < x < 0, which of the following is correct?

A. $$x^{-3} < x^{-2} < x^{-1}$$

B. $$x^{-1} < x^{-2} < x^{-3}$$

C. $$x^{-1} < x^{-3} < x^{-2}$$

D. $$x^{-2} < x^{-3} < x^{-1}$$

E. $$x^{-3} < x^{-1} < x^{-2}$$

We can let x = -1/2, thus:

(-1/2)^-3 = (-2)^3 = -8

(-1/2)^-2 = (-2)^2 = 4

(-1/2)^-1 = (-2^)1 = -2

Thus, x^-3 < x^-1 < x^-2.

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Re: If -1 < x < 0, which of the following is correct?   [#permalink] 10 Feb 2019, 08:49
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