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

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Bunuel
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If -1 < x < 0, which of the following is correct? [#permalink] New post   07 Feb 2019, 01:36
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64% (01:30) correct 36% (01:32) wrong based on 264 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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E
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kunalcvrce
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Re: If -1 < x < 0, which of the following is correct? [#permalink] New post   07 Feb 2019, 02:11
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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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Re: If -1 < x < 0, which of the following is correct? [#permalink] New post   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] New post   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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Re: If -1 < x < 0, which of the following is correct? [#permalink] New post   07 Feb 2019, 02:47
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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] New post   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] New post   10 Feb 2019, 08:49
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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.

Answer: E
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Re: If -1 < x < 0, which of the following is correct? [#permalink] New post   31 May 2023, 21:50
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Re: If -1 < x < 0, which of the following is correct? [#permalink]
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