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Considering the positions on the number line above, which of the follo

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Considering the positions on the number line above, which of the follo [#permalink]

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New post 16 May 2016, 02:34
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Considering the positions on the number line above, which of the following could be a value for x?

A. 5/3
B. 3/5
C. -2/5
D. -5/2
E. none

[Reveal] Spoiler:
Attachment:
p006-3.gif
p006-3.gif [ 476 Bytes | Viewed 2702 times ]
[Reveal] Spoiler: OA

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Re: Considering the positions on the number line above, which of the follo [#permalink]

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New post 16 May 2016, 04:08
Considering the image above,
x^3 < x^2

This can only happen if x is negative

Cancel out Options A and B

Also, x < x^3

This means x lies between -1 and 0

Option C satisfies the conditions
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Re: Considering the positions on the number line above, which of the follo [#permalink]

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New post 16 May 2016, 04:25
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ronny123 wrote:
Considering the image above,
x^3 < x^2

This can only happen if x is negative


Cancel out Options A and B

Also, x < x^3

This means x lies between -1 and 0

Option C satisfies the conditions


highlighted portion is not correct...
\(x^3<x^2\) can be possible-
1) when x is negative as shown by you
2) Also when x is between 0 and 1..
example 1/2..
\(x^3 = \frac{1}{8}\)and \(x^2 = \frac{1}{4}\)..
so it means x<1 except when x=0..
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Re: Considering the positions on the number line above, which of the follo [#permalink]

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New post 16 May 2016, 04:34
Very true.

I had taken both the conditions into account before I cancelled the options A and B

Also , when x < x^3

x can either lie between -1 and 0
Or
x can be any integer above 1
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Considering the positions on the number line above, which of the follo [#permalink]

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New post 16 May 2016, 04:35
Bunuel wrote:
Image
Considering the positions on the number line above, which of the following could be a value for x?

A. 5/3
B. 3/5
C. -2/5
D. -5/2
E. none

[Reveal] Spoiler:
Attachment:
p006-3.gif


lets see the values x can take..



1) \(x^3<x^2.................x^3-x^2<0...............x^2(x-1)<0...................\)
this means \(x<1\) as \(x^2\) cannot be negative...

2) \(x<x^3............. x^3-x>0...........x(x^2-1)>0.........\)...
so both x and x^2-1 will be of the same sign..

a) if x is +ive, \(x^2-1>0...............x^2>1............ x>1... OR ...x<-1.......\) BUT x is +ive so x>1..
But we have seen above x<1.. so this is not possible

b) if x is -ive, \(x^2-1<0...............x^2<1............ x<1... OR ...x>-1.......\) BUT x is -ive so x lies between -1 and 0.....

From above 2 points, x lies between -1 and 0..... so x is -3/5
C
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Re: Considering the positions on the number line above, which of the follo [#permalink]

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New post 21 Jun 2017, 20:56
We are looking for a number where x < x^3 < x^2 .

This particular question can be easily solved through options.

A) 5/3.. this number is >1, so its square would be lesser than its cube. Eliminated.

B) 3/5.. this number lies between 0 and 1. So with increasing powers, value will keep on decreasing. So its cube will be lesser than the number itself . Eliminated.

C) -2/5 or -0.4. Its cube = -0.064, which is closer to zero hence greater than the number itself. Its square is positive and hence will be greater than both number and its cube. This is the one.

D) -5/2 or -2.5. This number is less than 1, its cube will be lesser than the number, not greater. Eliminated.

Hence C answer
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Re: Considering the positions on the number line above, which of the follo [#permalink]

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New post 14 Apr 2018, 09:38
+1 for option C. It is clear that this combination is possible only for negative numbers. Try out with negative options available. Only option C fits the bill.
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Re: Considering the positions on the number line above, which of the follo   [#permalink] 14 Apr 2018, 09:38
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