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

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Math Expert
Joined: 02 Sep 2009
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Considering the positions on the number line above, which of the follo  [#permalink]

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16 May 2016, 02:34
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Difficulty:

35% (medium)

Question Stats:

67% (01:02) correct 33% (01:00) wrong based on 159 sessions

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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

Attachment:

p006-3.gif [ 476 Bytes | Viewed 3482 times ]

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

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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
Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: Considering the positions on the number line above, which of the follo  [#permalink]

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16 May 2016, 04:25
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 12 Jun 2015
Posts: 79
Re: Considering the positions on the number line above, which of the follo  [#permalink]

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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
Math Expert
Joined: 02 Aug 2009
Posts: 6800
Considering the positions on the number line above, which of the follo  [#permalink]

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16 May 2016, 04:35
Bunuel wrote:

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

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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Posts: 1343
Location: India
Re: Considering the positions on the number line above, which of the follo  [#permalink]

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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.

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

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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 &nbs [#permalink] 14 Apr 2018, 09:38
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