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# If x is an integer, is x|x| < 2^x?

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Senior Manager
Joined: 07 Nov 2009
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If x is an integer, is x|x| < 2^x? [#permalink]  22 Mar 2010, 20:59
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Difficulty:

5% (low)

Question Stats:

86% (01:46) correct 14% (01:11) wrong based on 139 sessions
If x is an integer, is x|x| < 2^x?

(1) x < 0
(2) x = -10

[Reveal] Spoiler:
I can understand the second part:
-10|-10| < 2^-10 --> -10 * 10 < 1/2 ^ 10
|-10| --> reduced to 10 as its numeric.. is my reasoning correct?
B is sufficient

For (1) .. however i am not able to decipher anything..
-x|-x| < 2^-x --> -x * -x < 1/2 ^x
|-x| --> reduced to -x as x < 0 .. is my reasoning correct?
[Reveal] Spoiler: OA
Senior Manager
Joined: 07 Nov 2009
Posts: 313
Followers: 5

Kudos [?]: 201 [0], given: 20

Re: x|x| < 2^x? [#permalink]  23 Mar 2010, 01:42
Thanks Kp.

But if x<0 so we get |-x| => -x
Am i missing something?
Math Expert
Joined: 02 Sep 2009
Posts: 28243
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Kudos [?]: 45003 [2] , given: 6638

Re: x|x| < 2^x? [#permalink]  23 Mar 2010, 05:33
2
KUDOS
Expert's post
rohitgoel15 wrote:
Sorry to open a new thread for an already existing question. was not satisfied with the answers.
another-absolute-value-question-41274.html

If x is an integer, is x|x| < 2^x?
(1) x<0
(2) x=-10

I can understand the second part:
-10|-10| < 2^-10 --> -10 * 10 < 1/2 ^ 10
|-10| --> reduced to 10 as its numeric.. is my reasoning correct?
B is sufficient

For (1) .. however i am not able to decipher anything..
-x|-x| < 2^-x --> -x * -x < 1/2 ^x
|-x| --> reduced to -x as x < 0 .. is my reasoning correct?

If x is an integer, is x|x| < 2^x?

Question: is $$x|x| < 2^x$$? Notice that the right hand side (RHS), $$2^x$$, is always positive for any value of $$x$$.

(1) $$x<0$$ --> $$LHS=x*|x|=negative*positive=negative$$ --> $$(LHS=negative)<(RHS=positive)$$. Sufficient.

(2) $$x=-10$$ --> LHS is negative --> $$(LHS=negative)<(RHS=positive)$$. Sufficient.

rohitgoel15 wrote:
But if x<0 so we get |-x| => -x
Am i missing something?

For $$x<0$$, $$|x|=-x$$ yes. So for (1) $$LHS=x*(-x)$$, $$x$$ is negative, $$-x$$ is positive. So $$LHS=x*(-x)=negative*positive=negative$$.

Hope it helps.
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Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 45003 [0], given: 6638

Re: If x is an integer, is x|x| < 2^x? [#permalink]  22 Feb 2014, 11:25
Expert's post
Bumping for review and further discussion.
_________________
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Joined: 14 Jul 2013
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Kudos [?]: 8 [0], given: 38

Re: If x is an integer, is x|x| < 2^x? [#permalink]  14 Apr 2014, 02:30
If x is an integer, is x|x| < 2^x?

(1) x < 0
(2) x = -10

Sol.

(1) Pick two numbers for x
a. x = -2 =>
LHS = -2.|-2| = -4
RHS = 2^-2 i.e. positive
=> LHS<RHS
b.LHS = -1/3.|-1/3| = -9
RHS = 2^-1/3 i.e. positive
=> LHS<RHS
therefore, (1) is sufficient to answer

(2) case covered in statement (1) a
hence, sufficient

Re: If x is an integer, is x|x| < 2^x?   [#permalink] 14 Apr 2014, 02:30
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