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

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If x is an integer, is x|x| < 2^x? [#permalink] New post 22 Mar 2010, 20:59
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D
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85% (01:47) correct 15% (01:07) wrong based on 125 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?
But what should be the next steps .. Please help
[Reveal] Spoiler: OA
Senior Manager
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Kudos [?]: 79 [0], given: 20

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

But if x<0 so we get |-x| => -x
Am i missing something?
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Re: x|x| < 2^x? [#permalink] New post 23 Mar 2010, 05:33
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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?
But what should be the next steps .. Please help


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.

Answer: D.

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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Expert Post
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Re: If x is an integer, is x|x| < 2^x? [#permalink] New post 22 Feb 2014, 11:25
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Re: If x is an integer, is x|x| < 2^x? [#permalink] New post 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

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