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If x is an integer, is xx<2^x ? [#permalink]
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18 Dec 2012, 08:31
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If x is an integer, is xx<2^x ? (1) x < 0 (2) x = 10
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Re: If x is an integer, is xx<2^x ? [#permalink]
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DS from OG [#permalink]
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30 Dec 2013, 11:42
If x is an integer, is x x < 2^x ? (1) x < 0 (2) x = –10 DS from OG.
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Re: DS from OG [#permalink]
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seabhi wrote: If x is an integer, is x x < 2x ?
(1) x < 0 (2) x = –10
DS from OG. OA is D for the following reasons: When you first see a DS question, see if there is anyway to simplify the question stem In this case, since x is positive, we can divide both sides by x giving us a new question stem > is x < 2?S1: x<0, therefore x must be <2 = sufficientS2: x = 10 and 10 < 2 = sufficientLet me know if this helps!



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Re: DS from OG [#permalink]
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30 Dec 2013, 21:36
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bparrish89 wrote: seabhi wrote: If x is an integer, is x x < 2x ?
(1) x < 0 (2) x = –10
DS from OG. OA is D for the following reasons: When you first see a DS question, see if there is anyway to simplify the question stem In this case, since x is positive, we can divide both sides by x giving us a new question stem > is x < 2?S1: x<0, therefore x must be <2 = sufficientS2: x = 10 and 10 < 2 = sufficientLet me know if this helps! The OA is wrong here because of the following reasons: (1) if x=10 then 100<20, on the other hand if x= 1, x<0 then the inequality changes from < to >, namely, 1 > 2 ; This statement is absolutely insufficient! (2) This statement is obviously sufficient! So, the correct answer is not D, but B



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Re: DS from OG [#permalink]
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31 Dec 2013, 02:46
Apologies for the confusion, the Question has been corrected. It was not 2x but 2^x
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Re: DS from OG [#permalink]
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If x is an integer, is xx<2^x ? [#permalink]
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If x is an integer, is xx<2^x ?
(1) x < 0 (2) x = 10



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If x is an integer, is xx<2^x ? [#permalink]
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27 Jul 2015, 06:43
reza52520 wrote: If x is an integer, is xx<2^x ?
(1) x < 0 (2) x = 10 Question : Is xx<2^x ?Statement 1: x < 0For x to be Negative LHS i.e. xx will always be NEGATIVE and 2^x will be positive for any value of x i.e. xx<2^x will always be true SUFFICIENTStatement 1: x = 10For x =10 LHS i.e. xx will always be NEGATIVE (100) and 2^x will be positive for given x (1/2^10) i.e. xx<2^x will always be true SUFFICIENTAnswer: option D
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Re: If x is an integer, is xx<2^x ? [#permalink]
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27 Jul 2015, 06:44
reza52520 wrote: If x is an integer, is xx<2^x ?
(1) x < 0 (2) x = 10 Hi, we have an equation and the RHS 2^x will be positive irrespective of value of x and LHS xlxl will depend on the value of x.. 1) x is ive .. so LHS is ive and RHS is +ive.. suff 2) x=10... again LHS is ive and RHS is +ive.. suff ans D
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Re: If x is an integer, is xx<2^x ? [#permalink]
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13 Dec 2015, 11:47
For, and 2^x will be positive for any value of x
2 power x, X can be negative no? since its x, we dont know positive or negative.. What am I missing?



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Re: If x is an integer, is xx<2^x ? [#permalink]
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13 Dec 2015, 12:04
paidlukkha wrote: For, and 2^x will be positive for any value of x
2 power x, X can be negative no? since its x, we dont know positive or negative.. What am I missing? You are missing a crucial thing here. Even if x is <0, \(2^x\) with x<0 = \(1/2^x\) , it is still >0...(1) Thus with x<0, x = x and hence xx = \(x^2\) As, x^2 is always \(\geq\) 0 for all x, \(x^2\)<0 ...(2) Thus, from (1) and (2), you get a definite "yes" for the question "is \(xx < 2^x\)" for x<0. Hope this helps.
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Re: If x is an integer, is xx<2^x ? [#permalink]
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24 Apr 2016, 15:22
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This question can be solved as follows.
stmt1) it says that x /x/ < 2^x. and also we are told that x< 0. So if x is zero and the abs of x is always positive then we know that x/x/ will be negative. In addition to that, we know that 2^negative number will be positive because it will be in the form of 1/2^x, it will be less than 1 but it will be greater than a negative number. So stmt1 is SUFF.
stmt2) this is a repetition of stmt1 because the left side is negative and the right side is positive. SUFF.
Answer is D!



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Re: If x is an integer, is xx<2^x ? [#permalink]
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24 Nov 2016, 06:03
I would say statement 1 is insufficient... Am I doing something incorrect?
\(x x < 2^x\)
\(x < \frac{2^x}{x}\)
For x = 1
\(1 < \frac{1}{2}/1\) \(1 <  \frac{1}{2}\)



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Re: If x is an integer, is xx<2^x ? [#permalink]
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24 Nov 2016, 07:17



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Re: If x is an integer, is xx<2^x ? [#permalink]
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23 Jan 2017, 09:30
1, x < 0 x = 1 1 < \(\frac{1}{2}\) x = 2 4 < \(\frac{1}{4}\) AD 2, X = 10 100 < \(\frac{1}{2}\)^10 D
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If x is an integer, is x*lxl<2^x [#permalink]
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28 Jan 2017, 06:54
1. If x is an integer, is x*lxl<2^x
(1) x<0 (2) x=10



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Re: If x is an integer, is x*lxl<2^x [#permalink]
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28 Jan 2017, 07:37
praveen27sinha wrote: 1. If x is an integer, is x*lxl<2^x
(1) x<0 (2) x=10 x is positive so is 2^x so if we can find whether x is positive or negative we can find our solution. both of the option says x is negative. so answer is D



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Re: If x is an integer, is xx<2^x ? [#permalink]
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28 Jan 2017, 07:47



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Re: If x is an integer, is xx<2^x ? [#permalink]
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17 Apr 2017, 02:20
Bunuel wrote: Walkabout wrote: If x is an integer, is xx<2^x ?
(1) x < 0 (2) x= 10 If x is an integer, is xx<2^x ?Notice that the RHS (right hand side) of the expression is always positive (\(2^x>0\)), but the LHS is positive when \(x>0\) (\(x>0\) > \(x*x=x^2\)), negative when \(x<0\) (\(x<0\) > \(x*x=x^2\)) and equals to zero when \(x={0}\). (1) x < 0. According to the above \(x*x<0<2^x\). Sufficient. (2) x = 10. The same here \(x*x=100<0<\frac{1}{2^{10}}\). Sufficient. Answer: D. just for the sake of time saving: (2) x = 10 > we could test it! done.... next question
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