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If x is an integer, is xx < 2^x?
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22 Mar 2010, 21:59
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If x is an integer, is xx < 2^x? (1) x < 0 (2) x = 10 I can understand the second part: 1010 < 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.. xx < 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
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Re: xx < 2^x?
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23 Mar 2010, 02:42
Thanks Kp.
But if x<0 so we get x => x Am i missing something?



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Re: xx < 2^x?
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23 Mar 2010, 06:33
rohitgoel15 wrote: Sorry to open a new thread for an already existing question. was not satisfied with the answers. anotherabsolutevaluequestion41274.htmlIf x is an integer, is xx < 2^x? (1) x<0 (2) x=10 I can understand the second part: 1010 < 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.. xx < 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 xx < 2^x?Question: is \(xx < 2^x\)? 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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Re: If x is an integer, is xx < 2^x?
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22 Feb 2014, 12:25



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Re: If x is an integer, is xx < 2^x?
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14 Apr 2014, 03:30
If x is an integer, is xx < 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.



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If x is an integer, is xx < 2^x?
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07 Mar 2016, 20:57
rohitgoel15 wrote: If x is an integer, is xx < 2^x? (1) x < 0 (2) x = 10 I can understand the second part: 1010 < 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.. xx < 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 here => see in first case x<0 => x=x => x*x<2^x => x^2<2^x statement 2 i would say you should not even check as the specific value will yield a result hence sufficient. => D
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Re: If x is an integer, is xx < 2^x?
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13 Mar 2016, 06:15
A quick takeaway from this question is that whenever we encounter a negative sign in front of a square => its a negative value and offcourse the second big takeaway => if the base if positive => THE value is positive irrespective of the exponent being positive or negative
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If x is an integer, is xx < 2^x?
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Updated on: 18 Jul 2016, 23:54
rohitgoel15 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? (1) x < 0 Means x is negative , the product on LHS will be negative therefore RHS will become \(2^{x}\) \(2^{x}\) is equal to \(\frac{1}{2^{x}}\) \(\frac{1}{2^{x}}\) (which is a positive decimal/positive fraction) will always be GREATER than x (which is a negative integer) SUFFICIENT (2) x = 10 We just proved it, through statement 1 SUFFICIENT EACH ALONE IS SUFFICIENT ANSWER IS D
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Last edited by LogicGuru1 on 18 Jul 2016, 23:54, edited 2 times in total.



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Re: If x is an integer, is xx < 2^x?
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18 Jul 2016, 23:45
hrs always +ve in this case.
so D
coz both statements say LHS is negative



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Re: If x is an integer, is xx < 2^x?
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30 Jun 2017, 02:19
I feel like this question doesn't really touch upon a more tricky inequality when x is positive (both statements indicate x as negative, so it's enough to answer the question).
Notice how things change when x > 0
x x*x 2^x 1 1 2 Y 2 4 4 N 3 9 8 N 4 16 16 N 5 25 32 Y 6 36 64 Y 7 49 128 Y 8 64 256 Y... so on



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Re: If x is an integer, is xx < 2^x?
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10 Mar 2018, 23:46
rohitgoel15 wrote: If x is an integer, is xx < 2^x?
(1) x < 0 (2) x = 10 Question: Is xx < 2^x? Given x = Integer St 1: x < 0 x = x , when x < 0 means we have, x * x = 2^x or (x)^2 = 1/(2)^x As LHS is negative and RHS always be positive, we can say xx < 2^x Sufficient.St 2: x = 10 means 1010 < 2^10 100 < 2^10 Sufficient(D)
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Re: If x is an integer, is xx < 2^x?
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15 Jul 2018, 05:33
stonecold wrote: rohitgoel15 wrote: If x is an integer, is xx < 2^x? (1) x < 0 (2) x = 10 I can understand the second part: 1010 < 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.. xx < 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 here => see in first case x<0 => x=x => x*x<2^x => x^2<2^x statement 2 i would say you should not even check as the specific value will yield a result hence sufficient. => D I always gets confused many times in absolute value questions. x = x when x < 0, now my question is; You wrote x * x = x * x, but why not x * x. Does it not affect the other "x" which is not inside the modulus sign? It may sound silly, but I lose many points because of this confusion. .
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Re: If x is an integer, is xx < 2^x? &nbs
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