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If x is an integer, is xx<2^x ?
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13 Sep 2019, 22:14
Walkabout wrote: If x is an integer, is xx < \(2^x\) ? (1) x < 0 (2) x = 10 Edit: Formating Given: x is an integer Asked: Is xx < \(2^x\) ? (1) x < 0 x = x x^2 < 2^x x^2 < 0 2^x >0 x^2 < 2^x \(xx < 2^x\) SUFFICIENT (2) x = 10 x = 10 xx = 10 * 10 = 100 \(2^x = 2^{10} = \frac{1}{1024}\) \(100 < \frac{1}{1024}\) \(xx < 2^x\) SUFFICIENT IMO D
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Re: If x is an integer, is xx<2^x ?
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22 Feb 2020, 03:30
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. Hi Bunuel, Please correct me if I am wrong 1) xx<2^x x=1 so, 11<2^1 1<1/2 which will always be true for any negative value of x and also with positive values it will remain true and sufficient 2) condition 2 is already giving fix value so it will be sufficient
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Re: If x is an integer, is xx<2^x ?
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22 Feb 2020, 13:25
Farina wrote: 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. Hi Bunuel, Please correct me if I am wrong 1) xx<2^x x=1 so, 11<2^1 1<1/2 which will always be true for any negative value of x and also with positive values it will remain true and sufficient 2) condition 2 is already giving fix value so it will be sufficient Hi Farina, Most of what you wrote is correct. This DS question is based on a couple of Number Properties: when X is NEGATIVE.... XX will ALWAYS be NEGATIVE 2^(X) will ALWAYS be POSTIIVE This means that the answer to the question is ALWAYS YES and Fact 1 is SUFFICIENT. However, what you noted about POSITIVE values is not true. For example.... when X = 1... 11 = 1 2^1 = 2 so the answer to the question "is XX < 2^X?".... is YES. when X = 2... 22 = 4 2^2 = 4 so the answer to the question "is XX < 2^X?".... is NO. This means that when X is POSITIVE, the answer to the question changes and this situation would be INSUFFICIENT. GMAT assassins aren't born, they're made, Rich
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Re: If x is an integer, is xx<2^x ?
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25 May 2020, 02:29
BrentGMATPrepNow wrote: Walkabout wrote: If x is an integer, is xx<2^x ?
(1) x < 0 (2) x = 10 Target question: Is xx< 2^x ? Given: x is an integer Statement 1: x < 0 In other words, x is NEGATIVE So, xx = (NEGATIVE)(NEGATIVE) = (NEGATIVE)(POSITIVE) = NEGATIVE IMPORTANT: 2^x will be POSITIVE for all values of x. Since xx must be NEGATIVE, and since 2^x must be POSITIVE, we can be certain that xx< 2^x Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: x = 10 So, xx = (10)(10) = (10)(10) = 100 = a NEGATIVE On the other hand, 2^x = 2^(10) = 1/(2^10) = some POSITIVE number Since xx is NEGATIVE, and since 2^x must be POSITIVE, we can be certain that xx< 2^x Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: Hi Brent, you have mentioned So, xx = (NEGATIVE)(NEGATIVE) = (NEGATIVE)(POSITIVE) = NEGATIVEbut isn't x = x when x<0 ? based on this logic it should be Negative * Negative = + ive isn't it ?? can you please clarify ?



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If x is an integer, is xx<2^x ?
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25 May 2020, 02:54
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. Hi @Bunuel  Opening up an old thread but need some clarification. In this question you have taken x as x = x when x<0 However, in another question  https://gmatclub.com/forum/isx11x1 ... 34652.htmlyou have taken x as x when x<0  can you please clarify the conditions wherein we have to take two different things ?



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Re: If x is an integer, is xx<2^x ?
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25 May 2020, 03:01
Anuragjn wrote: 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. Hi @Bunuel  Opening up an old thread but need some clarification. In this question you have taken x as x = x when x<0However, in another question  https://gmatclub.com/forum/isx11x1 ... 34652.htmlyou have taken x as x when x<0  can you please clarify the conditions wherein we have to take two different things ? Not sure I understand from where you've taken the red part. When x < 0, then x = x, so in this case \(x*x=x*(x)=x^2\).
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Re: If x is an integer, is xx<2^x ?
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25 May 2020, 03:09
Bunuel wrote: Anuragjn wrote: 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. Hi [b]Bunuel[/b]  Opening up an old thread but need some clarification. In this question you have taken x as x = x when x<0However, in another question  https://gmatclub.com/forum/isx11x1 ... 34652.htmlyou have taken x as x when x<0  can you please clarify the conditions wherein we have to take two different things ? Not sure I understand from where you've taken the red part. When x < 0, then x = x, so in this case \(x*x=x*(x)=x^2\). Hi Bunuel  Thanks for quick response. I have taken it from this explanation  https://gmatclub.com/forum/ifxisani ... ml#p703553You have mentioned when x<0; xx as Negative * positive = x^2 is x<0, should it be Negative * negative = X^2 ? Can you please clarify further ?



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Re: If x is an integer, is xx<2^x ?
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25 May 2020, 03:17
Anuragjn wrote: Bunuel wrote: Anuragjn wrote: 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. Hi [b]Bunuel[/b]  Opening up an old thread but need some clarification. In this question you have taken x as x = x when x<0However, in another question  https://gmatclub.com/forum/isx11x1 ... 34652.htmlyou have taken x as x when x<0  can you please clarify the conditions wherein we have to take two different things ? Not sure I understand from where you've taken the red part. When x < 0, then x = x, so in this case \(x*x=x*(x)=x^2\). Hi Bunuel  Thanks for quick response. I have taken it from this explanation  https://gmatclub.com/forum/ifxisani ... ml#p703553You have mentioned when x<0; xx as Negative * positive = x^2 is x<0, should it be Negative * negative = X^2 ? Can you please clarify further ? An absolute value is never negative (NEVER). When x < 0, then x = x, but x, since x is negative, is (negative), so still POSITIVE (x = negative = positive). So, again, when x < 0, xx = x*(x) = negative*positive = x^2 = negative.
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Re: If x is an integer, is xx<2^x ?
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10 Jun 2020, 10:39
cucrose wrote: If x is an integer, is xx < 2^x?
(1) x < 0 (2) x = 10 xx<0 if x<0 xx>=0 if x>=0 In xx < 2^x RHS will be always positive i.e 2^x>0 for any value of x So We need to know the sign of x in order to solve this question, 1.x<0 Sufficient xx < 2^x is true 2.x=10 Sufficient xx < 2^x is true Hence answer is D




Re: If x is an integer, is xx<2^x ?
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