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If x/x, which of the following must be true for all
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Updated on: 09 Jul 2013, 08:56
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If \(\frac{x}{x} \lt x\), which of the following must be true about \(x\)? (\(x \ne 0\)) A. \(x\gt 2\) B. \(x \in (1,0) \cup (1,\infty)\) C. \(x \lt 1\) D. \(x = 1\) E. \(x^2 \gt 1\) M24
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Originally posted by praveenvino on 15 Jan 2011, 11:44.
Last edited by Bunuel on 09 Jul 2013, 08:56, edited 1 time in total.
Renamed the topic and edited the question.




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Re: range of root  GMAT Club test  M24
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15 Jan 2011, 13:47
praveenvino wrote: X/X < X . Which of the following must be true for all ?
a. X > 1 b. X is an element in (1,0) U (1,inf) c. X < 1 d. X = 1 e. X^2 > 1
Can some one explain how X can be zero for the above condition? x is in the denominator so it can not equal to zero as division be zero is undefined. Correct form of this question is below (m09 q22, discussed here: m09q2269937.html): If \(\frac{x}{x} \lt x\), which of the following must be true about \(x\)? (\(x \ne 0\))A. \(x\gt 2\) B. \(x \in (1,0) \cup (1,\infty)\) C. \(x \lt 1\) D. \(x = 1\) E. \(x^2 \gt 1\) \(\frac{x}{x}< x\) Two cases: A. \(x<0\) > \(\frac{x}{x}<x\) > \(1<x\). But as we consider the range \(x<0\) then \(1<x<0\) B. \(x>0\) > \(\frac{x}{x}<x\) > \(1<x\). So the given inequality holds true in two ranges \(1<x<0\) and \(x>1\). Answer: B. For more check: mathabsolutevaluemodulus86462.htmlHope it helps.
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Re: range of root  GMAT Club test  M24
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15 Jan 2011, 14:03
Thanks Bunuel. X not equals zero condition was actually missing in the question in m24. Thanks for your help.



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Re: If x/x, which of the following must be true for all
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11 Dec 2014, 23:00
A must be true too. If x>1 satisfy x/x<x then x>2 will do too. can anyone explain choice A? thanks!



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Re: If x/x, which of the following must be true for all
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12 Dec 2014, 05:51
pinguuu wrote: A must be true too. If x>1 satisfy x/x<x then x>2 will do too. can anyone explain choice A? thanks! x > 2 is NOT necessarily true. Consider x = 1/2.
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Re: If x/x, which of the following must be true for all
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22 Apr 2015, 18:22
Brunel, Can you please explain why option E is not feasible?



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Re: If x/x, which of the following must be true for all
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22 Apr 2015, 19:19
praveenvino wrote: If \(\frac{x}{x} \lt x\), which of the following must be true about \(x\)? (\(x \ne 0\))
A. \(x\gt 2\) B. \(x \in (1,0) \cup (1,\infty)\) C. \(x \lt 1\) D. \(x = 1\) E. \(x^2 \gt 1\)
M24 x < x*x xx*x< 0 roots of this equation are : 1,0,1 rest is explained in the attached image ... Answer B.
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If x/x, which of the following must be true for all
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23 Apr 2015, 00:44
AverageGuy123 wrote: Brunel, Can you please explain why option E is not feasible? Dear AverageuGuy123 As Bunuel explained above, Either 1 < x < 0Or x > 1Now, x as you know, represents the magnitude of x. Option E says that x^2 must be greater than 1. Let's first consider the case when 1 < x < 0A possible value of x in this case is 0.5 So, what is the value of x^2? It is equal to 0.25 Is it greater than 1? NOLet's now consider the case when x > 1A possible value of x in this case is 2. So, what is the value of x^2? It's 4. Is it greater than 1? YESSo, as we see, that x^2 CAN BE greater than 1. But can we say that x^2 MUST BE greater than 1? NO, because x^2 is not greater than 1 for all possible values of x. So, the key takeaway from this discussion is that: we need to be careful whether the question is asking about MUST BE TRUE statements or about CAN BE TRUE statements.Hope this helped!  Japinder
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Re: If x/x, which of the following must be true for all
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23 Apr 2015, 03:36
AverageGuy123 wrote: Brunel, Can you please explain why option E is not feasible? You can plug in numbers to eliminate options. "which of the following must be true about x" means that every acceptable value of x must lie in the range given in the correct option. The acceptable values of x are the values for which x/x < x. A. x>2 Must x be greater than 2? This should make you check for 2. 2/2 < 2 1 < 2 (True) So 2 is an acceptable value of x. But 2 is not greater than 2. So this option is not correct. This also makes you eliminate options (C) and (D). E. x^2>1 Must x be greater than 1 or less than 1? Check for 1/2 (1/2)/1/2 < 1/2 1 < 1/2 (False) Check for 1/2 (1/2)/1/2 < 1/2 1 < 1/2 (True) So x = 1/2 is an acceptable value but it does not lie in this range. Hence option (E) is also incorrect. Answer must be (B)
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Re: If x/x, which of the following must be true for all
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24 Apr 2015, 10:21
Hi All, This question can be dealt with in a variety of ways. It's actually really susceptible to TESTing VALUES, which we can use to determine possibilities and eliminate answers. We're told that X/X < X. The question asks what must be TRUE about X. While this inequality looks complicated, you can quickly prove some things about X.... IF.... X = 1 1/1 is NOT < 1 So X CANNOT be 1 Eliminate D. IF..... X = 2 2/2 IS < 2 So X CAN be 2 Eliminate A and C. IF.... X = 2 2/2 is NOT < 2 So X CANNOT be 2 Eliminate E. There's only one answer left.... Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If x/x, which of the following must be true for all
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26 Jan 2018, 23:48
Given: x/x < x since x >= 0 always multiply both LHS and RHS by x x < xx => x  xx < 0 => x(1  x) < 0 if x > 0, then 1  x < 0 to hold the above inequality => x > 1 => x(since x is positive in this case) > 1 if x < 0, then 1  x > 0 => x < 1 => 1 < x < 0 (to hold the above inequality)
Option B captures the above range perfectly



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Re: If x/x, which of the following must be true for all
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28 May 2020, 11:47
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Re: If x/x, which of the following must be true for all
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