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If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
30 Nov 2016, 13:40
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If \(2 < x \leq {5}\), then which of the following MUST be true? A) \(1 < x^2 < 16\) B) \(4 < x^2 \leq {25}\) C) \(0 \leq {x^2} \leq {16}\) D) \(0 < x^2 \leq {25}\) E) \(4 \leq {x^2} < 36\)
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Re: If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
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GreenlightTestPrep wrote: If \(2 < x \leq {5}\), then which of the following MUST be true?
A) \(1 < x^2 < 16\)
B) \(4 < x^2 \leq {25}\)
C) \(0 \leq {x^2} \leq {16}\)
D) \(0 < x^2 \leq {25}\)
E) \(4 \leq {x^2} < 36\) If 2 < x < 5, then it's possible that x = 5, in which case x² = 25 In other words, it's possible that x² = 25 When we check the answer choices, we see that... Answer choice A says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE A Answer choice C says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE C Also, if 2 < x < 5, then it's possible that x = 0, in which case x² = 0 In other words, it's possible that x² = 0 When we check the remaining answer choices, we see that... Answer choice B says that 4 < x². In other words, it says that x² cannot equal 0. ELIMINATE B Answer choice D says that 0 < x². In other words, it says that x² cannot equal 0. ELIMINATE D We're left with 1 answer choice...E Cheers, Brent
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Re: If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
03 Dec 2016, 08:05
Brent
I understand your reasoning in your explanation, but I still don't see how x^2 could be a negative number? or exceed 25?
I can see that answer E is still technically valid even though it might not explicitly define the boundaries of x, but if the actual range is 0 <= x <= 25, this still falls within the bounds defined by E. Is this the correct reasoning?



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Re: If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
03 Dec 2016, 13:21
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rsudhakar wrote: Brent
I understand your reasoning in your explanation, but I still don't see how x^2 could be a negative number? or exceed 25?
I can see that answer E is still technically valid even though it might not explicitly define the boundaries of x, but if the actual range is 0 <= x <= 25, this still falls within the bounds defined by E. Is this the correct reasoning? Hi rsudhakar, Many students will assume that E is incorrect, because x² CANNOT equal 4. However, answer choice E does not suggest that x² can equal 4, it only states that x² must be GREATER THAN or equal to 4. Here's a similar example: If Joe has more than 5 shirts, which of the following can we conclude with certainty? A) Joe owns more than 6 shirts. NO. We can't conclude this, because it's possible that Joe owns exactly 6 shirts, and 6 is not greater than 6. B) Joe owns more than 3 shirts. YES. If Joe owns more than 5 shirts, then he definitely owns more than 3 shirts? Does this mean that Joe COULD own 2 shirts? No. If just means that we can be certain that he owns more than 3 shirts. Does that help? Cheers, Brent _________
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Re: If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
04 Dec 2016, 05:50
Brent
Thanks for the prompt response! Definitely makes sense now.



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Re: If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
11 Feb 2017, 04:07
While this makes sense, it's a really nasty question. Answer E, while correct, deliberately presents a misleading boundary. I guess like many other people, I answered D.



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Re: If [m]2 < x \leq {5}[/m], then which of the following MUST [#permalink]
08 Aug 2019, 22:32
I got it correct. Choice D doesn't cover when x is 0.
Choice E looks out of boundary, but, it covers everything question asks.




Re: If [m]2 < x \leq {5}[/m], then which of the following MUST
[#permalink]
08 Aug 2019, 22:32





