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# If [m]-2 < x \leq {5}[/m], then which of the following MUST

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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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12% (00:41) correct 87% (00:53) wrong based on 33 sessions
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) $$-4 \leq {x^2} < 36$$
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 1647
Followers: 57

Kudos [?]: 1572 [3] , given: 8

Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]  30 Nov 2016, 13:42
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Expert's post
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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Brent Hanneson – Creator of greenlighttestprep.com

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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?
GRE Instructor
Joined: 10 Apr 2015
Posts: 1647
Followers: 57

Kudos [?]: 1572 [0], given: 8

Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink]  03 Dec 2016, 13:21
Expert's post
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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Brent Hanneson – Creator of greenlighttestprep.com

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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.
Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST   [#permalink] 11 Feb 2017, 04:07
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