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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] New post 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) \(-4 \leq {x^2} < 36\)
[Reveal] Spoiler: OA

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Re: If [m]-2 < x \leq {5}[/m], then which of the following MUST [#permalink] New post 30 Nov 2016, 13:42
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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] New post 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] New post 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] New post 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] New post 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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