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If 2 < x < 6, Which of the following must be true?

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If 2 < x < 6, Which of the following must be true?  [#permalink]

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New post 04 Oct 2016, 08:05
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A
B
C
D
E

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If 2 < x < 6, Which of the following must be true?

(A) 9 <= x^2 <= 25
(B) 5 < x^2 < 35
(C) 4 < x^2 < 36
(D) 4 <= x^2 <= 36
(E) 5 <= x^2 <= 35
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Re: If 2 < x < 6, Which of the following must be true?  [#permalink]

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New post 05 Oct 2016, 10:26
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sankalpvishu wrote:
If 2 < x < 6, Which of the following must be true?

(A) 9 <= x^2 <= 25
(B) 5 < x^2 < 35
(C) 4 < x^2 < 36
(D) 4 <= x^2 <= 36
(E) 5 <= x^2 <= 35

Dear sankalpvishu,

I'm happy to respond. :-)

My friend, I don't have a high opinion of this question. It's very much a one-trick-pony. I don't think highly of whatever the source might be.

The whole question depends on understanding that not all numbers are integers. If 2 < x < 6, then x could equal 3, 4, 5, or it could have values such as 5.8 or 2.00000001. It could be infinitely close to 2 or 6 without equaling those numbers. Thus, x^2 could be infinitely close to 4 or 36 without equaling those numbers. The answer must be (C).

Does this make sense?
Mike :-)
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Mike McGarry
Magoosh Test Prep


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If 2 < x < 6, Which of the following must be true?  [#permalink]

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New post 19 Jul 2018, 04:53
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Re: If 2 < x < 6, Which of the following must be true?  [#permalink]

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New post 06 Jan 2020, 20:40
sankalpvishu wrote:
If 2 < x < 6, Which of the following must be true?

(A) 9 <= x^2 <= 25
(B) 5 < x^2 < 35
(C) 4 < x^2 < 36
(D) 4 <= x^2 <= 36
(E) 5 <= x^2 <= 35

Taking square throughout the inequality in all the options.

(1) 3 <= x <= 5. Incorrect
(2) 2.25 < x < 5.9. Incorrect
(3) 2 < x < 6. Matches correct
(D) 2 <= x <= 6 . Incorrect
(E) 2.25 <= x <= 5.9. Incorrect

C is correct
GMAT Club Bot
Re: If 2 < x < 6, Which of the following must be true?   [#permalink] 06 Jan 2020, 20:40
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If 2 < x < 6, Which of the following must be true?

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