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If 3 < x < 7, Which of the following must be true?

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by Gmat_mission » Mon Apr 23, 2018 12:39 am
If 3 < x < 7, Which of the following must be true?

(A) 10 <= x^2 <= 48
(B) 10 < x^2 < 48
(C) 9.0001 < x^2 < 48.9999
(D) -100 < x^2< 100
(E) 10 < x^2 < 49


[spoiler]OA=D[/spoiler].

I am confused by this question. Shouldn't be B the correct answer? I'd appreciate some help, please.
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by Brent@GMATPrepNow » Mon Apr 23, 2018 6:19 am
Gmat_mission wrote:If 3 < x < 7, Which of the following must be true?

(A) 10 <= x^2 <= 48
(B) 10 < x^2 < 48
(C) 9.0001 < x^2 < 48.9999
(D) -100 < x^2< 100
(E) 10 < x^2 < 49


[spoiler]OA=D[/spoiler].

I am confused by this question. Shouldn't be B the correct answer? I'd appreciate some help, please.
If x > 3, then x COULD equal 3.00000000000000000000000001, in which case x^2 will be less than 9.0001
This means we can ELIMINATE answer choices A, B, C and E

By the process of elimination, we're left with D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Tue Apr 24, 2018 10:42 am
Gmat_mission wrote:If 3 < x < 7, Which of the following must be true?

(A) 10 <= x^2 <= 48
(B) 10 < x^2 < 48
(C) 9.0001 < x^2 < 48.9999
(D) -100 < x^2< 100
(E) 10 < x^2 < 49
Squaring our inequality, we have:

9 < x^2 < 49

Since -100 < 9 and 49 < 100, we can also say:

-100 < x^2 < 100

Alternate Solution:

Squaring our inequality, we have:

9 < x^2 < 49

We see that x^2 is any value strictly between 9 and 49. Looking at the answer choices, the only choice that includes this entire interval is choice D, -100 < x^2 < 100.

Note that the question stem did NOT ask for the solution set for x^2; instead, it asked which answer choice is true. Since we know that x^2 is any value strictly between 9 and 49, it is also true that x^2 is between -100 and 100, since all values between 9 and 49 are contained in the interval between -100 and 100.

Answer: D

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