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

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