If it is true that \(x > -2\) and \(x < 7,\) which of the following must be true?

[Gmat_mission]

If it is true that \(x > -2\) and \(x < 7,\) which of the following must be true?

A. \(x > 2\)
B. \(x > -7\)
C. \(x< 2\)
D. \(-7 < x < 2\)
E. none of the above.

Answer: B

Source: Official Guide

[Scott@TargetTestPrep]

If it is true that \(x > -2\) and \(x < 7,\) which of the following must be true?

A. \(x > 2\)
B. \(x > -7\)
C. \(x< 2\)
D. \(-7 < x < 2\)
E. none of the above.

Answer: B

Source: Official Guide

Solution:

If x > -2 and x < 7, the value of x is between -2 and 7. Because all of these values are greater than -7, then we know that x > -7.

This type of problem gives rise to a lot of confusion. Let’s consider two easier examples, to display the logic used in this question. If we know that x = 0, is it true that x > -5? Yes, it is. Here’s another one: If 3 < x < 7, is it true that x >1? Yes, it is true (because all possible values of x (any number between 3 and 7) are greater than 1). Notice that in both of these examples, we are NOT trying to reconstruct the domain of x, as this was already accomplished in the question stem. Rather, we are simply making a true statement about the value(s) of x.

Answer: B