Manhattan Prep Algebra Guide 1 Problem Set #1 p.97

[arnfarn]

If 4x-12 ≥ x + 9, which of the following must be true?
(a) x > 6
(b) x < 7
(c) x > 7
(d) x > 8
(e) x < 8

The answer is supposed to be (a) but I don't think this is correct. If you solve the problem then the answer turns out to be x ≥ 7. x > 6 includes decimal numbers (i.e. 6.1, 6.2, 6.3) so that is a bad answer. Are we supposed to assume on the GRE that all variables are integers unless stated otherwise?

[tommywallach]

Hey Arnfarn,

Always very important to focus on the specific question that's being asked. The question says "Which of the following must be true?" This is very different than, for example, "Which of the following is a restatement of the above equation?" If all you had to do was rephrase the question, you'd be absolutely right. The rephrase is x >= 7.

However, that isn't an answer choice. But here's something you do know, if x is either equal to or greater than 7, it MUST be greater than 6 (because anything that is 7 or above is greater than 6), so answer choice (a) must be true.

(b) is not always true, because x could equal 7.
(c) is not always true, because x could equal 7.
(d) is not always true, because x could equal 7.5
(e) is not always true, because x could equal 10

Hope that helps!

-t