MGRE online exam 3 Math question

[hilda.ho]

If |x+3| is less than or equal to 12 then which of the following must be true?

x > –15
x>= -12
x>=9
x < 8
x < 12


I was able to solve the question to get
x is greater than or equal to -15
x is les than or equal to 9


but I don't understand the MGRE reasoning as to why x is less than 12 ("all numbers in that range is definitely less than 12").
Ie. -16 is less than 12 but if you plug it into the equation it doesnt work. Also, if all of x is less than 12, then wouldn't x<8 be a correct answer as well?

I'm definitely misunderstanding something, and it would be really great for someone to lend me a hand!

Thanks in advance :)!

[tommywallach]

Hey Hilda,

This type of answer choice if often confusing to students, but it's a common trick on the GMAT.

Consider this:

x < 5, what must be true?

If x < 5, then also:

x < 12
x < 100
x < 1 billion

You're attempting to switch the logic (what we KNOW and what we're being ASKED) to disprove it, but you can't do that. Here's why:

Anything less than 5 is also less than 12,

BUT

Anything less than 12 is not also less than 5.

To connect to this question, we know:

-15 < x < 9 (with equal signs)

Anything in that range is less than 12, so x must be less than 12.

You are write that just because something is less than 12 doesn't mean it's in the range of -15 to 9, but that doesn't matter.

A metaphor would be:

Shape S is a square. What must be true?

CORRECT ANSWER: Shape S is a rectangle.

Because, by definition, any square is a rectangle. It doesn't work the other way around (every rectangle is not a square), but it doesn't have to.

Make sense?

-t