What is the value of |x|? (1) |x2 + 16| – 5 = 27

[amk250]

What is the value of |x|?

(1) |x2 + 16| - 5 = 27

(2) x2 = 8x - 16

The answer to this problem was D - Both statements alone are sufficient.

But for Statement 1, since there is an abolute value in the equation, don't you need to solve for both x2 + 16 and x2 - 16?

[StaceyKoprince]

Hi - can you please post the source for this problem? For copyright reasons, we need to have all sources posted.

Please list the name of the company or book and problem name or number.

Thanks!

[amk250]

Sorry, I meant Practice Exam problem.

This is a problem that I came across in one of the Manhattan GMAT practice Tests.

[StaceyKoprince]

Great, thanks. In future, it is really important to make sure you state that this is a question from the practice exam in the title of the thread - some people will want to avoid the thread so they aren't "spoiled" when they take practice exams.

You do need to solve for 2 values in statement 1, but that is not how you solve. Below is the correct math:
|x^2 + 16| - 5 = 27
|x^2 + 16| = 32
x^2 + 16 = 32 AND x^2 + 16 = -32
x^2 = 16 AND x^2 = -48
For the first of the 2 equations, x = +4 and -4
For the second of the 2 equations, there is no solution, because it is impossible to square something and get a negative number.
So the only 2 solutions are 4 and -4. The problem asks for |x| so 4 is the sole answer. Sufficient.