What is the value of |x|?

Question

(1) |x^2 + 16| – 5 = 27

(2) x^2 = 8x – 16

my question about the answer:
 Answer is D.

Why is statement 1 sufficient?

the answer explanation states that x^2 must be positive. I do not understand why. Is it assuming that because the question asks what the value of |x| is that we can assume we only care about the negative value? This doens't make sense in my mind as a way to evaluate the statements because we're told to find the value of the |x|, and that we would find the values X COULD be, before utilize this to eliminate potential values of |x|?

official explanations;

Note that the question is asking for the absolute value of x rather than just the value of x. Keep this in mind when you analyze each statement.

(1) SUFFICIENT: Since the value of x2 must be non-negative, the value of (x2 + 16) is always positive, therefore |x2 + 16| can be written x2 +16. Using this information, we can solve for x:
|x^2 + 16| – 5 = 27
x^2 + 16 – 5 = 27
x^2 + 11 = 27
x^2 = 16
x = 4 or x = -4

Since |-4| = |4| = 4, we know that |x| = 4; this statement is sufficient.

(2) SUFFICIENT:
x^2 = 8x – 16
x^2 – 8x + 16 = 0
(x – 4)2 = 0
(x – 4)(x – 4) = 0 
x = 4

Therefore, |x| = 4; this statement is sufficient.

preetamsaha · Answer

What is the value of |x|?

(1) |x^2 + 16| – 5 = 27
or, (x^2 + 16) – 5 = 27  (irrespective of any value of x i.e. either positive or negative , x^2 always becomes positive ) 
or,x^2 = 16
or, |x| = 4  sufficient 
 
(2) x^2 = 8x – 16
or,x^2- 8x + 16 =0
or, (x-4)^2=0
or,x-4 = 0 
or, x=4 
so, IxI = 4   sufficient  
 
correct answer D

Lazybum · Answer

Why is x^2 always positive isn't the definition of absolute value |x|=+-x

Posted from my mobile device

preetamsaha · Answer

say, x= 5 , ---> x^2 = 25 , |x| = 5 
say, x= -5 , ---> x^2 = 25 , |x| = 5 
so, in both cases , both x^2 and |x| positive .

again. x^2 = 25 , ---> |x| = 5 ---> x= 5 or -5

so, thumb rule is |x| always POSITIVE .
x^2 is always POSITIVE .

Lazybum · Answer

okay interesting, we're allowed to use the question as a constraint in our evaluation. i thought you couldn't use |x| to evaluate it until the last step. meaning i thought we had to evalute staement 1 for both possible +/- solutions before inputting into |x|.

but it seem s like the reverse, we can use |x| to limit the cases.

preetamsaha · Answer

What is the value of |x|?

here, the question wants us to find the value of |x| , not the value of x. 
so, from both statement we have to find |x| only, rather than x. 
if, the question asked What is the value of x , statement 1 would NOT be sufficient then as x can take both +4 and -4. 
BUT, on the other side statement 2 would be sufficient because from it we can only get x= +4 ( or, +4 both are exactly identical )

so, a simple mod can change a different answer to an exactly same question.

Lazybum · Answer

such is the beauty of 1 element. thanks for taking the time to explain

preetamsaha · Answer

Lazybum 
You're welcome .

Bunuel · Answer

Discussed here: what-is-the-value-of-x-188356.html In case of questions please post there. Hope it helps. THIS TOPIC IS LOCKED AND ARCHIVED.

What is the value of |x|?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards