|x|

[j_shreyans]

What is the value of |x|?

(1) |x^2 + 16| - 5 = 27

(2) x^2 = 8x - 16

My doubt : Statement 1 can't be solved by putting positive and then negative sign?

|x^2 + 16| - 5 = 27 and |x^2 + 16| - 5 = -27

So how statement 1 is sufficient because will get different value.

Please advise and correct me if I am wrong.

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Hi j_shreyans,

This question requires a bit of arithmetic and some Number Property knowledge. We're asked for the value of |X|.

Fact 1: |X^2 + 16| - 5 = 27

First, we can combine like terms...

|X^2 + 16| = 32

Since X^2 can never be negative, there is no way to end up with |-32| in this calculation. Thus, we have to look for the options that will create |+32|...

IF....
X = 4, then the result will be |32| = 32....and the answer to the question is |4| = 4
X = -4, then the result will also be |32| = 32...and the answer to the question is |-4| = 4
Fact 1 is SUFFICIENT

Fact 2: X^2 = 8X - 16

With a bit of algebra, we end up with...

X^2 - 8X + 16 = 0
(X-4)(X-4) = 0

Here, the ONLY value of X is +4, so |4| = 4
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[j_shreyans]

Hi Rich ,

Thanks for your reply , but have we to solve by putting negative sign also?

|x^2 + 16| - 5 = -27

Please advise.[/b]

[nikhilgmat31]

Hi Rich ,

Thanks for your reply , but have we to solve by putting negative sign also?

|x^2 + 16| - 5 = -27

Please advise.[/b]

x^2 + 16 can't be negative. You can't put 27 as negative. since 5 is out of mod symbol.

|x^2 + 16| - 5 = 27

|x^2 + 16| = 32

x^2 = 16

x=+- 4

|x| = 4 Statement 1 is sufficient.


Statement 2
x^2 -8x +16 =0
(x-4)^2 =0
x=4

statement 2 is sufficient

Answer is D

[nikhilgmat31]

shyrens - In simple terms -

you can't put - in front of 27
another option is
|x^2 + 16| -5 = 27

-(x^2 + 16) -5 = 27
-x^2 -16 -5 = 27
-x^2 = 27 + 21 = 48 which is not possible so x^2+16 can't be negative.

Hope it helps.