What is the value of |x + 4|?

Question

(1) x^2 + 8x + 12 = 0
(2) x^2 + 6x = 0

GMATinsight · Accepted Answer

Question : |x + 4| = ?

Statement 1: x^2 + 8x + 12 = 0

x^2 + 6x + 2x + 12 = 0
i.e. (x+6)(x+2) = 0
i.e. x = -2 or -6

i.e. |x + 4| = |-2 + 4| or |-6 + 4| = 2

SUFFICIENT

Statement 2: x^2 + 6x = 0

i.e. x(x+6) = 0
i.e. x = 0 or 6

i.e. |x + 4| = |0 + 4| or |-6 + 4| = 4 or 2

NOT SUFFICIENT

Answer: Option  A

NavenRk · Answer

From 1) simplyfying the equation, (x+2) (x+6) = 0 , Insufficient 
fROM 2) x (x+6) = 0 , Insufficient.

1 + 2 we infer x+6 = 0 & x=-6. |x + 4| = 2. Hence C

GMATinsight · Answer

Hi NaveenRK,

Looks like you didn't try to calculate the value of |x + 4| by substituting the two values obtained from the First statement.

Fortunately Both values obtained from Statement 1 result in the identical value of |x + 4|   hence Statement 1 Alone is SUFFICIENT

bluesquare · Answer

1: factors to (x+6)(x+2) -> x = -6 or -2. so |x+4| = either |-6+4|=|-2|=2 or |-2+4|=|2|=2. Sufficient.
2: factors to x(x+6)=0. x can be 0 or -6. |x+4| can either be 2 from above, or |0+4|=4 if x=0. Insufficient. 
Answer is A>

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Statement (1) tells us that x^2 + 8x + 12 = 0. Factoring:
(x + 2)(x + 6) = 0
x = –2 or –6

The question asks for the value of |x + 4|. At first glance, it might appear that we have 2 values for x, and thus do not know the value of |x + 4|. However:
|(–2) + 4| = |2| = 2 |(–6) + 4| = |–2| = 2

Therefore Statement (1) is SUFFICIENT.

Statement (2) tells us that x^2 + 6x = 0. Factoring:
x(x + 6) = 0
x = 0 or –6

Testing both values for x:
|(0) + 4| = 4 |(–6) + 4| = |–2| = 2

We get two different values for x, so Statement (2) is INSUFFICIENT.

If we had not  Computed to Completion , we might have fallen into the trap of thinking that because Statement (1) gave us two values for x, we would get two different answers to the question. That was  not  the case: we got the same answer from both values.

The correct answer is A.

RAHUL_GMAT · Answer

Just my 2 cents on the question for Option A

Faster way to do this :

X^2+8x+12 = 0 
OR 
X^2+8X+16 - 4 = 0
OR
(X+4)^2 - 4 = 0
or
(X+4)^2 = 2^2
OR
|X+4|=2
Sufficient

bumpbot · Answer

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What is the value of |x + 4|?

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