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# What is the value of |x + 4|?

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Math Expert
Joined: 02 Sep 2009
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What is the value of |x + 4|?  [#permalink]

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18 Jun 2015, 03:18
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Difficulty:

55% (hard)

Question Stats:

58% (01:14) correct 42% (01:17) wrong based on 288 sessions

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What is the value of |x + 4|?

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

Kudos for a correct solution.

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What is the value of |x + 4|?  [#permalink]

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18 Jun 2015, 06:47
2
1
Bunuel wrote:
What is the value of |x + 4|?

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

Kudos for a correct solution.

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

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Re: What is the value of |x + 4|?  [#permalink]

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18 Jun 2015, 07:58
Bunuel wrote:
What is the value of |x + 4|?

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

Kudos for a correct solution.

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
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Re: What is the value of |x + 4|?  [#permalink]

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18 Jun 2015, 08:01
NavenRk wrote:
Bunuel wrote:
What is the value of |x + 4|?

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

Kudos for a correct solution.

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

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
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Re: What is the value of |x + 4|?  [#permalink]

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18 Jun 2015, 23:53
1
Bunuel wrote:
What is the value of |x + 4|?

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

Kudos for a correct solution.

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.
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Re: What is the value of |x + 4|?  [#permalink]

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22 Jun 2015, 05:38
1
Bunuel wrote:
What is the value of |x + 4|?

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

Kudos for a correct solution.

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.

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Re: What is the value of |x + 4|?  [#permalink]

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16 Aug 2018, 02:22
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Re: What is the value of |x + 4|?   [#permalink] 16 Aug 2018, 02:22
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