What is the value of x + 7 ? : GMAT Data Sufficiency (DS)
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# What is the value of x + 7 ?

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What is the value of x + 7 ? [#permalink]

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06 Sep 2010, 14:00
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What is the value of │x + 7│?

(1) │x + 3│= 14
(2) (x + 2)^2 = 169
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Apr 2013, 00:17, edited 1 time in total.
Edited the OA.
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06 Sep 2010, 14:05
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Are you sure?
What is the source?

For example, in the case of (1), x could be 11 or -17.
So │x + 7│ could be 18 or 10.

The same in (2).

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06 Sep 2010, 14:10
I totally agree but this is making me crazy
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06 Sep 2010, 14:14
mehdiov wrote:
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x + 2)2 = 169

OA must be wrong here.

(1) $$|x+3|=14$$ --> $$x=11$$ or $$x=-17$$, so $$|x+7|=18$$ or $$|x+7|=10$$;
(2) $$(x+2)^2=169$$ --> $$x=11$$ or $$x=-15$$, so $$|x+7|=18$$ or $$|x+7|=8$$;

(1)+(2) $$|x+7|=18$$. Sufficient.

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06 Sep 2010, 14:16
Bunuel wrote:
mehdiov wrote:
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x + 2)2 = 169

OA must be wrong here.

(1) $$|x+3|=14$$ --> $$x=11$$ or $$x=-17$$, so $$|x+7|=18$$ or $$|x+7|=10$$;
(2) $$(x+2)^2=169$$ --> $$x=11$$ or $$x=-15$$, so $$|x+7|=18$$ or $$|x+7|=8$$;

(1)+(2) $$|x+7|=18$$. Sufficient.

Many thanks again ... I this the OA I have are definitly wrong
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06 Sep 2010, 15:54
Please, repost the question, in the second stem, I can not see that (x+2)2 is equal to (x+2)^2
Thank you
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06 Sep 2010, 19:50
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it should be C.....Since the master Bunuel himself says the OA must be C , M all but sure it is C
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02 Apr 2013, 19:33
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x + 2)2 = 169

I feel the answer should be E as in both the option we will get 2 different values of x.

Am I going wrong?
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02 Apr 2013, 21:05
3
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akshayb2 wrote:
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x + 2)2 = 169

I feel the answer should be E as in both the option we will get 2 different values of x.

Am I going wrong?

STAT1
|x+3| = 14
will give you two solutions
x+3 = 14 and x+3 = -14
x = 11, -17
SO, NOT SUFFICIENT

STAT2
(x+2)^2 = 169
x+2 = +-13
x = -15, 11
So, NOT SUFFICIENT

If you take STAT1 and STAT2 together then there is only one value of x which satisfies both the Statements and is x=11
so, x=11

Hope it helps!
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02 Apr 2013, 21:40
Guess I made calculation mistake....Anyways thanks a lot Ankit.. Its very clear explanation
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03 Apr 2013, 00:18
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Expert's post
akshayb2 wrote:
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x + 2)2 = 169

I feel the answer should be E as in both the option we will get 2 different values of x.

Am I going wrong?

Merging similar topics.

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Re: What is the value of x + 7 ? [#permalink]

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26 Jun 2013, 09:17
What is the value of │x + 7│?

Two cases:

If x≥7: (x+7) ===> x+7
if x≤7: -(x+7) ===> -x-7

(1) │x + 3│= 14

Two cases:

If x≥-3: (x+3) = 14 ===> x=11
Valid, as 11 falls within the range of x≥-2

If x<-3: -(x+3)=14 ===> -x-3=14 ===> -x=17 ===> x=-17
Valid, as -17 falls within the range of x≤-3

This presents us with two valid solutions for x.
INSUFFICIENT

(2) (x + 2)^2 = 169

(x + 2)^2 = 169
√(x + 2)^2 = √169
(square root of a function squared results in the absolute value of said function)
|x+2|=13

Two cases:

If x≥-2: |x+2|=13 ===> x+2=13 ===> x=11
Valid, as 11 falls within the range x≥-2

If x<-2: -(x+2)=13 ===> -x-2=13 ===> -x=15 ===> x=-15
Valid, as -15 falls within the range of x<-2
INSUFFICIENT

1+2) 1 and 2 share one identical answer (11)
SUFFICIENT

(C)
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Re: What is the value of x + 7 ? [#permalink]

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31 Oct 2015, 11:13
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Re: What is the value of x + 7 ? [#permalink]

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18 Sep 2016, 09:17
Correct answer is C. Here's why:

(1) │x + 3│= 14

You need to break this into the two corresponding values x could take on, thus we get the following to equations

x+3 =14 --> x = -11
x+3 = -14 --> x = 11

INSUFFICIENT - we don't know which value we are using in the main equation

(2) (x+2)^2 = 169
factors into x^2 + 4x + 4 = 169
simplifies to x^2 + 4x - 165 = 0 --> (x-11)(x+15) = 0

Thus x = 11 or -15

INSUFFICIENT - same reason as (1)

Together - (1) + (2) - We know the values x can take on between (1) and (2), therefore, putting them together we are able to cross of -15 and -11 because they are not common to both (1) and (2). We end up with x = 11
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Re: What is the value of x + 7 ? [#permalink]

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28 Sep 2016, 15:15
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mehdiov wrote:
What is the value of │x + 7│?

(1) │x + 3│= 14
(2) (x + 2)^2 = 169

Target question: What is the value of |x+7|?

Statement 1: |x+3| = 14
When solving questions involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots

So, x+3 = 14
OR
x+3 = -14
When we solve the two equations, we get x = 11 OR x = -17

NOTE: Although we got two different answers, we must check whether we get 2 different answers to the target question.

If x = 11, then |x + 7| = |11 + 7| = 18
If x = -17, then |x + 7| = |-17 + 7| = 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (x+2)² = 169
This means EITHER (x+2) = 13 OR (x+2) = -13
When we solve the two equations, we get x = 11 OR x = -15
If x = 11, then |x + 7| = |11 + 7| = 18
If x = -15, then |x + 7| = |-15 + 7| = 8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that |x + 7| = 18 OR 10
Statement 2 tells us that |x + 7| = 18 OR 8
So, if BOTH statements are true, then |x + 7| must equal 18
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

[Reveal] Spoiler:
C

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Re: What is the value of x + 7 ?   [#permalink] 28 Sep 2016, 15:15
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