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Intern  Joined: 22 Jun 2010
Posts: 29
What is the value of x + 7 ?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 66% (01:31) correct 34% (01:28) wrong based on 1087 sessions

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What is the value of │x + 7│?

(1) │x + 3│= 14
(2) (x + 2)^2 = 169

Originally posted by mehdiov on 06 Sep 2010, 15:00.
Last edited by Bunuel on 03 Apr 2013, 01:17, edited 1 time in total.
Edited the OA.
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Re: nightmare :)  [#permalink]

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1
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).

IMO, the answer is C.
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Re: nightmare :)  [#permalink]

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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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Re: nightmare :)  [#permalink]

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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.

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Re: nightmare :)  [#permalink]

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1
it should be C.....Since the master Bunuel himself says the OA must be C , M all but sure it is C GMAT Tutor G
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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
Hence, Answer will be C

Hope it helps!
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Re: What is the value of x + 7 ?  [#permalink]

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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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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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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

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

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Statement 1: |x+3| = 14

We need to consider the modulus sign and build cases

Case I : x + 3 > 0

If X + 3 > 0 then |x+3| will be positive and hence we will get x+3 = 14 => x=11

Substitute back and see if satisfies the condition; 11+3 = 14 > 0 --> Keep it

Case II: X+3 < 0

If x+3 < 0; then |x+3| will be negative => -(x+3) =14 => -x -3 =14 => -x=17 => x=-17

Substitute back and see if satisfies the condition; -17 +3 = -14 < 0 --> Keep it

Two different values => A alone is not sufficient

Statement II: $$(x+2)^{2}$$ = 169

$$\sqrt{(x^{2})}$$ = |x| and hence we can say that |x+2|=13

Case I: x+2>0

Similar to st. 1: we can say that |x+2| will be positive and hence it will be x+2=13 => x=11

Substitute back and see if satisfies the condition; 11 +2 = 13 > 0 --> Keep it

Case II: x+2<0

Similar to st. 1: we can say that |x+2| will be negative and hence it will be -(x+2) => -x-2=13 => x=-15

Substitute back and see if satisfies the condition; -15+2 = -13 < 0 --> Keep it

Two different values => B alone is not sufficient

Combining A and B, we get a common value of 11 and hence C is sufficient to answer the question.
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Re: What is the value of x + 7 ?  [#permalink]

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mehdiov wrote:
What is the value of │x + 7│?

(1) │x + 3│= 14
(2) (x + 2)^2 = 169

Break down each statement

Stmnt 1

Pos

x + 3 =14
x= 11

Neg

- l x +3l =14
-x -3 =14
-x = 17
x= -17

Insuff

Stmnt 2

(x +2)^2 =169

x= 11, -15

Insuff

Stmnt 1 & 2

X must be 11

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