What is the value of x + 7 ?

What is the value of |x + 7|?

(1) \(|x+3|=14\) --> \(x=11\) or \(x=-17\), so \(|x+7|=18\) or \(|x+7|=10\). Not sufficient.

(2) \((x+2)^2=169\) --> \(x=11\) or \(x=-15\), so \(|x+7|=18\) or \(|x+7|=8\). Not sufficient.

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

Answer: C.
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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!

Watch the following video to learn the Basics of Absolute Values


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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

Answer =

RELATED VIDEO

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.

The working is fairly simple here. My only doubt is we getting lX+7l=18 in each of the statement 1 and 2. So, the answer is C
But we also getting lX+7l = 10 (from statement 1 ) and lX+7l=8 (statement 2). So why we ignoring this values of lX+7l. And both of these are different values of lX+7l
Thanks

In DS when you have say a = 1 or a = 2 in (1) and a = 1 or a = 3 in (2), then when considering (1)+(2) you are taking the common value, so a = 1.

The same in the given question, both (1) and (2) give two possible values of |x+7|. When considering (1)+(2) |x+7| could only be one of those value, the one which is common for (1) and (2).
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S1:
|x+3| =14
=> x = -3 +/- 14
=> x = -17 or x = 11
NOT SUFFICIENT

S2:
\((x + 2)^2 = 169\)
=> |x+2| = 13
=> x =-2 +/-13
=> x = -15 or x = 11
NOT SUFFICIENT

Combining S1 & S2
x = 11
SUFFICIENT

IMO C

From a strategy point of view(question specific) i am posting.

|x+7| suggests that it would vary depending on x. So statements 1 and 2 both should give a unique value in order for either of them(A or B) or both of them individually(D) or together(C or E) to be sufficient.
But before that we must realise that |x+7| calls for us to know the sign of x first(x < 0, x = 0, x > 0) and then its unique value.

Both the statements we see are not suggesting any specific sign for x or it being '0'.
Statement 1: |x+3| is more or less same as |x+7| if we are trying to find the sign of x.
Statement 2: \((x + 2)^2 = 169\) = \((|x + 2|)^2 = 169\). Again we have |x+2| which is not helpful at all.

So, we can straight eliminate A, B & D(since both statement either deal in mod or squares) and jump to get to C or E. Hence doing that i solve it, saving precious time. Solving St.1 we have x = 11 or -17 and solving St. 2: x = 11 or -15.

If we have 'a' common value of x then the answer is C, else its E.
Here the common value is 11. So Answer is C.
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