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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 \(|x+7|=8\);

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.

Answer: C.

Many thanks again ... I this the OA I have are definitly wrong

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

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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

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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