jimmyjamesdonkey wrote:

What is the value of y?

(1) 3|(x^2) – 4| = y – 2

(2) |3 – y| = 11

I try to elaborate this problem step by step.

1. Statement 1. the left side of the statement is always positive and can be in a range [0..+inf). Therefore, y can be in a range [2,+inf), or y>=2. The statement insufficient.

2. Statement 2. Apply If/then approach:

3. if (3-y)>=0 then 3-y=11 --> y=-8

4. Our answer must satisfy our condition: (3-(-8))=11>=0 - it satisfies. the condition (3-y)>=0 need only for checking our answer.

5. if (3-y)<0 then -3+y=11 --> y=14

6. Our answer must satisfy our condition: (3-14)=-11<0 - it satisfies. The condition (3-y)<0 need only for checking our answer.

7. Now, you should forget about the equation in the second statement and remember only that the second statement says: there is two possibilities: y=-8 and y=14. Your conditions were necessary only for opening modulus and verification of solutions.

8. Therefore, the second statement is insufficient to answer the question.

9. 1&2 statements. only y=14 satisfies y>=2 condition. Therefore, the answer is C.

Jimmyjamesdonkey, to clarify this question, you should ask yourself: For what purpose do we use conditions y>=3 and y<3. The purpose is to open modulus and check solution. No more.

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