Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

Given $p$ : $|x| > 2$ is a condition for $q$ : $x < -2$ .

Options:

Pick one

Solution

Analysis of the problem: If $|x| > 2$ , then $x 2$ ; If $x 2$ . Therefore, $p$ is a necessary but not sufficient condition for $q$ . Hence, the correct option is C.

Key Points:
1. Solving absolute value inequalities;
2. Sufficient and necessary conditions.

Therefore, the answer is $\boxed{\text{C}}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.