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Algebra Difficulty 2.1 Junior Find the answer

"x > 3" is a ( ) condition for "x > 5".
A: Sufficient but not necessary
B: Necessary but not sufficient
C: Necessary and sufficient
D: Neither sufficient nor necessary

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is \text{B}, and the solution below works it through.

Solution

If "x > 3", then "x > 5" does not hold, for example, when x = 4;
Conversely, if "x > 5", then "x > 3" holds,
Therefore, "x > 3" is a necessary but not sufficient condition for "x > 5".
Hence, the correct option is B.

B \boxed{\text{B}}

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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.