Value of Positive Integer x

Very Hard Problem Solving Arithmetic

Let x be a positive integer. What is the value of x?

Statement (1): $x^2 - 5x + 6 = 0$

Statement (2): $x$ is an even number and $x < 10$.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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% Correct78%