Determine the Value of a + b

Very Hard Data Sufficiency Determining Sufficiency

Let a and b be positive integers. We want to determine the value of a + b.

Statement (1): The product of a and b is 36.

Statement (2): The difference between a and b is 2.

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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