Ironduke wrote:

Is the product of three integers P, Q, and R even?

1. (p-1) (r+1) is odd

2. Square of (q-r) is odd

a. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

b. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

d. EACH statement ALONE is sufficient

e. Statements (1) and (2) TOGETHER are NOT sufficient

Let me know your reasoning too.

product P Q R can be even only if one of them is even.

1. (p-1)(r+1)

both p-1 and r+1 are odd

means p and r are even => pqr is even suff.

2. (q-r)^2 is odd => q-r is odd.

there can be following cases for q-r to be odd

q is odd and r is even or q is even and r is odd

in any case one of either q or r are even so pqr will be even

hence d

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My debrief: done-and-dusted-730-q49-v40