Official Solution:


For a product of 3 integers to be even, at least one integer must be even. For example \(1 * 3 * 5 = 15\), odd vs. \(5 * 7 * 2 = 70\), even.

Statement (1) by itself is sufficient. For \((p - 1)(r + 1)\) to be odd, both \(p - 1\) and \(r + 1\) must be odd. Therefore, both \(p\) and \(r\) are even.

Statement (2) by itself is sufficient. The product of two integers is odd only if both integers are odd, therefore the result of \(q - r\) is odd. For a difference of two integers to be odd, one of the two must be even. One even integer is sufficient to make the product \(pqr\) even.


Answer: D
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zero is even number

I think this is a high-quality question and I don't agree with the explanation. For option 2, is it not possible that q is odd and r is 0, which makes (q-r) * (q-r) as odd and hence the statement is not sufficient because it will depend on the value of P.

Please clarify

I think this is a poor-quality question and I don't agree with the explanation. No you don't know if Q is 0 or not for 1) or if P is 0 in 2)

I think this is a poor-quality question and I don't agree with the explanation. What if one of p, r, q was zero?

I think we must keep our politeness whenever possible. The questions are repeated over and over. The simple fact of not getting it right worth analyzing it and putting it in you error log. Next time this mistake won't happen.