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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

I chose e too with 0 value as deciding factor for my choice but it turns out the 0 is considered an even number. I just googled it and found it out. Hope the understanding is correct.

First of all zero is an even number. Second answer can not be C, it should be D.

The product of three integers P, Q, and R is even if either of them is even.

(1) \((p-1)(r+1)=odd\). Product of two integers is odd only if both are odd. Hence \(p-1=odd\) and \(r+1=odd\), which means \(p\) and \(r\) are even. Sufficient.

(2) \((q-r)^2=odd\) --> \(q-r=odd\). Difference of two integers is odd only if one of them is odd and another is even. Hence \(p\) or \(r\) is even. Sufficient.

First of all zero is an even number. Second answer can not be C, it should be D.

The product of three integers P, Q, and R is even if either of them is even.

(1) \((p-1)(r+1)=odd\). Product of two integers is odd only if both are odd. Hence \(p-1=odd\) and \(r+1=odd\), which means \(p\) and \(r\) are even. Sufficient.

(2) \((q-r)^2=odd\) --> \(q-r=odd\). Difference of two integers is odd only if one of them is odd and another is even. Hence \(p\) or \(r\) is even. Sufficient.

I chose e too with 0 value as deciding factor for my choice but it turns out the 0 is considered an even number. I just googled it and found it out. Hope the understanding is correct.

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

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
_________________

The key here is any multiplication by an even number results in an even.

So therefore we're on the hunt for even numbers:

1) (p-1)(r+1) is odd. Only odd x odd gives = odd, so both p-1 and r+1 are odd and hence both are even. An even number in qpr will given an even results

Sufficient

2)Similar to above, odd x odd = odd. So q-r must be odd, and therefore one of q or r must be even. An even number in qpr makes it eve