If p, q and r and integers, and pqr/4 is an odd integer, is p an even

Statement 1: pq + r is an even integer
pq=ODD and r=ODD is not viable, since pqr is a multiple of 4 and thus must be EVEN.
Implication:
pq=EVEN and r=EVEN

Case 1: p=1, q=2 and r=2, with the result that \(\frac{pqr}{4} = 1\) and \(pq+r = 4\)
In this case, the answer to the question stem is NO.
Case 2: p=2, q=1 and r=2, with the result that \(\frac{pqr}{4} = 1\) and \(pq+r = 4\)
In this case, the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2: qr + p is an odd integer
Either qr=EVEN AND p=ODD or qr=ODD and p=EVEN.

The blue combination is satisfied by the values in Case 1 above:
Case 1: q=2, r=2 and p=1, with the result that \(\frac{pqr}{4} = 1\) and \(qr+p = 5\)
In this case, the answer to the question stem is NO.
An example of the red combination:
Case 3: q=1, r=1 and p=4, with the result that \(\frac{pqr}{4} = 1\) and \(qr+p = 5\)
In this case, the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 3, INSUFFICIENT.

Statements combined:
The red combination is not viable, since Statement 1 requires that r=EVEN.
Since only the blue combination is viable, p=ODD.
Thus, the answer to the question stem is NO.
SUFFICIENT.