If p is an even integer and q is an odd integer

To solve this problem, we need to know our even/odd number properties:
even+even=even
even+odd=odd
odd+odd=even
even*even=even
even*odd=even
odd*odd=odd

Looking over the answer choices, we see that C is the only option that will work: 2p + q = even*even + odd = even + odd = odd.

lheiannie07 wrote:If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q
B. pq
C. 2p+q
D. 2(p+q)
E. 3p/q

Another approach is to take each answer choice and plug in an even number for p and an odd number for q, and see which answer choices yield an ODD value.
The easiest numbers to test are p = 0 (which is EVEN) and q = 1 (which is ODD)

We get:
A. p/q = 0/1 = 0, which is EVEN. ELIMINATE A
B. pq = (0)(1) = 0, which is EVEN. ELIMINATE B
C. 2p+q = 2(0) + 1 = 1, which is ODD. KEEP C
D. 2(p+q) = 2(0 + 1) = 2, which is EVEN. ELIMINATE D
E. 3p/q = (3)(0)/1 = 0, which is EVEN. ELIMINATE E

Answer: C

Cheers,
Brent

lheiannie07 wrote:If p is an even integer and q is an odd integer, which of the following must be an odd integer?

A. p/q
B. pq
C. 2p+q
D. 2(p+q)
E. 3p/q

Let’s examine our answer choices to determine which must produce an odd integer.

A) p/q

Since p is even and q is odd, p/q will never be an odd integer. (For example, 6/3 = 2.)

B) pq

Again, since p is even and q is odd, pq will never be an odd integer. (For example, 2 x 3 = 6.)

C) 2p+q

Since 2p is even and q is odd, 2p + q = even + odd = odd. Thus, 2p + q MUST BE an odd integer.

Answer: C