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
Can some experts show me the easiest solution in this problem?
OA C
If p is an even integer and q is an odd integer
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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.
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.
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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.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
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
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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
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