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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Feb 27, 2018 6:52 pm

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

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Source: Beat The GMAT — Problem Solving | Tue Feb 27, 2018 6:52 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Wed Feb 28, 2018 6:05 am

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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 28, 2018 7:01 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Mar 01, 2018 5:37 pm

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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