• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

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

tagged by: Brent@GMATPrepNow

Top Member

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

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

GMAT/MBA Expert

GMAT Instructor
Joined
25 Apr 2015
Posted:
1467 messages
Followed by:
13 members
43
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.

_________________
Scott Woodbury-Stewart Founder and CEO

GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12122 messages
Followed by:
1237 members
5254
GMAT Score:
770
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

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Legendary Member
Joined
20 Jul 2017
Posted:
503 messages
Followed by:
10 members
86
GMAT Score:
770
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.

_________________

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/

Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial

Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog

Top First Responders*

1 Jay@ManhattanReview 84 first replies
2 Brent@GMATPrepNow 73 first replies
3 fskilnik 50 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 fskilnik

GMAT Teacher

199 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

166 posts
3 Scott@TargetTestPrep

Target Test Prep

118 posts
4 Jay@ManhattanReview

Manhattan Review

98 posts
5 Max@Math Revolution

Math Revolution

95 posts
See More Top Beat The GMAT Experts