• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If P is an odd integer and (P^2 + Q * R) is an even integer,

This topic has 2 expert replies and 0 member replies

If P is an odd integer and (P^2 + Q * R) is an even integer,

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true?

A. either Q or R is an odd integer
B. either Q or R is an even integer
C. both Q and R are odd integers
D. both Q and R are even integers
E. nothing can be concluded

OA=E.

I need help here. I've got confused. Help, please.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Gmat_mission wrote:
If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true?

A. either Q or R is an odd integer
B. either Q or R is an even integer
C. both Q and R are odd integers
D. both Q and R are even integers
E. nothing can be concluded
Let P=1.

Case 1: (P² + QR) = 2
Plugging P=1 into the equation above, we get:
1² + QR = 2
QR = 1.

If Q=1 and R=1, then B and D are not true.
Eliminate B and D.
If Q=2 and R=1/2, then A and C is not true.
Eliminate A and C.

The correct answer is E.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
Gmat_mission wrote:
If P is an odd integer and (P^2 + Q * R) is an even integer, then which of the following must be true?

A. either Q or R is an odd integer
B. either Q or R is an even integer
C. both Q and R are odd integers
D. both Q and R are even integers
E. nothing can be concluded
Since P is odd, P^2 is also odd.In order for P^2 + Q * R to be even, Q * R must be odd, since odd + odd = even. If we knew that both Q and R were integers, then necessarily both Q and R would have to be odd. However, Q could be 2 and R could be 1/2, in which case the product Q * R = 2 x 1/2 = 1 is still an odd integer. Therefore, we cannot conclude anything about the parity of Q and R. Thus, the answer is E.

Answer: E

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Top First Responders*

1 Brent@GMATPrepNow 69 first replies
2 fskilnik@GMATH 54 first replies
3 Jay@ManhattanReview 48 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

128 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 image description Max@Math Revolution

Math Revolution

92 posts
4 image description Jay@ManhattanReview

Manhattan Review

86 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

78 posts
See More Top Beat The GMAT Experts