• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • 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

If positive integers a and b are both odd,

This topic has 3 expert replies and 1 member reply

If positive integers a and b are both odd,

Post Mon Sep 25, 2017 6:57 pm
If positive integers a and b are both odd, which of the following must not be odd?

A) ab
B) a(ab)
C) b - a - 1
D) (a + b)/2
E) a - b

The OA is E.

If we set a=3 and b=5 the (a+b)/2 is 4 and it is not odd. Why option D is wrong?

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Most Active Expert Most Responsive Expert Most Thanked Expert
Top Reply
Post Tue Sep 26, 2017 4:50 pm
You asked about D specifically, so I'll only address that.

It actually comes down to the remainder of our odd integers when divided by 4. If they have different remainders (one has remainder 1, one has remainder 3), then the average of the two will be even. If they have the same remainder by 4 (both remainder 1 or both remainder 3), then the average will be odd.

A few examples:

5 + 7 => 12, average = 6
5 + 9 => 14, average = 7
7 + 11 => 11, average = 9

As a good follow up exercise, see if you can explain why this must be. (Hint: a multiple of 4 can be written as 4*some integer.)

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
Top Reply
Post Tue Sep 26, 2017 11:17 am
Hi Vincen,

This question can be approached with Number Property rules. We're told that A and B are both ODD, POSITIVE INTEGERS. We're asked which of the following MUST NOT be odd.

Answer A: (A)(B) = (odd)(odd) = odd
Answer B: (A)(A)(B) = (odd)(odd)(odd) = odd
Answer C: B - A - 1 = (odd) - (odd) - (odd) = odd
Answer D: (A+ B)/2 = (odd + odd)/2 = (even)/2 = COULD be even (re: 4/2 = 2) OR odd (re: 6/2 = 3)
Answer E: A - B = (odd) - (odd) = EVEN

There's only one answer that can NEVER be odd.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Most Active Expert Most Responsive Expert Most Thanked Expert
Post Tue Sep 26, 2017 4:50 pm
You asked about D specifically, so I'll only address that.

It actually comes down to the remainder of our odd integers when divided by 4. If they have different remainders (one has remainder 1, one has remainder 3), then the average of the two will be even. If they have the same remainder by 4 (both remainder 1 or both remainder 3), then the average will be odd.

A few examples:

5 + 7 => 12, average = 6
5 + 9 => 14, average = 7
7 + 11 => 11, average = 9

As a good follow up exercise, see if you can explain why this must be. (Hint: a multiple of 4 can be written as 4*some integer.)

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
Post Tue Sep 26, 2017 11:17 am
Hi Vincen,

This question can be approached with Number Property rules. We're told that A and B are both ODD, POSITIVE INTEGERS. We're asked which of the following MUST NOT be odd.

Answer A: (A)(B) = (odd)(odd) = odd
Answer B: (A)(A)(B) = (odd)(odd)(odd) = odd
Answer C: B - A - 1 = (odd) - (odd) - (odd) = odd
Answer D: (A+ B)/2 = (odd + odd)/2 = (even)/2 = COULD be even (re: 4/2 = 2) OR odd (re: 6/2 = 3)
Answer E: A - B = (odd) - (odd) = EVEN

There's only one answer that can NEVER be odd.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 lheiannie07 116 topics
2 LUANDATO 68 topics
3 swerve 65 topics
4 ardz24 65 topics
5 Roland2rule 64 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

198 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

181 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

168 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

134 posts
5 image description GMATGuruNY

The Princeton Review Teacher

119 posts
See More Top Beat The GMAT Experts