• 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
  • 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
  • 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
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

If m, n, and p are integers, is m + n odd?

This topic has 3 expert replies and 0 member replies

Top Member

rsarashi Master | Next Rank: 500 Posts Default Avatar
Joined
24 Dec 2016
Posted:
182 messages
Followed by:
2 members
Thanked:
4 times
Most Conversational Member

If m, n, and p are integers, is m + n odd?

Post Sat May 27, 2017 9:56 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If m, n, and p are integers, is m + n odd?

    (1) m = p2 + 4p + 4

    (2) n = p2 + 2m + 1

    OAC

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun May 28, 2017 5:06 am
    rsarashi wrote:
    If m, n, and p are integers, is m + n odd?

    (1) m = p² + 4p + 4

    (2) n = p² + 2m + 1
    Statement 1:
    No information about n.
    INSUFFICIENT.

    Statement 2:
    Case 1: p=0, m=0, n=1
    Here, m+n = 0+1 = 1, with the result that the answer to the question stem is YES.
    Case 2: p=1, m=0, n=2
    Here, m+n = 0+2 = 2, with the result that the answer to the question stem is NO.
    INSUFFICIENT.

    Statements combined:
    m = (p+2)².
    n = p² + 2m + 1.

    Case 1: p = 0
    In this case:
    m = (0+2)² = 4.
    n = 0² + 2*4 + 1 = 9.
    m+n = 4+9 = 13.
    Here, the answer to the question stem is YES.

    Case 2: p = 1
    In this case:
    m = (1+2)² = 9.
    n = 1² + 2*9 + 1 = 20.
    m+n = 9+20 = 29.
    Here, the answer to the question stem remains YES.

    Cases 1 and 2 indicate that -- whether p is EVEN or ODD -- the answer to the question stem will always be YES.
    SUFFICIENT.

    The correct answer is C.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.



    Last edited by GMATGuruNY on Mon May 29, 2017 5:25 am; edited 1 time in total

    Thanked by: rsarashi, hdrupp
    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.
    Post Sun May 28, 2017 5:11 am
    I assume that statement 2 should be as follows...

    rsarashi wrote:
    If m, n, and p are integers, is m + n odd?

    (1) m = p² + 4p + 4

    (2) n = p² + 2p + 1

    OAC
    Target question: Is m + n odd?

    Statement 1: m = p² + 4p + 4
    No information about n.
    So, there's no way to answer the target question with certainty.
    Statement 1 is NOT SUFFICIENT

    Statement 2: n = p² + 2m + 1
    No information about n.
    So, there's no way to answer the target question with certainty.
    Statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Since both m and n both rely on the value of p, and since p is EITHER an odd integer or an EVEN integer. Let's examine each possible case.
    Case a: p is ODD.
    m = p² + 4p + 4 = (p +2 )² = (ODD +2 )² = (ODD )² = ODD
    n = p² + 2p + 4 = (p +1 )² = (ODD +1 )² = (EVEN)² = EVEN
    So, if p is odd, m+n = ODD + EVEN = ODD

    Case b: p is EVEN.
    m = p² + 4p + 4 = (p +2 )² = (EVEN+2 )² = (EVEN)² = EVEN
    n = p² + 2p + 4 = (p +1 )² = (EVEN +1 )² = (ODD )² = ODD
    So, if p is odd, m+n = EVEN + ODD = ODD

    So, regardless of whether p is even or odd, m+n will ALWAYS be ODD

    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer: C

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    Thanked by: rsarashi, hdrupp
    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!
    Post Tue May 30, 2017 12:29 am
    rsarashi wrote:
    If m, n, and p are integers, is m + n odd?

    (1) m = p^2 + 4p + 4

    (2) n = p^2 + 2m + 1

    OAC
    (m+n) would be odd if one of m and n is odd and the other is even.

    Statement 1: m = p^2 + 4p + 4

    => m+n = (p^2 + 4p + 4) + n = (p^2 + n) + EVEN + EVEN; since (p^2 + n) can be even or odd, we cannot determine whether m+n is odd.

    Statement 2: n = p^2 + 2m + 1

    => m+n = (p^2 + 2m + 1) + m = (p^2 + 3m) + ODD; since (p^2 + 3m) can be even or odd, we cannot determine whether m+n is odd.

    Statement 1 & 2:

    Adding Statement 1 and 2, we get

    m+n = (p^2 + 4p + 4) + (p^2 + 2m + 1)

    => m+n = 2p^2 + 4p + 2m + 5 = EVEN + EVEN + EVEN + ODD = ODD.

    Thus, m+n is odd. Sufficient.

    The correct answer: C

    Hope this helps!

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Singapore | Doha | Lausanne | and many more...

    Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

    Thanked by: hdrupp

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 65 topics
    3 Roland2rule 49 topics
    4 ardz24 44 topics
    5 LUANDATO 23 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    147 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    103 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    102 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    94 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts