• EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist 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

For consecutive integers x, y, and z, where x > y > z,

This topic has 6 expert replies and 2 member replies
hazelnut01 Master | Next Rank: 500 Posts Default Avatar
Joined
19 Nov 2016
Posted:
161 messages
Followed by:
4 members
Thanked:
2 times

For consecutive integers x, y, and z, where x > y > z,

Post Sat May 20, 2017 5:43 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x^2 - y^2 ) ( y^2 - z^2)?

    (A) 63

    (B) 99

    (C) 195

    (D) 276

    (E) 323

    Source : Veritas Prep
    OA=D

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    GMATinsight Legendary Member
    Joined
    10 May 2014
    Posted:
    998 messages
    Followed by:
    21 members
    Thanked:
    203 times
    Post Sat May 20, 2017 7:14 pm
    ziyuenlau wrote:
    For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x^2 - y^2 ) ( y^2 - z^2)?

    (A) 63

    (B) 99

    (C) 195

    (D) 276

    (E) 323

    Source : Veritas Prep
    OA=D
    The difference/sum of two consecutive number must be odd because two consecutive numbers involve one even and one odd so their sum and difference is always odd

    Also product of odd numbers will always be odd

    Hence Option D is not possible due to being and even number

    Answer: Option D

    _________________
    Prosper!!!
    Bhoopendra Singh & Sushma Jha
    "GMATinsight"
    Contact Us
    Testimonials
    To register for One-on-One FREE ONLINE DEMO Class Call/e-mail
    e-mail: info@GMATinsight.com
    Mobile: +91-9999687183 / +91-9891333772
    Get in touch for SKYPE-Based Interactive Private Tutoring
    One-On-One Classes fee - US$40 per hour &
    for FULL COURSE (38 LIVE Sessions)-US$1000

    "Please click on 'Thank' if you like my post/response."

    Classroom Centres Address:
    GMATinsight
    Dwarka, New Delhi-110075 and Shivalik New Delhi

    Post Sun May 21, 2017 4:57 am
    ziyuenlau wrote:
    For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of (x² - y²)(y² - z²)?

    (A) 63

    (B) 99

    (C) 195

    (D) 276

    (E) 323

    The keyword here is CONSECUTIVE INTEGERS.
    Notice that consecutive integers alternate ODD, EVEN, ODD, EVEN, ODD, EVEN, ....

    Also notice that we can factor the given expression as follows:
    (x² - y²)(y² - z²) = (x + y)(x - y)(y + z)(y - z)

    Since x and y are consecutive integers, one must be ODD and one must be EVEN
    This means that (x + y) is ODD and (x - y) is ODD

    Likewise, y and z are consecutive integers, one must be ODD and one must be EVEN
    This means that (y + z)is ODD and (y - z) is ODD

    So, (x² - y²)(y² - z²) = (x + y)(x - y)(y + z)(y - z)
    = (ODD)(ODD)(ODD)(ODD)
    = ODD

    So, the expression must evaluate to be odd.

    Answer: D (since 276 is EVEN)

    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: gmatdestroyer13
    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 Sun May 21, 2017 10:08 am
    Hi ziyuenlau,

    GMAT questions are almost always built around patterns - even if you don't realize that the pattern is there, you can probably do a bit of 'brute force' work and define the pattern. By extension, if you know the pattern, then you should be able to use that knowledge to your advantage to either answer the question immediately (or do another step or two of work to get the answer).

    Here, we're given some specific facts to work with:
    1) X, Y and Z are CONSECUTIVE integers
    2) X > Y > Z

    We're asked for what CANNOT be the value of (X^2 - Y^2)(Y^2 - Z^2).

    Let's TEST VALUES and see if a pattern emerges...

    IF... X = 3, Y = 2, Z = 1....
    (9 - 4)(4 - 1) = (5)(3) = 15

    So "15" is a possible answer. Also note that we ended up multiplying two ODD numbers together... Let's try another TEST....

    IF... X = 4, Y = 3, Z = 2....
    (16 - 9)(9 - 4) = (7)(5) = 35

    So "35" is a possible answer. Notice that we again ended up multiplying two ODD numbers together... That looks like a pattern. If the end result is just going to be an ODD number every time, then there's clearly an answer that CANNOT be the value...

    If you're not convinced yet, then try another example (and feel free to try as many as you like - as the numbers increase, you'll eventually hit all 4 of the possible answers, at which point you'll know which answer is NOT possible.

    Final Answer: D

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: gmatdestroyer13
    Post Sun May 21, 2017 3:26 pm
    You can always represent consecutive integers algebraically, because they have a known relationship:
    If x, y, and z are consecutive integers where x > y > z, then:
    y = z + 1
    x = z + 2

    So you could rephrase: (x² - y²)(y² - z²)
    ((z + 2)² - (z + 1)²)((z + 1)² - z²)
    ((z² + 4z + 4) - (z² + 2z + 1))((z² + 2z + 1) - z²)
    (2z + 3)(2z + 1)
    4z² + 8z + 3

    4z² and 8z will always be even, so 4z² + 8z + 3 will always be odd.

    That said, it would be easier to just think in terms of EVEN and ODD from the beginning, as other posters have pointed out.

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


    Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

    Thanked by: gmatdestroyer13
    Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
    hoppycat Senior | Next Rank: 100 Posts Default Avatar
    Joined
    21 May 2017
    Posted:
    36 messages
    Post Fri Jun 23, 2017 9:51 am
    I tried eliminating by finding values that worked.
    I gave up after 3 minutes. Any pointers for going that way?

    Post Fri Jun 23, 2017 11:29 am
    Hi hoppycat,

    Before we can discuss how you might speed up on these types of questions, it would help to know what you actually did for those 3 minutes. What was your first TEST case? What other examples did you try? How much of your work did you write down (and how much did you do 'in your head?')? Did you recognize that the end calculation was ALWAYS an ODD number?

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: lywalk
    Post Sat Jun 24, 2017 12:12 am
    hazelnut01 wrote:
    For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x^2 - y^2 ) ( y^2 - z^2)?

    (A) 63

    (B) 99

    (C) 195

    (D) 276

    (E) 323

    Source : Veritas Prep
    OA=D
    Very good solutions by experts. One more from my side.

    We know that x, y and are consecutive integers such that x > y > z.

    By looking at the expression (x^2 - y^2)*(y^2 - z^2), we see that the expression can have many possible values. Secondly, if you scan the options, you find that only one option is even, which is option D. So let's think in that direction.

    If z is odd, then y is even and x is odd.

    => (x^2 - y^2)*(y^2 - z^2) = (Odd^2 - Even^2)*(Even^2 - Odd^2)

    => (Odd - Even)*(Even - Odd) = Odd*Odd = Odd

    If z is even, then y is odd and x is even.

    => (x^2 - y^2)*(y^2 - z^2) = (Even^2 - Odd^2)*(Odd^2 - Even^2)

    => (Even - Odd)*(Odd - Even) = Odd*Odd = Odd

    Thus, in each case, the resultant value is ODD, or option D, 276 is not a possible value.

    The correct answer: D

    Hope this helps!

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Jakarta | Nanjing | Berlin | and many more...

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

    Thanked by: lywalk
    Post Sat Jun 24, 2017 12:15 am
    hazelnut01 wrote:
    For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x^2 - y^2 ) ( y^2 - z^2)?

    (A) 63

    (B) 99

    (C) 195

    (D) 276

    (E) 323

    Source : Veritas Prep
    OA=D
    Very good solutions by experts. One more from my side.

    We know that x, y and are consecutive integers such that x > y > z.

    By looking at the expression (x^2 - y^2)*(y^2 - z^2), we see that the expression can have many possible values. Secondly, if you scan the options, you find that only one option is even, which is option D. So let's think in that direction.

    If z is odd, then y is even and x is odd.

    => (x^2 - y^2)*(y^2 - z^2) = (Odd^2 - Even^2)*(Even^2 - Odd^2)

    => (Odd - Even)*(Even - Odd) = Odd*Odd = Odd

    If z is even, then y is odd and x is even.

    => (x^2 - y^2)*(y^2 - z^2) = (Even^2 - Odd^2)*(Odd^2 - Even^2)

    => (Even - Odd)*(Odd - Even) = Odd*Odd = Odd

    Thus, in each case, the resultant value is ODD, or option D, 276 is not a possible value.

    The correct answer: D

    Hope this helps!

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Jakarta | Nanjing | Berlin | and many more...

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

    Thanked by: lywalk

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 LUANDATO 44 topics
    5 ardz24 40 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

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

    EMPOWERgmat

    110 posts
    3 image description EconomistGMATTutor

    The Economist GMAT Tutor

    109 posts
    4 image description GMATGuruNY

    The Princeton Review Teacher

    107 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    72 posts
    See More Top Beat The GMAT Experts