• 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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

Must be a multiple of what number?

This topic has 6 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
Joined
02 Jul 2017
Posted:
191 messages
Followed by:
1 members
Thanked:
1 times

Must be a multiple of what number?

Post Mon Jul 03, 2017 8:34 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

    A) 3

    B) 6

    C) 7

    D) 8

    E) 10

    E

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Mon Jul 03, 2017 8:46 pm
    AbeNeedsAnswers wrote:
    If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

    A) 3

    B) 6

    C) 7

    D) 8

    E) 10
    RULE:
    (multiple of k) ± (multiple of k) = multiple of k.

    Since y is a multiple of 5, let y=5a.
    Substituting y=5a into 3x + 4y = 200, we get:
    3x + 4(5a) = 200.
    3x + 20a = 200
    3x = 200 - 20a.
    3x = (multiple of 20) - (multiple of 20).

    In accordance with the rule above:
    (multiple of 20) - (multiple of 20) = multiple of 20.
    Thus:
    3x = multiple of 20.
    For 3x to be a multiple of 20, x must be a multiple of 20.
    Thus, x must also be a multiple of 10.

    The correct answer is E.

    _________________
    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.

    Thanked by: gmatdestroyer13
    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 Mon Jul 03, 2017 9:37 pm
    AbeNeedsAnswers wrote:
    If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

    A) 3

    B) 6

    C) 7

    D) 8

    E) 10

    E
    We have 3x + 4y = 200, such that y is a multiple of 5 and x and y are positive integers.

    Say y = 5k; where k is a positive integer

    => 3x + 20k = 200

    => 3x = 200 - 20k

    => x = 20(10 - k)/3

    => x is a multiple of 20.

    => x is a multiple of all the factors of 20: 1, 2, 4, 5, 10, and 20.

    Only one option qualifies, i.e. option E, the correct answer!

    The correct answer: E

    Hope this helps!

    Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Barcelona | Manila | Melbourne | and many more...

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

    Post Tue Jul 04, 2017 8:04 am
    I would recommend relying on strategy whenever possible; on this problem, using the rule that Mitch pointed out is probably the fastest approach. However, you could also TEST NUMBERS here.

    Since y is a multiple of 5, just test any multiple of 5:

    y = 5
    4y = 20
    3x + 4y = 200
    3x + 20 = 200
    3x = 180
    x = 60

    Eliminate C and D.

    Test another value:
    y = 10
    4y = 40
    3x + 40 = 200
    x = 160
    x = 160/3 --> not an integer. We have to test another value.

    y = 15
    4y = 60
    3x + 60 = 200
    3x = 140
    x = 140/3 --> not an integer

    y = 20
    4y = 80
    3x + 80 = 200
    3x = 120
    x = 40
    Eliminate A and B.

    The only answer left is E.

    This strategy is more cumbersome, but in a pinch it would get you there!

    _________________


    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.

    GMAT/MBA Expert

    Post Wed Jul 05, 2017 12:58 am
    We can write "y is a multiple of 5" as y = 5m, where m is some integer whose value we don't need.

    From there:

    3x + 4y =>

    3x + 4*5m =>

    3x + 20m

    We're told this equals 200, so

    3x + 20m = 200

    3x = 200 - 20m

    3x = 20 * (10 - m)

    So x must be a multiple of 20. 20 is itself a multiple of 10, so answer E fits.

    Thanked by: gmatdestroyer13
    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!

    GMAT/MBA Expert

    Post Wed Jul 05, 2017 1:00 am
    Alternatively, start with

    3x + 4y = 200

    3x = 200 - 4y

    3x = 4 * (50 - y)

    From this, we know x is a multiple of 4. We're told in the prompt that it's a multiple of 5. Since it's a multiple of 4 and of 5, it must also be a multiple of 4*5, or 20. That tells us x is also a multiple of ANY factor of 20 and E fits the bill.

    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!

    GMAT/MBA Expert

    Post Wed Jul 12, 2017 4:26 pm
    AbeNeedsAnswers wrote:
    If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

    A) 3

    B) 6

    C) 7

    D) 8

    E) 10
    Since y is a multiple of 5, we can let y = 5k and we have:

    3x + 4(5k) = 200

    3x = 200 - 20k

    3x = 20(10 - k)

    x = [20(10 - k)]/3

    Since x is an integer, (10 - k) must be divisible by 3. Then, x is the product of 20 times some integer [which is the quotient of (10 - k)/3]. Thus, x must be a multiple of 10. For instance, when k = 1, x = 90, when k = 4, x = 40, and when k = 7, k = 20.

    Answer: E

    _________________

    Scott Woodbury Stewart Founder & CEO
    GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
    5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 ardz24 40 topics
    5 LUANDATO 32 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    141 posts
    2 image description EconomistGMATTutor

    The Economist GMAT Tutor

    107 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

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

    EMPOWERgmat

    104 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts