Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register
 

Properties Of Integers - OG

This topic has 1 expert reply and 5 member replies
Bookmark
Previous Topic Next Topic
shanice Really wants to Beat The GMAT! Default Avatar
Joined
05 Apr 2012
Posted:
110 messages
Followed by:
1 members
Thanked:
3 times
Target GMAT Score:
730
Properties Of Integers - OG Post Sat Apr 07, 2012 12:49 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

    (A) 3 (B)4 (c)7 (D)8 (E)12

    Answer is C.

    I arrived at this final equation 14=qn+n=n(q+1). I don't understand why the OG says that n must be a factor of 14 and so n=1,2,7 or 14 since n is a positive integer. The only positive integer factor of 14 given in the answer choices is 7.

    Can someone please explain to me in detail , why n must be a factor of 14?

    Please help. Thank you.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    neelgandham Community Manager
    Joined
    13 May 2011
    Posted:
    1060 messages
    Followed by:
    46 members
    Thanked:
    305 times
    Test Date:
    October 15th 2012
    Target GMAT Score:
    740
    Post Sat Apr 07, 2012 2:50 am
    I haven't checked the OG solution but here is what I think.

    When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

    We know that remainder is always greater than 0. i.e., n-4 > 0, implies n>4. Now going by your explanation..

    Quote:
    I arrived at this final equation 14=qn+n=n(q+1). I don't understand why the OG says that n must be a factor of 14 and so n=1,2,7 or 14 since n is a positive integer. The only positive integer factor of 14 given in the answer choices is 7.
    We can, now, eliminate the values n=1,2 as n(1)-1,n(2)-1 <4. so n = 7 or 14 and is always a factor of 14.

    p.s: I will check the OG solution and will get back to you with a better explanation, if any.

    _________________
    Anil Gandham
    Welcome to BEATtheGMAT
    My Quant Blog | Photography | Getting Started | BTG Community rules | MBA Watch
    Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/

    Thanked by: shanice
    shanice Really wants to Beat The GMAT! Default Avatar
    Joined
    05 Apr 2012
    Posted:
    110 messages
    Followed by:
    1 members
    Thanked:
    3 times
    Target GMAT Score:
    730
    Post Sat Apr 07, 2012 3:08 am
    Thanks for your fast response. But I still can't understand. Can you please explain further?

    Thank you.

    neelgandham Community Manager
    Joined
    13 May 2011
    Posted:
    1060 messages
    Followed by:
    46 members
    Thanked:
    305 times
    Test Date:
    October 15th 2012
    Target GMAT Score:
    740
    Post Sat Apr 07, 2012 4:06 am
    Hey Shanice,

    No problem! I will try to explain it further to the best of my knowledge.

    If a = b*c, where a,b,c are positive integers, then b,c are factors of a. Similarly, if 14 = n*(q+1), then n and (q+1) are factors of 14

    Let me solve this for you!
    The School way
    Firstly, do you agree that remainder is a non-negative value? If the answer is NO please read the quoted
    Quote:
    If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r and 0 ≤ r < x. - Source: Official Guide-12 Page 108
    Now that we agree that remainder is a non-negative value, we know n-4>0, which implies n>4. We also know that 14=qn+n=n(q+1), where q is the quotient and q>0.

    14 = n(q+1)
    14 = 1*14, 2*7, 7*2, 14*1 are the only possible combinations as n and q+1 are positive integers.

    Case 1: 14 = 1*14 = n(q+1), n = 1 and q =13, but n-4= -3<0, which should not be the case, as n>4
    Case 2: 14 = 2*7 = n(q+1), n = 2 and q =6, but n-4= -3<0, which should not be the case, as n>4
    Case 3: 14 = 14*1 = n(q+1), n = 14 and q =0, but n-4= 10>0, so n = 14 can be the answer
    Case 4: 14 = 7*2 = n(q+1), n = 7 and q = 1, but n-4= 3>0, so n = 7 can be the answer

    So, since n should be one among 1,2,7,14 Official Guide stated that n must be a factor of 14. I hope that answers your question.

    Here is an easier and a quicker solution to this question, the GMAT way

    Quote:
    When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?
    (A) 3, if n=3,the remainder = n-4 = -1, but when 10 is divided by 3 the remainder is 1. Incorrect!
    (B) 4, if n=4, the remainder = n-4 = 0, but when 10 is divided by 4 the remainder is 2. Incorrect!
    (c) 7, if n=7, the remainder = n-4 = 3, and when 10 is divided by 7 the remainder is 3. Correct!
    (D) 8 - Don't bother
    (E) 12 - Don't bother

    _________________
    Anil Gandham
    Welcome to BEATtheGMAT
    My Quant Blog | Photography | Getting Started | BTG Community rules | MBA Watch
    Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/



    Last edited by neelgandham on Sat Apr 07, 2012 9:02 am; edited 2 times in total

    Thanked by: shanice

    GMAT/MBA Expert

    Bill@VeritasPrep GMAT Instructor
    Joined
    29 Mar 2012
    Posted:
    1002 messages
    Followed by:
    138 members
    Thanked:
    389 times
    Target GMAT Score:
    800
    GMAT Score:
    780
    Post Sat Apr 07, 2012 7:30 am
    Once you're at the equation 14=n(q+1), you know that n * (q + 1) gives you a product of 14. Since we know n must be an integer, it (and by extension, q + 1) must be a factor of 14.

    _________________
    Take your GMAT prep on the go!

    For the first time, you can complete a full GMAT prep course on your mobile device. Download each of Veritas Prep’s 12 GMAT lessons directly on your iPad and iPhone.

    Download the Veritas Prep GMAT On Demand App Free

    Thanked by: shanice
    Access The Veritas Prep GMAT Simulator™- for FREE! Veritas Prep has launched their new GMAT Practice Test. Sign up to access the realistic testing environment and challenge yourself today! Get Started Now.
    shanice Really wants to Beat The GMAT! Default Avatar
    Joined
    05 Apr 2012
    Posted:
    110 messages
    Followed by:
    1 members
    Thanked:
    3 times
    Target GMAT Score:
    730
    Post Sat Apr 07, 2012 10:37 am
    A big thank you to neelgandham. I'm so happy as I could understand it now. Thank you for putting the effort to explain it to me in detail. I really appreciate it.

    And also not forgetting, Mr.Smith. Thank you.

    f430spy Just gettin' started! Default Avatar
    Joined
    31 Mar 2012
    Posted:
    1 messages
    Post Thu Apr 12, 2012 2:09 am
    10/n=q+(n-4)/n where q is an integer.

    14=n(q+1)->(q+1)=14/n

    Given that q+1 should be an integer, then n have to be a factor of 14.

    Best Conversation Starters
    1 varun289 40 topics
    2 guerrero 21 topics
    3 sana.noor 20 topics
    4 killerdrummer 19 topics
    5 sanaa.rizwan 14 topics
    See More Top Beat The GMAT Members...

    Most Active Experts
    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    		 203 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    		 140 posts
    3 image description Jim@StratusPrep

    Stratus Prep

    		 100 posts
    4 image description Anju@Gurome

    Gurome

    		 99 posts
    5 image description Jon@Admissionado

    Admissionado

    		 49 posts
    See More Top Beat The GMAT Experts