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

Exponents - If n and t are positive integers, is n a factor

This topic has 15 member replies
Goto page
  • 1,
  • 2
Next
II GMAT Destroyer!
Joined
10 Dec 2007
Posted:
400 messages
Thanked:
18 times
Target GMAT Score:
700
GMAT Score:
680
Exponents - If n and t are positive integers, is n a factor Post Sun Aug 17, 2008 12:10 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Hi, Interested in seeing the various approachs people have in answering this question ... please illustrate your logic/thinking when answering this. Thanks.

    If n and t are positive integers, is n a factor of t ?

    (1) n = 3^(n-2)

    (2) t = 3^n

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    sudhir3127 GMAT Destroyer! Default Avatar
    Joined
    07 Jul 2008
    Posted:
    829 messages
    Followed by:
    3 members
    Thanked:
    82 times
    Target GMAT Score:
    700+
    Post Sun Aug 17, 2008 12:14 am
    II wrote:
    Hi, Interested in seeing the various approachs people have in answering this question ... please illustrate your logic/thinking when answering this. Thanks.

    If n and t are positive integers, is n a factor of t ?

    (1) n = 3^(n-2)

    (2) t = 3^n
    are u sure abt the statement 1. it doesnt say anything abt "T"?

    sudhir3127 GMAT Destroyer! Default Avatar
    Joined
    07 Jul 2008
    Posted:
    829 messages
    Followed by:
    3 members
    Thanked:
    82 times
    Target GMAT Score:
    700+
    Post Sun Aug 17, 2008 12:22 am
    II wrote:
    Hi, Interested in seeing the various approachs people have in answering this question ... please illustrate your logic/thinking when answering this. Thanks.

    If n and t are positive integers, is n a factor of t ?

    (1) n = 3^(n-2)

    (2) t = 3^n
    are u this is not the question.. because i have seen such a question on some forum..

    If n and t are positive integers, is n a factor of t?
    (1) n = 3^(n-z)
    (2) t = 3^n

    II GMAT Destroyer!
    Joined
    10 Dec 2007
    Posted:
    400 messages
    Thanked:
    18 times
    Target GMAT Score:
    700
    GMAT Score:
    680
    Post Sun Aug 17, 2008 12:39 am
    Hi Sudhir,
    I have posted the question correctly. Everything you see there is correct.
    Also see attachment, which is screen shot of the question.
    Attachments

    This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.

    sudhir3127 GMAT Destroyer! Default Avatar
    Joined
    07 Jul 2008
    Posted:
    829 messages
    Followed by:
    3 members
    Thanked:
    82 times
    Target GMAT Score:
    700+
    Post Sun Aug 17, 2008 1:28 am
    i go with C.

    here the explanation.

    Statement 1. it doesnt say anything abt t .. hence in suffcient.

    statement 2.

    assume if n= 1 then t= 3 , n is a factor of t but if n= 2 t=9 but if n= 2 then t = 9 .. then n is not a factor of t. hence insufficient..

    when we take both together..

    statement 1 :
    n has to greater than or equal to 2 to be an interger.. thus the possible values of n are 1,3,9,27.....

    and statement 2. the t can be 3, 27......

    thus we are clear that every for all the values of n and t... n is a factor of t.

    Hope it helps..

    do let me know if u have any doubts..

    pepeprepa GMAT Destroyer! Default Avatar
    Joined
    08 Jul 2008
    Posted:
    661 messages
    Thanked:
    46 times
    Post Sun Aug 17, 2008 1:37 am
    If n and t are positive integers, is n a factor of t ?

    (1) n = 3^(n-2)
    Alone, this has no sens, the logic is just that there is no "t" in the equation so it is useless.

    (2) t = 3^n
    If n=2 then t=9, n is not a a factor of t
    But if n=1 and t=3, n is a factor of t (3=3*1)
    So it is insufficient, given we have example and counter-example.

    (1) & (2)
    n = 3^(n-2) can be written like that: n=(3^n)/(3^2)
    Then, 9*n=3^n

    Thanks to the 2) we have,
    t=9*n

    So it is clear n is a factor of t given they are both integers.
    My answer is C

    II GMAT Destroyer!
    Joined
    10 Dec 2007
    Posted:
    400 messages
    Thanked:
    18 times
    Target GMAT Score:
    700
    GMAT Score:
    680
    Post Sun Aug 17, 2008 1:42 am
    pepeprepa wrote:
    If n and t are positive integers, is n a factor of t ?

    (1) n = 3^(n-2)
    Alone, this has no sens, the logic is just that there is no "t" in the equation so it is useless.

    (2) t = 3^n
    If n=2 then t=9, n is not a a factor of t
    But if n=1 and t=3, n is a factor of t (3=3*1)
    So it is insufficient, given we have example and counter-example.

    (1) & (2)
    n = 3^(n-2) can be written like that: n=(3^n)/(3^2)
    Then, 9*n=3^n

    Thanks to the 2) we have,
    t=9*n

    So it is clear n is a factor of t given they are both integers.
    My answer is C
    Excellent explanation ... thanks !

    II GMAT Destroyer!
    Joined
    10 Dec 2007
    Posted:
    400 messages
    Thanked:
    18 times
    Target GMAT Score:
    700
    GMAT Score:
    680
    Post Sun Aug 17, 2008 4:16 am
    did anyone else have other approaches to this one ?

    sharad Just gettin' started! Default Avatar
    Joined
    24 Jul 2008
    Posted:
    6 messages
    Test Date:
    4-sept-08
    Post Mon Aug 18, 2008 8:02 am
    IMO a

    this gives n as 1

    n = 3^(n-2) or 3 = 3^(1)

    1 is factor for all the numbers...

    B is insufficient

    pepeprepa GMAT Destroyer! Default Avatar
    Joined
    08 Jul 2008
    Posted:
    661 messages
    Thanked:
    46 times
    Post Mon Aug 18, 2008 8:37 am
    yep sharad you seem to be right the only solution for n=3^(n-2) is 1 ...
    Need to check more the proposals and not skip them so fast

    II can you give OA

    kiran.raze Rising GMAT Star Default Avatar
    Joined
    19 May 2007
    Posted:
    45 messages
    Thanked:
    2 times
    Test Date:
    TBD
    Target GMAT Score:
    760
    GMAT Score:
    710
    Post Mon Aug 18, 2008 9:30 am
    Hi Pepeprepa,

    The solution to n=3^(n-2) is not 1 but n=3, when we have 3=3;

    which only means n=3 and so we cannot be sure whether it can be a factor of
    t,

    and option 2 alone is not sufficient i.e t=3^n because t/n = 3^n/n , which for n=1 is divisible and n=2 is not divisible , therefore insufficient.

    Together, of course we have t/n= 3^(n-2)/3^n which equals 9

    therefore sufficient ...

    Thanks,
    Kiran

    pepeprepa GMAT Destroyer! Default Avatar
    Joined
    08 Jul 2008
    Posted:
    661 messages
    Thanked:
    46 times
    Post Mon Aug 18, 2008 9:36 am
    Thanks for claryfing this post man, I don't know why I bugged between 1 and 3.
    Kind of small things which make you doubt, I was right indeed Very Happy

    II GMAT Destroyer!
    Joined
    10 Dec 2007
    Posted:
    400 messages
    Thanked:
    18 times
    Target GMAT Score:
    700
    GMAT Score:
    680
    Post Mon Aug 18, 2008 1:34 pm
    yes ... official answer is C.

    arorag GMAT Destroyer! Default Avatar
    Joined
    21 Jan 2008
    Posted:
    343 messages
    Thanked:
    4 times
    Post Mon Aug 18, 2008 6:56 pm
    There is no need to put the values.

    key point:
    Is t/n= integer

    Combining

    3^n/3^(n-2)= 9

    Post Wed Sep 16, 2009 9:20 pm
    Yes, combining by dividing expressions for t and n is great. Don't you need to be careful to test B with numbers, though? To see that you can get yes and no with varying n values?

    Thanks,
    J

    Best Conversation Starters

    1 j_shreyans 86 topics
    2 aditya8062 41 topics
    3 RiyaR 30 topics
    4 kamalakarthi 29 topics
    5 anksm22 27 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description GMATGuruNY

    The Princeton Review Teacher

    170 posts
    2 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    151 posts
    3 image description MBAPrepAdvantage

    MBAPrepAdvantage

    94 posts
    4 image description CriticalSquareMBA

    Critical Square

    60 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    58 posts
    See More Top Beat The GMAT Experts