Sponsored Ad:
Results 1 to 5 of 5

Thread: Logic Question

  1. #1
    Trying to make mom and pop proud
    Join Date
    Dec 2011
    Posts
    3
    Rep Power
    9


    Good post? Yes | No

    Logic Question

    Sponsored Ad:
    If the sequence X 1 (X one), X 2 (X two), X 3 (X three), .....Xn is such that X 1= 3 and X n+1 = 2 Xn -1 for n=1 , then X 20 - X 19 =

    A) 2 ^ 19
    B) 2 ^ 20
    C) 2 ^ 21
    D) (2 ^ 20) -1
    E) (2 ^ 21) -1


    Can some one please explain how this problem can be solved without making the lengthy calculations.

  2. #2
    Trying to make mom and pop proud
    Join Date
    Dec 2011
    Location
    United States
    Posts
    29
    Rep Power
    9


    Good post? Yes | No
    Quickly write out the first three terms:
    X1 = 3
    X2 = 2*X1=2*3
    X3=2*X2=2(2*3)=2^(2)*3

    Immediately you should see that XN=2^(n-1)*3. Then X20-X19=2^(19)*3-2^(18)*3=3*2^(18)[2-1]=3*2^(18)=X19.

  3. #3
    Trying to make mom and pop proud
    Join Date
    Oct 2010
    Posts
    7
    Rep Power
    10


    Good post? Yes | No
    Xn+1 = (2Xn) - 1 or Xn = (Xn-1) - 1

    X1 = 3 = 2^1 + 1
    X2 = 2*(3) - 1 = 5 = 2^2 + 1
    X3 = 2*5 - 1 = 9 = 2^3 + 1

    So, it follows that the nth term of the sequence is obviously Xn = 2^n + 1

    Therefore, X^20 - X^19 = 2^20 + 1 - 2^19 - 1 = 2^20 - 2^19 = 2^19 * (2-1) = 2^19.
    (Choice A is the answer)

  4. #4
    Trying to make mom and pop proud
    Join Date
    Feb 2012
    Posts
    10
    Rep Power
    9


    Good post? Yes | No
    X1 = 3
    X2 - X1 = 2 = 2^1
    X2 = 5
    X3 - X2 = 4 = 2^2
    X3 = 9
    X4 - X3 = 8 = 2^3
    X4 = 17
    We can clearly see the pattern of difference. Xn+1 - Xn = 2^n
    So, X20 - X19 = 2^19

  5. #5
    Within my grasp! sandeep_chads's Avatar
    Join Date
    Jan 2007
    Posts
    437
    Rep Power
    15


    Good post? Yes | No
    Mujtaba please clarify the question:

    Is it:
    X(n+1) = 2 X(n -1)

    OR
    X(n+1) = 2 X(n) -1

    If the former is true then none of the above choices are correct
    If the
    latter is true then A looks like the correct answer
    Hey Harvard, I am right here!!
    rep me if I made some sense

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Can't get the logic of this SC question
    By Incoan in forum GRE Sentence Completions
    Replies: 4
    Last Post: 11-07-2010, 05:07 AM
  2. Not seeing the logic to answer the following question
    By Darkthriller in forum GRE Math
    Replies: 2
    Last Post: 10-01-2010, 10:37 AM
  3. PowerPrep Question:Logic Problem
    By mickgreen58 in forum GRE Math
    Replies: 5
    Last Post: 04-04-2008, 07:43 AM
  4. Powerprep Question:Logic Type
    By mickgreen58 in forum GRE Math
    Replies: 5
    Last Post: 02-23-2008, 03:25 AM
  5. logic question
    By amathur in forum GRE Computer Science
    Replies: 2
    Last Post: 11-11-2005, 05:33 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •