Results 1 to 5 of 5

Math Help - How many numbers in the set {1, 2, . . . , 240} are divisible by...

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    3

    How many numbers in the set {1, 2, . . . , 240} are divisible by...

    Hey guys. Ive been having trouble with this question. Can someone show me how its done ?

    How many numbers in the set {1, 2, . . . , 240} are divisible by (a) at least ONE of the
    numbers 6, 8, or 9? (b) precisely TWO of the numbers 6, 8, or 9?

    thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    3
    I having trouble understanding that wiki article. How do I use it in my situation ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2010
    Posts
    11
    this problem is a pretty nice one.

    you should investigate what happens with de gcd and lcm first and "think about tiny cases" what if we are interested in {1,2,3,...20}?? make a reasoning there and then think about de whole question.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2010
    Posts
    193
    Let A_6,A_8,A_9 be the sets of integers between 1 and 240 that are divisible by 6, 8, and 9 respectively.

    We want to know how many of these integers are divisible by at least one of 6, 8, 9; this is the same as asking how many of these integers are in at least one of the sets I defined above.

    Saying something is in at least one of those sets is the same as saying that number is in the union of the sets. So we want to know how many elements there are in the set A_6\cup A_8\cup A_9.

    Apply the Inclusion-Exclusion principle to find |A_6\cup A_8\cup A_9|.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 30th 2011, 09:24 PM
  2. Replies: 4
    Last Post: July 18th 2011, 07:16 PM
  3. sum of the numbers less than p divisible by p?
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: March 9th 2011, 06:19 PM
  4. Replies: 2
    Last Post: November 4th 2010, 11:13 AM
  5. Replies: 3
    Last Post: April 30th 2010, 11:01 PM

Search Tags


/mathhelpforum @mathhelpforum