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Numbers Question

  1. May 7, 2008 #1
    I have a quick question. How many number less than 100,000 are odd numbers but START with an even number??
    I was thinking there are 50,000 odd numbers less than 100,000 but how many of those start with an even number?

    thanks
     
  2. jcsd
  3. May 7, 2008 #2
    Take it one digit at a time. Start within the one's digit. 1, 2, 3, 4, 5, 6, 7, 8, 9.. HOw many of those are even. Then move on to the 10's digit, 10 - 99 how many of those are even, and do you see a pattern between the one's digit place, and the 10's digit place, if so can you extend that to the 100's? 1,000's? 10,000's?
     
  4. May 7, 2008 #3
    not sure if you have learnt how to use AP to tackle this qns.

    2 4 6 8

    For numbers starting with 2, we have 2, (20-29) , (200-299), (2000-2999), (20000-29999)

    same for 4 6 and 8

    For odd # starting with 2 :

    For 2,
    0

    For 20-29,
    1st odd term is 21 , d is 2, last term is 29
    Tn = a + (n -1 )d
    29 = 21 + (n-1)2
    n = 5

    For 200 to 299,
    1st odd term is 201 , d is 2, last term is 299
    Tn = a + (n -1 )d
    299 = 201 + (n-1)2
    n = 50

    For 2000 to 2999,
    1st odd term is 2001 , d is 2, last term is 2999
    Tn = a + (n -1 )d
    2999 = 2001 + (n-1)2
    n = 500

    For 20000 to 29999,
    1st odd term is 20001 , d is 2, last term is 29999
    Tn = a + (n -1 )d
    29999 = 20001 + (n-1)2
    n = 5000

    Total # of terms = 4 x (5 + 50 + 500 + 5000) = 22220

    I hope this will be of some help
     
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