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John checks every 8th item for color, and Colin checks every 12th item for durability. If 1,920 items passed by both of them, how many items were checked by both John and colin?

How do I figure this?

  • math -

    1920/12 = 160
    1920/8 = 240

    Can you do anything with that?

  • math -

    still confused! do they want to know how many items were checked by BOTH john and calvin, meaning the same item?

  • math -

    John checks items
    #8 #16 #24 #32 #40 .... #1920
    the 8 means he checks item #8 , not 8 items
    so isn't the above just like the times table for 8 ?
    how many entries are there to get to 1920 ?
    that would be 1920/8 or 160
    So John had to check 160 items and that last item would be item # 1920.
    Use the same argument for Colin.

    So John checked 160 items and Colin checked 240 items
    So number of items checked by BOTH John AND Colin = 400

    (I assumed that they were not looking at the same items, if they are checking the same line , then we have to subtract all common items from the total.
    A slightly more difficult question, but ...
    what numbers would be divisible by both 8 and 24 ? )

  • math -

    Its a multible choice question and the choices are 20,40,60,80 and I still don't see how to come up with any of these answers

  • Correction -math -

    You are right, I should have taken the intersection of the two sets, I mis-read the question

    so we are looking for numbers which are both divisible by 8 and by 12
    the smallest of these would be the LCM of 8 and 12 which is 24
    so the 24th is checked by both, the 48th is checked by both, etc
    then 1920/24 = 80

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