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March 27, 2017

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Jonah has a large collection of marbles. He notices that if he borrows 5 marbles from a friend, he can arrange the marbles in rows of 13 each. What is the remainder when he divides his original number of marbles by 13?

  • math - ,

    Now that he has the extra 5 marbles, his number must be a multiple of 13, that is, it divides evenly by 13
    So obviously before he had the 5 his number must have had a remainder of 5 when divided by 13

    e.g suppose he originally had 320
    when divided by 13 we get 24 rown with 5 marbles left over. So he gets 5 from his friend and now has 325 , which divides by 13 to get 25 rows.

  • argh - fuzzy math - ,

    let me try this again.


    Now that he has the extra 5 marbles, his number must be a multiple of 13, that is, it divides evenly by 13
    So obviously before he had the 5 his number must have had a remainder of 13-5 or 8 when divided by 13

    e.g suppose he originally had 320
    when divided by 13 we get 24 rown with 8 marbles left over. So he gets 5 from his friend and now has 325 , which divides by 13 to get 25 rows.
    325÷13=25 R 0
    324÷13 =24 R 12
    323÷13=24 R 11
    322÷13 = 24 R 10
    321÷13 = 24 R 9
    320÷13 = 24 R 8
    320÷13 = 24 R 7
    etc

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