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Math_Moron

  • 4 years ago

How many positive integers less than 100 have a remainder of 3 when divided by 7?

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  1. abtrehearn
    • 4 years ago
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    14.

  2. satellite73
    • 4 years ago
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    \[3,7+3,2\times 7+3,3\times 7+3,...\]

  3. satellite73
    • 4 years ago
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    so abtrehearn is right. since \[14\times 7+3=101\] which tells us that there are 13 +1 because of the first one

  4. Math_Moron
    • 4 years ago
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    Are u counting zero? If so why?

  5. LA-MrC
    • 4 years ago
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    I'm thinking 13.

  6. satellite73
    • 4 years ago
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    because 7 goes in to 3 zero times with a remainder of 3

  7. Math_Moron
    • 4 years ago
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    I was thinking what LA-Mrc said but my book says the answer is 14. If 7 doesn't go into 3 wouldn't the remainder be 7 : ?

  8. LA-MrC
    • 4 years ago
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    Here's how I worked it out: 10 is the first positive integer that can be divide by 7 with a remainder of 3. The next is 17, then 24, ... all the way to 94.

  9. LA-MrC
    • 4 years ago
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    10, 17, 24, ..., 94 That should be 13 terms.

  10. abtrehearn
    • 4 years ago
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    The number 3 is also in the list of positive integers less than 100 whose remainder is 3 upon dividing by 7. The list is {3, 10, 17, ... , 94}.

  11. LA-MrC
    • 4 years ago
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    I guess I missed the first one, i.e., 3.

  12. LA-MrC
    • 4 years ago
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    Good job, abtrehearn,

  13. Math_Moron
    • 4 years ago
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    I'm not sure I understand how 3 works also : /

  14. abtrehearn
    • 4 years ago
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    Ten-four, IA-MrC :^)

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