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2016 Math Kangaroo

Problem 5

Problem 5 · 2016 Math Kangaroo Medium
Number Theory divisibility

If a positive whole number x is divided by 6, the remainder is 3. What is the remainder if 3x is divided by 6?

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Answer: B — 3
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Hint 1 of 2
Write x as a multiple of 6 plus 3.
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Hint 2 of 2
Multiply by 3 and see what is left over mod 6.
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Approach: remainder arithmetic
  1. x leaves remainder 3, so 3x leaves the same remainder as 3×3 = 9.
  2. 9 divided by 6 leaves remainder 3.
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