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2013 Math Kangaroo

Problem 11

Problem 11 · 2013 Math Kangaroo Medium
Number Theory divisibility

Daniel had 36 sweets. He shared them equally between his siblings. How many siblings can he definitely not have?

Show answer
Answer: D — 5
Show hints
Hint 1 of 3
Sharing equally means the 36 sweets must split into equal groups with none left over.
Still stuck? Show hint 2 →
Hint 2 of 3
Try sharing 36 sweets among each number of siblings and see if any are left over.
Still stuck? Show hint 3 →
Hint 3 of 3
The number that leaves some sweets left over is the one he cannot have.
Show solution
Approach: test each option for dividing 36
  1. 36 divides evenly by 2, 3, 4 and 6 (giving 18, 12, 9, 6).
  2. But 36 ÷ 5 is not a whole number.
  3. So he definitely cannot have 5 siblings.
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