Problem 21 · 2011 Math Kangaroo
Stretch
Number Theory
divisibilitylast-digit
The five-digit number 24X8Y is divisible by 4, 5 and 9. What is the sum of X and Y?
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Answer: E — 4
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Hint 1 of 2
Use the rule for 5 first, then narrow Y with the rule for 4.
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Hint 2 of 2
Finally make the digit sum a multiple of 9 to find X.
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Approach: apply the divisibility rules for 5, 4, then 9
- Divisible by 5 means Y is 0 or 5; divisible by 4 needs the last two digits 8Y divisible by 4, forcing Y = 0.
- Divisible by 9 means 2+4+X+8+0 = 14+X is a multiple of 9, so X = 4.
- Then X + Y = 4 + 0 = 4.
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