Problem 13 · 2025 Math Kangaroo
Medium
Number Theory
divisibility
The four-digit number 80?? is missing its last two digits. We know that this number is divisible by 8 and 9. What is the product of the last two digits?
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Answer: D — 24
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Hint 1 of 2
Divisible by both 8 and 9 means divisible by 72.
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Hint 2 of 2
Find the multiple of 72 between 8000 and 8099, then multiply its last two digits.
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Approach: use divisibility by 72
- A number divisible by 8 and 9 is divisible by 72.
- The multiple of 72 of the form 80__ is 8064 (= 72×112).
- Last two digits 6 and 4: product = 24.
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