Problem 4 · 2010 Math Kangaroo
Medium
Counting & Probability
careful-countingdivisibility
How many four-digit numbers, made up of odd digits only, are divisible by 5?
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Answer: D — 125
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Hint 1 of 2
Divisible by 5 fixes the last digit, but it must also be odd.
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Hint 2 of 2
Count the free choices for the other three digits.
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Approach: fix the units digit, then multiply choices
- Odd digits are 1, 3, 5, 7, 9.
- Divisible by 5 means the units digit is 0 or 5; only 5 is odd, so units = 5.
- Each of the first three digits has 5 odd choices: 5×5×5×1 = 125.
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