SOLUTION: How many positive multiples of 7 that are less than 1000 have a units digit of 3?

Question 246693: How many positive multiples of 7 that are less than 1000 have a units digit of 3?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

7 as an integer divisor has the interesting characteristic that all 10 possible digits appear in the units digit position of numbers evenly divisible by it. What that means is that the number three appears as the units digit in every 10th integer that is evenly divisible by 7. 7 times 142 is 994, so there are exactly 142 positive multiples of 7 less than 1000. One tenth of these, ignoring the decimal fraction, end in a units digit of 3. Answer: 14.

John

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