Discussion
How many three-digit numbers are divisible by 7 ?
Answer: B
There are 128 three-digit numbers divisible by 7.
The smallest three-digit multiple of 7 is \(105 = 7 \times 15\) and the largest is \(994 = 7 \times 142\). Count the multipliers from 15 to 142:
\[ 142 - 15 + 1 = 128 \]
Another route: there are \(\lfloor 999/7 \rfloor = 142\) multiples of 7 up to 999 and \(\lfloor 99/7 \rfloor = 14\) up to 99, and \(142 - 14 = 128\). 129 is the off-by-one error of counting 14 to 142, and 126 or 131 come from misjudging the first or last multiple.
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