Discussion
The number of all three-digit numbers that are divisible by 7 is :
Answer: B
There are 128 three-digit numbers divisible by 7.
The smallest three-digit multiple of 7 is 105 (7 × 15) and the largest is 994 (7 × 142). Counting the multiples from the 15th to the 142nd:
\[ \begin{aligned} n &= \frac{994 - 105}{7} + 1 \\ &= 127 + 1 = 128 \end{aligned} \]
Equivalently, 142 - 15 + 1 = 128. Forgetting to add 1 gives 127, the most common slip; 129 and 130 overcount.
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