How many three-digit numbers are divisible by 7?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 128
The number of multiples of 7 from 1 to a number is the whole-number part of that number divided by 7. The three-digit multiples are those up to 999 minus those up to 99.
Multiples of 7 up to 999: \(999\div7=142.71\), so 142
Multiples of 7 up to 99: \(99\div7=14.14\), so 14
Three-digit multiples \(=142-14=128\)
There are 128 such numbers (105, 112, …, 994).
Why the other options are incorrect
Option (1) 127 — Incorrect. This is one too few: both the first multiple 105 and the last multiple 994 must be counted.
Option (3) 142 — Incorrect. This counts all multiples of 7 from 1 to 999, including those below 100.
Option (4) 129 — Incorrect. This is one too many: 105 is the first multiple and 994 the last, so the count is 128.