How many four-digit numbers are divisible by 13?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 693
The number of multiples of 13 from 1 to a number is the whole-number part of that number divided by 13. The four-digit multiples are those up to 9999 minus those up to 999.
Multiples of 13 up to 9999: \(9999\div13=769.15\), so 769
Multiples of 13 up to 999: \(999\div13=76.85\), so 76
Four-digit multiples \(=769-76=693\)
There are 693 such numbers (1001, 1014, …, 9997).
Why the other options are incorrect
Option (1) 694 — Incorrect. This is one too many: 1001 is the first multiple and 9997 the last, so the count is 693.
Option (2) 769 — Incorrect. This counts all multiples of 13 from 1 to 9999, including those below 1000.
Option (4) 692 — Incorrect. This is one too few: both the first multiple 1001 and the last multiple 9997 must be counted.