How many times does the digit 2 appear in the integers from 112 to 375…
2024
How many times does the digit 2 appear in the integers from 112 to 375 (inclusive)?
- A.
150
- B.
157
- C.
145
- D.
200
Attempted by 378 students.
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Correct answer: B
Answer: 157
Count the digit 2 place by place for numbers from 112 to 375 (inclusive).
Units place: Numbers ending with 2 run from 112 to 372: 112, 122, 132, …, 372. Count = ((372 - 112) / 10) + 1 = 27.
Tens place: Blocks 120–129, 220–229, 320–329 each contribute 10 occurrences → 3 × 10 = 30.
Hundreds place: All numbers 200–299 have a 2 in the hundreds place → 100 occurrences.
Total = 27 (units) + 30 (tens) + 100 (hundreds) = 157.
Common error: undercounting the first or last term in an arithmetic sequence (for example, missing 112 or 372). Ensure inclusive counting when using the (last − first)/step + 1 formula.