Question

How many times will you write even numerals if you write all the numbers from 291 to 300?

• A. 12
• B. 17
• C. 15
• D. 14
• E. 13

Hint:

When counting digits, consider each digit individually, especially when a number has repeated digits (like 292 has two 2's).

Answer 1

The Correct Option is D

Step 1: List the Numbers:
The numbers from 291 to 300 are: 291, 292, 293, 294, 295, 296, 297, 298, 299, 300.
Step 2: Identify Even Numerals:
Even numerals are 0, 2, 4, 6, 8.
Step 3: Count Even Numerals in Each Number:
291: digits 2,9,1. Even numerals = 1 (digit 2). Count = 1. 292: digits 2,9,2. Even numerals = 2 (two 2's). Count = 2. 293: digits 2,9,3. Even numerals = 1 (digit 2). Count = 1. 294: digits 2,9,4. Even numerals = 2 (digits 2 and 4). Count = 2. 295: digits 2,9,5. Even numerals = 1 (digit 2). Count = 1. 296: digits 2,9,6. Even numerals = 2 (digits 2 and 6). Count = 2. 297: digits 2,9,7. Even numerals = 1 (digit 2). Count = 1. 298: digits 2,9,8. Even numerals = 2 (digits 2 and 8). Count = 2. 299: digits 2,9,9. Even numerals = 1 (digit 2). Count = 1. 300: digits 3,0,0. Even numerals = 2 (two 0's). Count = 2.
Step 4: Sum the Counts:
Total = $1+2+1+2+1+2+1+2+1+2 = 15$. Wait, recount: 291 (1), 292 (2) => 3; 293 (1) =>4; 294 (2) =>6; 295 (1)=>7; 296 (2)=>9; 297 (1)=>10; 298 (2)=>12; 299 (1)=>13; 300 (2)=>15. Total is 15. But the optionss include 15. Let's double-check 300: digits 3,0,0. 0 is even, so two evens. Yes, total 15. However, the question asks "how many times will you write even numerals". For 300, you write the digit '0' twice. So total is 15. But the optionss also have 14. Let's recount the entire range carefully. 291: 2 (1) 292: 2, 2 (2) 293: 2 (1) 294: 2, 4 (2) 295: 2 (1) 296: 2, 6 (2) 297: 2 (1) 298: 2, 8 (2) 299: 2 (1) 300: 0, 0 (2) Sum = (1+2+1+2+1+2+1+2+1+2) = 15. It is 15. But perhaps there's an error in the original question or interpretation? "Even numerals" might mean counting each occurrence of an even digit. 15 is an options. Let's see if any number is missed. Possibly they mean from 291 to 300 inclusive, which we did. So the answer should be 15.
Step 5: Final Answer:
The total number of times even numerals are written is 15.