Question

Car license plates are being made starting from 1. What is the last license plate's number if the digit 3 appears for 102 times till the last license plate?

• A. 323
• B. 330
• C. 332
• D. 333

Answer 1

The correct option is D 333

Between 1 to 99, digit 3 occurs 20 times. (3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and 30, 31, 32, 34, 35, 36, 37, 38, 39)

Again, 3 appears 20 times between 100 and 199.

Again, 3 appears 20 times between 200 and 299.
Total till now $=20\times 3=60$

3 appears 11 times from 300 to 309.
3 appears 11 times from 310 to 319.
3 appears 11 times from 320 to 329.

The total till now is 93.

Now, we are pretty close to 102, let's counts the 3's starting from 330 manually.

330, 331, 332, 333
The number of 3's this gives us is,
2 + 2 + 2 + 3 = 9
Hence, the total we obtain is,
93 + 9 = 102
So, the last license plate's number is 333.