If all positive integers that have at least 1 digit equal to 2 are lis

snow12snow
We're not concerned with how many total 2's we see, just with how many INTEGERS we see that have 2 in them. So whether our number is 2, 22, or 222, it still just counts as one case.

It may also help to note that the numbers from 101 to 199 will work just like the numbers from 1 to 99, since it's just the same list with a 1 in front. So once we establish that we have 19 in the first set (1 for each "decade," except for the 20's, where all 10 contain a 2), then we know that the next set is the same. So from 1-199, there are 38 integers containing a 2. We need 62 more. However, we now hit 200, at which point EVERY number contains a 2. So we just need to count the 62nd number in the 200's. Counting from 201 up to 262 would be 62 numbers, so from 200 we just need to count up to 261.

from 0 to 99
total digits with 2 in list are 19
100 to 199; again 19
38 listed numbers
100-38 ; 62
200 is 39th number so 61st number is 100th number
261
option A

Bunuel chetan2u this is an FE official question. Please tag it.

Added the tag. Thank you!

why does no one count 220-229? it adds 10 more numbers, so the final answer should be 251 not 261

gmatophobia , Can you please provide an easy explanation to this ?