How many times does the digit “2” appear in the set of integers {1,2,…,1000}?

a)590 b)600 c)300 d)299

We have to count how many times 2 appear in the set of integers {1,2,…..1000}. Now we can exclude 1000 itself and can focus in the set A= {1,2,3,…..,999}.

Now all the numbers in set A is 3 digit number. Hence we can fix the position of 2 in one’s,ten’s and hundred’s place to note the number of appearances.

The following scenarios can take place:

2 _ _: We can fill the blanks from numbers 00 to 99 i.e., 100 ways.

_ _ 2: We can the fill the blanks from numbers 00 to 99 , i.e., 100 ways again.

_ 2 _: Here each of the blanks can be filled by 10 ways that is from 0 to 9, Hence total number ways in fill the two blanks are 10*10 ways = 100 ways.

Hence total numbers in the above mentioned set containing 2 is 100+100+100= 300…….c) is the correct option.