Question

How many numbers are there between 100 and 1000 which exactly have one of their digits as 7?

Please answer efficiently.

Answer 1

Let's count the number of occurrences with only one 7:

(1) 7XX: 1 * 9 * 9 = 81
(2) X7X: 8 * 1 * 9 = 72
(3) XX7: 8 * 9 * 1 = 72

81 + 72 + 72 = 225

At this point we can already see that the answer must be D since the choice are very dispersed.

Anyways, let's count number of occurrences with two 7s:

(1) 77X: 1 * 1 * 9 = 9
(2) X77: 8 * 1 * 1 = 8
(3) 7X7: 1 * 9 * 1 = 9

9 + 8 + 9 = 26

Number 777 is missing. So the total becomes

225 + 26 + 1 = 252