The people who entered a room received upon entering distinct, consecu

Official Explanation

In this question, the room and the entering of the room is not so important. Rather the point is that there are people numbered 1000 to 1249. If we choose one person at random, the probability that that person will have a number with a hundreds digit of 1 will be

(number of ID's with a hundred digit of 1)/(total number of ID's)

The total number of ID's is 1249 - 1000 + 1 = 250. We can be sure of this by experimenting with smaller numbers. For example, if the ID's went from 1000 to 1001, the difference would be 1, but there would be 2 ID's, and so forth. Based on this alone, we can conclude right off the bat that the correct answer must be (A) or (D), since a denominator of 250 couldn't reduce to any of the other denominators (since they are not factors of 250).

As for the numerator: the number of ID's with a hundreds digit of 1 is the group from 1100 up to 1199. That is 1199 - 1100 + 1 = 100 ID's. Therefore:

(number of ID's with a hundred digit of 1)/(total number of ID's) = 100/250

Both the numerator and denominator can be divided by 50 to the simplest form of the fraction, 2/5.

The correct answer is (A).