Asked in Math and Arithmetic
How do you find How many numbers are there between 200 and 300 in which 9 occurs only once?
August 02, 2012 11:38AM
There are three digits. The numbers are between 200 and 300 so a 9 cannot occur in the first digit.
So there are three possibilities:
A: it appears ONLY in the second digit,
B: it appears in the second AND third digits
C: it appears only in the third digit.
You want to know the number of occurances of A and C but not B.
A: These are numbers of the form 29x where x can be any number other than 9 (in that case it would be type B). So there are 9 possible values of x in A.
C: These are numbers of the form 2y9 where y can be any number other than 9 (in that case it would be type B). So there are 9 possible values of y in C.
Incidentally, although you don't need it,
B: There is only one number, and that is 299. So there is 1 possible values in B.
So, number of type A + number of type B = 9 + 9 = 18.