For a positive integer n, let Pn denote the product of the digits of nn and Sn denote the sum of the digits of nn. The number of integers between 10 and 100 for which Pn+Sn=n
Choose the correct choice from the following options
A) 2
B) 3
C) 9
D) 12
E) None
Explanation:   Let the two digit number be 'ab'   Given, a × b + a + b = 10a + b   a × b = 9a   b = 9   Therefore, for b = 9, the above condition satisfies. So all the two digit numbers for which units digit is 9 are our solutions. They range from 19 to 99. Total 9 numbers.   9orrect option: c
<result>C</result>
For a positive integer n, let Pn denote the product of the digits of nn and Sn denote the sum of the digits of nn. The number of integers between 10 and 100 for which Pn+Sn=n