How many five-digit positive integers, divisible by 9 , can be written using only the digits 3 and 6 ?
(A) 5
(B) 2
(C) 12
(D) 10
(E) 8
How many five-digit positive integers, divisible by 9 , can be written using only the digits 3 and 6 ?
(A) 5
(B) 2
(C) 12
(D) 10
(E) 8

## Solution

If a five-digit number is composed of only 3's and 6's, there are just two cases to consider because these are the only ways that the digital sum can be a multiple of 9 .

Case 1 one 6, four 3's

In this case, there are five numbers: 63333,36 333, 33633,33363 and 33336.

Case 2 one 3, four 6's

In this case there are five numbers: 36 666, 63666, 66 366, 66636 and 66663.

In total there are 10 possible numbers.

ANSWER: (D)