A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12? Select the correct option
A) 11 B) 12 C) 10 D) 22 E) 44
DETAILED SOLUTION   Number should be a multiple of 3 and 4. So, the sum of the digits should be a multiple of 3. WE can either have all seven digits as 3, or have three 2's and four 3's, or six 2's and a 3. (The number of 2's should be a multiple of 3).   For the number to be a multiple of 4, the last 2 digits should be 32. Now, let us combine these two.   All seven 3's - No possibility.   Three 2's and four 3's - The first 5 digits should have two 2's and three 3's in some order. No of possibilities = 5!3!2! = 10   Six 2's and one 3 - The first 5 digits should all be 2's. So, there is only one number 2222232.   So, there are a total of  10 + 1= 
<gadget id="calculator"> 10 + 1</gadget>
<output>11</output>
11 solutions.   CORRECT 11NSWER : 11.
<result>A</result>
A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12?