Question

Let aa be a digit. If the 7-digit number 353808a353808a is divisible by 2, 3, 4, 5, 6, 8, and 9, then what is aa?

a) 1
b) 2
c) 3
d) 4

Answer 1

The digit aa that makes the 7-digit number divisible by 2, 3, 4, 5, 6, 8, and 9 is 2.

Step-by-step explanation:

To determine the value of aa, we need to find a digit that makes the 7-digit number 353808a353808a divisible by 2, 3, 4, 5, 6, 8, and 9. In order for a number to be divisible by 2, it must end in an even number, so a must be an even digit. In order for a number to be divisible by 3, the sum of its digits must be divisible by 3. The digits of the number add up to 38, so a must be the digit that makes 38 plus a divisible by 3. Testing the even digits, we find that a = 2 makes the total sum divisible by 3. Therefore, the value of aa is 2.