Question

3. I am a three-digit number divisible by 3. My hundreds digit is one-third of my
tens digit. If you reverse me, I am divisible by 6. What smallest number could
I be?​

Answer 1

Answer:

Of the possibilities 13x, 26x, and 39x, the only one that is even if it is reversed is 26x. In order for a number to be divisible by 3, the sum of the digits must be divisible by 3. 2 plus 6 plus 1 is 9, 2 plus 6 plus 4 is 12, and 2 plus 6 plus 7 is 15.

Answer 2

Answer:

If the hundreds digit is one-third of thetens digit, then the only possibilities are: 13x, 26x, or 39x.

Step-by-step explanation:

In order to be divisible by 6, a number must be divisible by 2 and 3. If it is divisible by 2, then it must be an even number. Of the possibilities 13x, 26x, and 39x, the only one that is even if it is reversed is 26x. 

In order for a number to be divisible by 3, the sum of the digits must be divisible by 3. 2 plus 6 plus 1 is 9, 2 plus 6 plus 4 is 12, and 2 plus 6 plus 7 is 15. So 261, 264, and 267 are all divisible by 3. 

But 162, 462, and 762 are also all divisible by 6. So all three answers are correct.