SOLUTION: If the 3 digit number 27d in which d is the ones digit, is evenly divisible by both 3 and 4 what is the value of d?

She blurted out the answer without telling why. 

To be divisible by 4 the number formed by the last 
two digits must be divisible by 4.  So the only 
possibilities are for the last two digits to be 72 
or 76.

27d is divisible by 3 if 2+7+d is divisible by 3.
Since 2+7 is 9, divisible by 3, d would have to be 
0,3,6, or 9

So the only possibility is 6.

Edwin