Hi VJesus12,
We're told that "A" represents a single digit and the four digit integer A12A is divisible by 6. We're asked for the value of A. This question can be solved with a mix of Number Property Rules and TESTing THE ANSWERS.
To start, if you weren't sure how to do anything else, then you could simply plug in each of the 5 answer choices and see which one ended up leading to a 4-digit number that is divisible by 6. Once you found that result, then you could stop working. There are some Number Property 'shortcuts' though, so we can use those to eliminate a couple of answers immediately.
For a number to be evenly divisible by 6, it must be divisible by BOTH 2 and 3. To be divisible by 2, the number must be EVEN. That would not occur with Answers B or E though, so we can eliminate both of those. For a number to be evenly divisible by 3, the DIGITS of that number must SUM to a number that is evenly divisible by 3. For example:
15 is divisible by 3 because 1+5 = 6. Since 6 is divisible by 3, we know that 15 is divisible by 3.
16 is NOT divisible by 3 because 1+6 = 7 is NOT divisible by 3.
Based on the remaining 3 answer choices, we have to consider these 3 values:
2122
4124
6126
Only one of those answers consists of digits that sum to a multiple of 3....
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
