If integer K is equal to 172,31# with # representing the units digit of integer K. What is the value of #?

(1) Integer K is not divisible by 9

(2) Integer K is divisible by 3

[spoiler]E**.**[/spoiler]

**Solution:**

Statement (1) – If K is NOT divisible by 9 then # cannot be 4 because 1 + 7 + 2 + 3 + 1 + 4 = 18. Any number with digits that add up to a number divisible by 9 is divisible by 9 itself. There are multiple possibilities for # (every digit besides 4). Insufficient.

Statement (2) – If K is divisible by 3 then # has three possibilities: 1, 4, and 7. Because 1 + 7 + 2 + 3 + 1 + 1 = 15, 1 + 7 + 2 + 3 + 1 + 4 = 18, and 1 + 7 + 2 + 3 + 1 + 7 = 21. If a number is divisible by 3 then the sum of its digits add to a number divisible by 3. Since there are multiple possibilities for # (1, 4, and 7) Statement (2) is insufficient.

Statement (1) + (2) – Putting then together still leaves two choices for #, 1 or 7. Insufficient.