We go into this question knowing that k is a positive integer with exactly two digits.

Statement 1
If the sum of the digits is 3, we only have a couple options for what the digits could be: 0 and 3 or 1 and 2. What numbers can we make with these digits?

03 --> NOT two digits
30
12
21

Based on Statement 1 alone, there are three options for k. Not sufficient.

Statement 2
If k is odd, k can be any odd number from 11 and 99. Not sufficient.

Both

Looking at our three options from Statement 1 (30, 12, 21), we can eliminate 30 and 12 for being even. 21 is the only odd option, so k must be 21. Sufficient.

Hi lehannie07,

We're told that K is a positive integer and has EXACTLY two digits. We're asked for the value of K. This question can be solved by TESTing VALUES.

1) The sum of the digits of K is 3.

Since K has exactly 2 digits, K could be 12, 21 or 30.
Fact 1 is INSUFFICIENT

2) K is ODD.

Since K has exactly 2 digits, K could be 11, 13, 15, or any other odd 2-digit number.
Fact 2 is INSUFFICIENT

Combined, we know:
-The sum of the digits of K is 3.
-K is ODD.

The only value that 'fits' both of the Facts is 21.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich