Hi All,
In these types of questions, the real issue is thoroughness - make sure that you're not "missing" any of the possibilities and make sure that you're not "counting" a possibility that should NOT be counted (or accidentally counting a possibility more than once). Your ability to pattern-match will help speed you up.
With the limitations posed by this question, we COULD break the numbers down into smaller groups and then total up all of these smaller numbers (it's a slightly longer way to do things, but if you don't immediately see the more complex calculations, you can still get to the correct answer with a bit of "hand math").
Let's start with making the first 2 digits the same...
66_
77_
88_
99_
Since the third digit has to be DIFFERENT from the matching pair, we have 9 options for each of the 4 groups above (you CAN'T count 666, 777, 888 or 999 - the numbers don't fit the restrictions).
Total of this group = 36
Next, let's make the first and third digits the same...
6_6
7_7
8_8
9_9
Here, we have a similar situation to the one we had above; we have 9 options for each of the 4 groups (you CAN'T count 666, 777, 888 or 999).
Total of this group = 36
Finally, let's make the second and third digits the same (I'll refer to those digits with the variable X)...
6XX
7XX
8XX
9XX
In this grouping, we have 1 "catch" - X can be any digit, BUT the number 600 is NOT permissible, since the prompt tells us for numbers GREATER THAN 600.
So, 6XX has 8 possibilities (you CAN'T count 600 or 666)
7XX, 8XX and 9XX have 9 possibilities each (you CAN'T count 777, 888 or 999)
Total of this group = 35
Overall total = 36 + 36 + 35 = 107
Final Answer:
GMAT assassins aren't born, they're made,
Rich