In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.

So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.

Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $3,000-$880=$2,120.

Answer: B.
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I somehow got confused with the wordings....

With the wording of the question or the wording of the solution? Please let me know if anything needs farther clarification.
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Your answer is perfect. I got confused with the question.

Great approach to min/max questions. With @bunuel around, I guess the learning never ends...thanks.

Min/max questions are quite common on the GMAT. Check our question banks for such kind of problems to practice:

DS: search.php?search_id=tag&tag_id=42
PS: search.php?search_id=tag&tag_id=63

Hope it helps.
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Answer:B
1- Largest amount of money that the gambler could have received back ⇒ the lost amount is minimum ⇒ $100 amount lost is minimum
2- $20 chips lost was 2 more or 2 less than the number of $100 chips lost ⇒ Lost $100 is minimum and $20 is maximum
-1- and -2- ⇒ $20 chips lost is 9 and $100 chips lost is 7 ⇒ total loss=20x9+100x7=$880 ⇒ He received back=3000-880= $2120

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