Chemistry Buffer Problem: Explanation Needed?

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IBHMC

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I was in my chemistry class the other day when my professor proposed the following hypothetical problem:

"Calculate the PH of a solution made by mixing 100ml of .1 Molar (X) with 100ml of .1 Molar (Y)"

He then corrected himself, saying that 100ml of Y would not make the solution a buffer system, so he changed the amount of Y to 50ml. I was under the impression that a buffer solution could not contain a strong acid or base, and could only contain a weak acid/base and its conjugate. If that is the case, then why would the amount of ml (Y) matter? Is there an exception to the rule that I do not know about? Any help you could give me would be greatly appreciated. As always, the best answer will get best answer points. Thank you in advance.
 
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