Joe bought only twenty cent stamps and thirty cent stamps.

I am not sure if this is the most accurate solution, but here's my explanation as to why the answer is C.

Looking at the first statement:

20 cent stamps: > 8

This is insufficient, so we can eliminate answer choices A and D

Now looking at second statement, we see that \(0.20a + 0.30 b = 2.5\)

But there are many possible values that will satisfy this condition, and hence this statement is insufficient by itself. So we can eliminate B.

Combining the two statements, we know that \(a > 8\), so let us assume \(a = x + 8\) where x can take the values of 1, 2, 3 and so on (Number of stamps can only be integers; you can't buy half a stamp :D)

Substituting \(a = x+8\) into the equation we had from statement 2 we get

0.20a + 0.30b = 2.5

0.20(x+8) + 0.30b = 2.5

0.20x + 1.60 + 0.30b = 2.5

0.20x + 0.30b = 2.5 - 1.6 = 0.9

Now, we know that x can take the values of 1, 2 and 3 and so on

For x = 1 b = \(\frac {0.7}{0.3}\) - Eliminate (Not an integer)

For x = 2 b = \(\frac {0.5}{0.3}\) - Eliminate (Not an integer)

For x = 3 b = 1 - This is an integer, that would give rise to the answer being a = 11 and b = 1. But to be sure, we can check one or two more values.

For x = 4, b = \(\frac{0.1}{0.3}\)

For x = 5, b becomes negative. So we can stop here.

Hence, on combining the statements we see it's sufficient to answer the question.

Hope this helps. I wonder if there are other shorter methods to figure this out?