**Quote:**

Each of the dinners served at a banquet was either chicken or beef or fish. The ratio of the number of chicken dinners to the number of beef dinners to the number of fish dinners served at the banquet was 7:5:2, respectively. If there were more than 5 fish dinners served at the banquet, what was the total number of dinners served at the banquet ?

(1) The total number of beef dinners and fish dinners served at the banquet was less than 30.

(2) The number of chicken dinners served at the banquet was less than 25.

I felt this was a pretty easy question.

So C:B:F ratio is 7:5:2.

W/ a restriction that states that fish is GREATER than 5. So F > 5.

Now moving on to S1

S1: The total number of beef dinners and fish dinners served at the banquet was less than 30.

Therefore, we can write B + F < 30.

Okay, so it can't be 5 + 2 (the original ratio of beef and fish because there was more than 5 fish dinners.)

So we move on to 15 + 6 < 30. Good

Try 20 + 8 < 30. Also good, therefore S1 is Not sufficient.

Statement 2:

The number of chicken dinner was less than 25.

Okay, so Chicken must be in multiples of 7.

It can be 7, 14, 21. However, we must remember the number of fish dinners too! The original restriction is that fish must be greater than 5!

So it can be 2, 4, 6, 8. However, you'll notice that chicken dinners can really be either 7, 14, or 21. However, the first two iterations (7, and 14) correspond to fish dinner of 2, and 4 which are both less than 5. Therefore, there must be 21 chicken dinners, 6 fish dinners, and 15 beef dinners.

SUFFICIENT (B)