Data Sufficiency

VJesus12 wrote: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.

We can let the number of chicken, beef and fish dinners be 7x, 5x, 2x, respectively, where x is a positive integer. We are given that more than 5 fish dinners served at the banquet; therefore, x must be at least 3. We need to determine the total number of dinners served at the banquet. That is, we need to determine the value of 7x + 5x + 2x = 14x.

Statement One Alone:

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

That is, 5x + 2x < 30, or 7x < 30. So x < 30/7 = 4 2/8. Since x must be an integer, x ≤ 4.

Also, since x ≥ 3, x could be either 3 or 4. Statement one alone is not sufficient.

Statement Two Alone:

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

That is, 7x < 25. So x < 25/7 = 3 4/7. Since x must be an integer, x ≤ 3.

Also, since x ≥ 3, x must be 3 and the number of dinners served is 17 x 3 = 51. Statement two alone is sufficient.

Answer: B