Question

A certain stadium is currently full to \(\frac{13}{16}\) of its maximum seating capacity. What is the maximum seating capacity of the stadium?
(1) If 1,250 people were to enter the stadium, it would be full to \(\frac {15}{16}\) of its maximum seating capacity.
(2) If 2,500 people were to leave the stadium, it would be full to \(\frac {10}{16}\) of its maximum seating capacity.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
• D. EACH statement ALONE is sufficient.

Hint:

Translate percentage or fraction capacity problems into linear equations to solve for total capacity quickly.

Answer 1

The Correct Option is D

From Statement (1):
Let capacity be \(C\).
Currently: \(\frac{13}{16}C\) people present.
After 1,250 more people: \(\frac{13}{16}C + 1250 = \frac{15}{16}C\).
Thus: \(1250 = \frac{2}{16}C \Rightarrow C = 1250 \times 8 = 10000\).
We find \(C\) directly ⇒ sufficient. From Statement (2):
Currently: \(\frac{13}{16}C\).
After 2,500 leave: \(\frac{13}{16}C - 2500 = \frac{10}{16}C\).
Thus: \(2500 = \frac{3}{16}C \Rightarrow C = 2500 \times \frac{16}{3} \approx 13333.33\).
We find \(C\) directly ⇒ sufficient.
Each statement alone is sufficient ⇒ \(\boxed{D}\).