Data Sufficiency

Of the guests at a charity fundraiser, 180 own both a house in the Hamptons and a house in Palm Beach. If not every guest at the fundraiser owns a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who own a house in Palm Beach but not in the Hamptons to the number of people who own a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests own a house in Palm Beach.

(2) Two-thirds of the guests own a house in the Hamptons.

Statement 1: One-half of the guests own a house in Palm Beach
No information about the Hamptons.
INSUFFICIENT.

Statement 2: Two-thirds of the guests own a house in the Hamptons.
No information about Palm Beach.
INSUFFICIENT.

Statements combined:
1. One-half of the guests own a house in Palm Beach.
2. Two-thirds of the guests own a house in the Hamptons.

Strategy:
TEST TWO CASES.
Let P = Palm Beach and H = the Hamptons.

Case 1: Guests = 600.
Total P = (1/2)600 = 300.
Thus:
Only P = (total P) - (both H and P) = 300-180 = 120.
Total H = (2/3)600 = 400.
Thus:
Only H = (total H) - (both H and P) = 400-180 = 220.
Resulting ratio:
Only P : Only H = 120:220 = 6:11.

Case 2: Guests = 900.
Total P = (1/2)900 = 450.
Thus:
Only P = (total P) - (both H and P) = 450-180 = 270.
Total H = (2/3)900 = 600.
Thus:
Only H = (total H) - (both H and P) = 600-180 = 420.
Resulting ratio:
Only P : Only H = 270:420 = 9:14.

Since the ratio can be different values, INSUFFICIENT.

The correct answer is E.