Statement 1: One-half of the guests own a house in Palm BeachOf 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.
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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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