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03 Aug 2026, 09:15
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During a wedding season, two event venues, Cedar Hall and Willow Hall, rented out their banquet spaces for private receptions. Was the range of rental fees charged at Cedar Hall greater than the range of rental fees charged at Willow Hall?
(1) The highest rental fee charged at Cedar Hall was greater than the highest rental fee charged at Willow Hall.
(2) The lowest rental fee charged at Cedar Hall was greater than the lowest rental fee charged at Willow Hall.
(1) The highest rental fee charged at Cedar Hall was greater than the highest rental fee charged at Willow Hall.
(2) The lowest rental fee charged at Cedar Hall was greater than the lowest rental fee charged at Willow Hall.
03 Aug 2026, 09:15
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Official Solution:
During a wedding season, two event venues, Cedar Hall and Willow Hall, rented out their banquet spaces for private receptions. Was the range of rental fees charged at Cedar Hall greater than the range of rental fees charged at Willow Hall?
(1) The highest rental fee charged at Cedar Hall was greater than the highest rental fee charged at Willow Hall.
This is clearly insufficient. Knowing only that Cedar Hall’s highest fee was greater than Willow Hall’s highest fee does not help determine which range was greater. Not sufficient.
(2) The lowest rental fee charged at Cedar Hall was greater than the lowest rental fee charged at Willow Hall.
This is also clearly insufficient. Knowing only that Cedar Hall’s lowest fee was greater than Willow Hall’s lowest fee does not help determine which range was greater. Not sufficient.
(1)+(2) Together, these statements tell us that both the highest fee and the lowest fee at Cedar Hall were greater than the corresponding fees at Willow Hall.
But that still does not determine whether Cedar Hall’s range was greater, because range depends on the size of the gap between the highest and lowest fees, not on whether both endpoints are higher.
For example, this is possible:
• Cedar Hall: lowest \(1,000\), highest \(1,200\), range \(200\)
• Willow Hall: lowest \(100\), highest \(1,000\), range \(900\)
Both statements are true, but the answer is no.
But this is also possible:
• Cedar Hall: lowest \(1,000\), highest \(2,000\), range \(1,000\)
• Willow Hall: lowest \(100\), highest \(1,000\), range \(900\)
Both statements are still true, but the answer is yes.
Since both yes and no are possible, the answer cannot be determined. Not sufficient.
Answer: E
During a wedding season, two event venues, Cedar Hall and Willow Hall, rented out their banquet spaces for private receptions. Was the range of rental fees charged at Cedar Hall greater than the range of rental fees charged at Willow Hall?
(1) The highest rental fee charged at Cedar Hall was greater than the highest rental fee charged at Willow Hall.
This is clearly insufficient. Knowing only that Cedar Hall’s highest fee was greater than Willow Hall’s highest fee does not help determine which range was greater. Not sufficient.
(2) The lowest rental fee charged at Cedar Hall was greater than the lowest rental fee charged at Willow Hall.
This is also clearly insufficient. Knowing only that Cedar Hall’s lowest fee was greater than Willow Hall’s lowest fee does not help determine which range was greater. Not sufficient.
(1)+(2) Together, these statements tell us that both the highest fee and the lowest fee at Cedar Hall were greater than the corresponding fees at Willow Hall.
But that still does not determine whether Cedar Hall’s range was greater, because range depends on the size of the gap between the highest and lowest fees, not on whether both endpoints are higher.
For example, this is possible:
• Cedar Hall: lowest \(1,000\), highest \(1,200\), range \(200\)
• Willow Hall: lowest \(100\), highest \(1,000\), range \(900\)
Both statements are true, but the answer is no.
But this is also possible:
• Cedar Hall: lowest \(1,000\), highest \(2,000\), range \(1,000\)
• Willow Hall: lowest \(100\), highest \(1,000\), range \(900\)
Both statements are still true, but the answer is yes.
Since both yes and no are possible, the answer cannot be determined. Not sufficient.
Answer: E
