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06 Aug 2026, 11:02
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A summer camp has several campers whose ages are all different, and the combined age of all the campers is 215 years. The 4 oldest campers are assigned to Cabin A, the 3 youngest campers are assigned to Cabin B, and the remaining campers are assigned to Cabin C. If the combined age of the 4 oldest campers is 110 years, how many campers are assigned to Cabin C?
(1) The combined age of the campers assigned to Cabin C is 60 years.
(2) The combined age of the campers assigned to Cabin B is 45 years.
(1) The combined age of the campers assigned to Cabin C is 60 years.
(2) The combined age of the campers assigned to Cabin B is 45 years.
06 Aug 2026, 11:02
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Official Solution:
A summer camp has several campers whose ages are all different, and the combined age of all the campers is 215 years. The 4 oldest campers are assigned to Cabin A, the 3 youngest campers are assigned to Cabin B, and the remaining campers are assigned to Cabin C. If the combined age of the 4 oldest campers is 110 years, how many campers are assigned to Cabin C?
(1) The combined age of the campers assigned to Cabin C is 60 years.
Since the total combined age is 215 years and the campers in Cabin A have a combined age of 110 years, the campers in Cabin B have a combined age of:
\(215 - 110 - 60 = 45\) years
The average age in Cabin A is:
\(\frac{110}{4} = 27.5\)
The average age in Cabin B is:
\(\frac{45}{3} = 15\)
Every camper in Cabin C is older than each camper in Cabin B and younger than each camper in Cabin A. Therefore, the average age in Cabin C must be between 15 and 27.5.
If there are \(n\) campers in Cabin C, then their average age is \(\frac{60}{n}\). So:
\(15 < \frac{60}{n} < 27.5\)
The only positive integer value of \(n\) that satisfies this inequality is 3.
Sufficient.
(2) The combined age of the campers assigned to Cabin B is 45 years.
Since the total combined age is 215 years and the campers in Cabin A have a combined age of 110 years, the campers in Cabin C have a combined age of:
\(215 - 110 - 45 = 60\) years
The average age in Cabin A is:
\(\frac{110}{4} = 27.5\)
The average age in Cabin B is:
\(\frac{45}{3} = 15\)
From here, the same logic as in statement (1) applies: the average age in Cabin C must be between 15 and 27.5, and since the combined age in Cabin C is 60 years, Cabin C must have exactly 3 campers.
Sufficient.
Answer: D
A summer camp has several campers whose ages are all different, and the combined age of all the campers is 215 years. The 4 oldest campers are assigned to Cabin A, the 3 youngest campers are assigned to Cabin B, and the remaining campers are assigned to Cabin C. If the combined age of the 4 oldest campers is 110 years, how many campers are assigned to Cabin C?
(1) The combined age of the campers assigned to Cabin C is 60 years.
Since the total combined age is 215 years and the campers in Cabin A have a combined age of 110 years, the campers in Cabin B have a combined age of:
\(215 - 110 - 60 = 45\) years
The average age in Cabin A is:
\(\frac{110}{4} = 27.5\)
The average age in Cabin B is:
\(\frac{45}{3} = 15\)
Every camper in Cabin C is older than each camper in Cabin B and younger than each camper in Cabin A. Therefore, the average age in Cabin C must be between 15 and 27.5.
If there are \(n\) campers in Cabin C, then their average age is \(\frac{60}{n}\). So:
\(15 < \frac{60}{n} < 27.5\)
The only positive integer value of \(n\) that satisfies this inequality is 3.
Sufficient.
(2) The combined age of the campers assigned to Cabin B is 45 years.
Since the total combined age is 215 years and the campers in Cabin A have a combined age of 110 years, the campers in Cabin C have a combined age of:
\(215 - 110 - 45 = 60\) years
The average age in Cabin A is:
\(\frac{110}{4} = 27.5\)
The average age in Cabin B is:
\(\frac{45}{3} = 15\)
From here, the same logic as in statement (1) applies: the average age in Cabin C must be between 15 and 27.5, and since the combined age in Cabin C is 60 years, Cabin C must have exactly 3 campers.
Sufficient.
Answer: D
