Question

A, B, C, D, E, and F form three couples that are traveling on a train. Their ages are 24, 28, 29, 32, 34, and 35 years, not necessarily in the same order. Two of them are assigned upper berths, while one each is assigned a lower, a middle, a side lower, and a side upper berth.

The sum of the ages of the females is 14 years less than the sum of the ages of the males.
E is the youngest of the males and is assigned one of the side berths.
None of the females is assigned an upper berth.
The 32-year-old is assigned the middle berth.
D is 28 years old and is assigned the middle lower berth.
Neither A nor C is assigned an upper berth.
F is older than B. Which of the following statements is definitely true?

• A. C is older than three other people.
• B. A is assigned a lower berth.
• C. The two oldest persons are assigned upper berths.
• D. A is older than B.
• E. One of the males is assigned a lower berth.

Hint:

In problems with multiple conditions and restrictions, break down the information step by step and use logical deduction to eliminate possibilities.

Answer 1

Answer: (E)

Step 1: Problem Setup
Six individuals (A, B, C, D, E, F) with ages 24, 28, 29, 32, 34, and 35 are to be assigned berths. Constraints:

1. Female ages sum is 14 less than male ages.
2. E (youngest male) has a side berth.
3. Females are not on upper berths.
4. The 32-year-old is in the middle berth.
5. D (28) is in the middle lower berth.
6. Neither A nor C is in an upper berth.
7. F is older than B.

We deduce ages and positions. Step 2: Determining Genders and Ages
- D (28) is male (middle lower berth). - E is the youngest male (24 years old). - With F older than B and the age sum condition, we determine genders: Males: E (24), D (28), F (35). Females: A (32), B (29), C (34). Step 3: Berth Assignments
- E (youngest male) has a side berth. - D (28) is in the middle lower berth. - A and C are not in upper berths, thus are in lower berths. - F (oldest male) is in an upper berth. - B is in the remaining side upper berth. Step 4: Statement Verification
We check the following statements: - (A) "C is older than three other people" - Not necessarily true (C is 34, F is 35). - (B) "A is assigned a lower berth" - Not true (A is assigned the middle berth). - (C) "The two oldest persons are assigned upper berths" - Not true (F is upper, C is not). - (D) "A is older than B" - Not necessarily true (A is 32, B is 29). - (E) "One of the males is assigned a lower berth" - Definitely true (D (28) is in the middle lower berth). Step 5: Conclusion
The correct answer is \( \boxed{(E)} \), "One of the males is assigned a lower berth."