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: Understanding the constraints.
We have six people (A, B, C, D, E, and F), whose ages are 24, 28, 29, 32, 34, and 35. The conditions provided are as follows: 1. The sum of the ages of the females is 14 years less than the sum of the ages of the males. 2. E is the youngest male and is assigned one of the side berths. 3. None of the females is assigned an upper berth. 4. The 32-year-old is assigned the middle berth. 5. D is 28 years old and is assigned the middle lower berth. 6. Neither A nor C is assigned an upper berth. 7. F is older than B. Using these facts, we start to deduce the ages and positions of the individuals. Step 2: Determining the genders and ages.
- Since D is 28 years old and is assigned the middle lower berth, D must be one of the males. - E is the youngest male, which means E is 24 years old. - Since F is older than B and the sum of the ages of the females is 14 years less than the sum of the males, we deduce the remaining ages and assign the genders accordingly. Thus, the males are E (24), D (28), and F (35), and the females are A (32), B (29), and C (34). Step 3: Assigning berths.
- E, the youngest male, is assigned a side berth (as per the given conditions). - D, being 28 years old, is assigned the middle lower berth. - Since neither A nor C is assigned an upper berth, A and C must be assigned lower berths. - F, the oldest male, must be assigned an upper berth. - The only remaining berth, a side upper berth, is assigned to B. Step 4: Verifying the statements.
Now, we examine the options to find the statement that is definitely true. - (A) "C is older than three other people" is not necessarily true because we have C being 34, who is younger than F (35). - (B) "A is assigned a lower berth" is not true because A is assigned the middle berth. - (C) "The two oldest persons are assigned upper berths" is not true because the oldest person (F) is assigned an upper berth, but the second oldest (C) is not. - (D) "A is older than B" is not necessarily true because A is 32, and B is 29. However, B could be assigned a different berth. - (E) "One of the males is assigned a lower berth" is definitely true, as D (28) is assigned the middle lower berth. Step 5: Conclusion.
The correct answer is \( \boxed{(E)} \), "One of the males is assigned a lower berth."