Question

A, B, C and D are to be seated in a row. But C and D cannot be together. Also, B cannot be at the third place. Which of the following must be false?

• A. A is at the first place
• B. A is at the second place
• C. A is at the third place
• D. A is at the fourth place

Hint:

When solving seating arrangement problems, pay careful attention to the restrictions and try to eliminate possibilities based on them.

Answer 1

The Correct Option is A

We have these constraints: 
1. C and D cannot sit together.
2. B cannot sit at the third place.
We need to find which statement must be false. Let's examine each option under these constraints:
Option 1: A is at the first place If A is at the first place, we can arrange the other three (B, C, D) in a way that satisfies the constraints (C and D are not together, and B is not in the third place).
This is possible, so Option 1 is true.
Option 2: A is at the second place If A is at the second place, we can still arrange B, C, and D, ensuring that B is not in the third place and C and D are not together.
This is possible, so Option 2 is true.
Option 3: A is at the third place If A is at the third place, we would have to place B elsewhere since B cannot sit at the third place. However, this would force C and D to be together, which violates the condition that C and D cannot sit together.
Thus, Option 3 is false.
Option 4: A is at the fourth place If A is at the fourth place, we can arrange the remaining three (B, C, D) such that B is not at the third place, and C and D are not together.
This is possible, so Option 4 is true. 
Conclusion: The statement that must be false is Option 1: "A is at the first place" because it is not feasible to arrange B, C, and D without violating the conditions when A is in the first position. So, the correct answer is: Option 1.