Question

Each of the five balls, such as red, blue, yellow, black, and green, is of a different weight. It is known that:
(i) Black ball is heavier than the Red and Blue balls.
(ii) Yellow ball is lighter than the Red ball.
(iii) Blue ball is heavier than the Red and Green balls.
Which ball could be the lightest one?

• A. Only Green
• B. Either Yellow or Green
• C. Only Yellow
• D. Either Yellow or Red

Answer 1

The Correct Option is B

To determine the lightest ball among the five, let's analyze the conditions given in the question:

1. Black ball is heavier than the Red and Blue balls. 
2. Yellow ball is lighter than the Red ball.
3. Blue ball is heavier than the Red and Green balls.

We need to establish the relative weight order of the balls based on these conditions:

• From condition (i), we know: \(B_{black} > B_{red}\) and \(B_{black} > B_{blue}\).
• From condition (ii), we know: \(B_{red} > B_{yellow}\).
• From condition (iii), we know: \(B_{blue} > B_{red}\) and \(B_{blue} > B_{green}\).

Now, by putting these together, let's derive possible weight rankings:

• If we consider the Blue ball: \(B_{black} > B_{blue} > B_{red}\), and hence, \(B_{blue} > B_{green}\) and \(B_{blue} > B_{red} > B_{yellow}\).

Therefore, since the Yellow and Green balls are not directly compared, either could be the lightest. The sequence can thus be:

• If \(B_{yellow} < B_{green}\), then \(B_{yellow}\) is the lightest.
• If \(B_{green} < B_{yellow}\), then \(B_{green}\) is the lightest.

Thus, the correct answer is Either Yellow or Green, as both conditions are possible based on the given information.