Question 55

# Saira, Mumtaz and Zeenat have a ball, a pen and a pencil, and each girl has just one object in hand. Among the following statements, only one is true and the other two are false. I. Saira has a ball. II. Mumtaz does not have the ball. III. Zeenat does not have the pen.Who has the ball?

Solution

Assume the first statement is true. So, Saira has the ball. The other two statements are false. But if Saira has the ball, the statement that Mumtaz does not have the ball is true. But that statement should be false. Therefore, the first statement cannot be true.

Assume the second statement is true. So, Mumtaz does not have the ball. Also, since the other two statements are false, Saira also does not have the ball. So, Zeenat has the ball. But the third statement "Zeenat does not have a pen" becomes true in this case, which is incorrect. So, the second statement also cannot be true.

The only possibility is the statement has to be true. So, the second statement is false => Mumtaz has the ball.

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