Four people think of a number, and then proceed to each tell you something about it.

• A: The number has 2 digits
• B: The number is a divisor of 150
• C: The number is not 150
• D: The number is divisible by 25

Unfortunately, one of these people is not telling the truth. Who is it?

Assume A is false.Then there is no number(a non 2-digit number) which satisfies conditions of B & D.so A is true.
Since the number is 2-digit number (as proved now)
C is correct.
Assume D is false.so the possible options (by the
statements of A & B)are 10,15,25,30,50,75.But
D is false,number should not be divisible by 25.
Hence if D is false,answers are 10,15 or 30.
If B is false,then from statements of A & D,
possible options are 25,50,75.But all these are
divisors of 150.
Hence finally answer could be 10,15 or 30.

Posted by ananth on 2002-12-21 16:58:51