P, Q, and R talk about S's car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. ...

Question

P, Q, and R talk about S's car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least 1 car. Only one of P, Q, and R is right.

The number of cars owned by S is:

A. 0
B. 1
C. 2
D. Cannot be determined

Accepted Answer

A. 0 Three people make claims about S's car count. Exactly one of the three claims is true. We test each possible value of S's car count to find which value makes exactly one claim true. If S owns 0 cars: P is wrong (0 is not >= 3), Q is wrong (0 is not < 3 is false — 0 < 3 is TRUE, so Q is right), and R is wrong (0 is not >= 1). Wait: 0 < 3 is true so Q is right. P: 0 >= 3 is false. R: 0 >= 1 is false. Exactly one (Q) is right. So S=0 works. If S=1 or 2: Q right (1 < 3), R right (1 >= 1). Two right. If S >= 3: P right, R right. Two right. Only S=0 gives exactly one person right.

P, Q, and R talk about S's car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least 1 car. Only one of P, Q, and R is right. The number of cars owned by S is: A. 0 B. 1 C. 2 D. Cannot be determined