Select the correct alternative from the given choices.
P, Q, and R when asked a question give three statements as a reply in the following manner.
P - always replies in only one type of statement - truth or lie.
Q - never replies in the same type of statements as P.
R - is neither consistent in all his statement types nor alternates between the two types of statements.
At the bus - stop, I asked: "Which bus goes to the airport?"
Their replies were as follows:
P: Take the North-bound bus.
The next bus arrives in 15 minutes.
It takes 45 minutes to reach the airport.
Q: The north-bound bus comes from the airport.
You have to wait for 20 minutes for the bus.
It takes 30 minutes to reach the airport.
R: Take the South-bound bus.
You have to wait for another quarter of an hour for the bus.
It takes anywhere between 1 hour to 1 hour 30 minutes to reach the airport.
Which of the following is definitely true?
- P always lies
- . Q always lies.
- . The North-bound bus goes to the airport.
Options
Only I
Only II
Only I and II
Only II and III
Solution
If P always speaks the truth, then Q always lies R.
If P always lies R then Q always speaks the truth.
In either case, R cannot be speaking all truths or all lies. R cannot alternate between truth and lies either.
So, we have the following:
Case (i)
I | II | III | |
P | T | T | T |
Q | F | F | F |
R | F | T | F |
Case (ii)
I | II | III | |
P | F | F | F |
Q | T | T | T |
R | T | F | F |
In case (i), R becomes an alternator which violates the given condition.
Hence case (ii) in the correct arrangement and the south bound bus goes to the airport.
Only I statement is true.