# 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 - Logical Reasoning

MCQ

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 represents the reply that R gave?

#### Options

• Truth - Truth - Lie

• Lie - Truth - Truth

• Lie-Lie-Truth

• Truth-Lie-Lie

#### 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.
R replies in the manner: Truth - lie - lie

Concept: Statement and Assumption (Entrance Exam)
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