Brain Teasers
Who Likes Whom ?
The relationships of a person X with 3 people P, Q and R are given below.
1) X likes at least one of the three people.
2) If X likes P, but not R, then he also likes Q.
3) X likes both R and Q, or he likes neither of them.
4) If X likes R, then he also likes P.
Which of the following statements can be deduced from the above?
A) X likes P, Q and R.
B) X likes only P.
C) X likes only Q.
D) X likes P and Q only.
NOTE: Out of the given set of 4 statements, it is not necessary that one and only one statement can be deduced. One or more statements may be possible to be deduced.
1) X likes at least one of the three people.
2) If X likes P, but not R, then he also likes Q.
3) X likes both R and Q, or he likes neither of them.
4) If X likes R, then he also likes P.
Which of the following statements can be deduced from the above?
A) X likes P, Q and R.
B) X likes only P.
C) X likes only Q.
D) X likes P and Q only.
NOTE: Out of the given set of 4 statements, it is not necessary that one and only one statement can be deduced. One or more statements may be possible to be deduced.
Answer
Only statement A which states that X likes P, Q and R can be deduced.The relationships given are
1) X likes at least one of the three people.
2) If X likes P, but not R, then he also likes Q.
3) X likes both R and Q, or he likes neither of them.
4) If X likes R, then he also likes P.
The statements given are
A) X likes P, Q and R.
B) X likes only P.
C) X likes only Q.
D) X likes P and Q only.
From relationship 3, we can get the following two cases:-
Case 1 : Let us assume that X neither likes R nor Q. It implies that he likes P since from relationship 1, he likes at least one of the three. However relationship 2 which says that if X likes P, but not R, then X also likes Q contradicts the above observation.
Case 2 : Let us assume that X likes both R and Q. Then from relationship 4, X likes P also, since he likes R. This does not violate any of the given relationships.
Since we know that only the above two cases are possible and Case 1 being ruled out due to contradictory statements, from observation 2 we can deduce only statement A which says that X likes P, Q and R.
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