GATE EC 2017 Set 2 — Question 62
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
Each of and has been married at most once. and are married and have two children and . is the grandfather of the daughter of . Further, and are married and are parents of . Which one of the following must necessarily be FALSE?
Correct answer
(D) Q cannot be married to R
Solution
Setting up the family. and are married with children and ; and are married with a child ; is the daughter of , and is a grandfather of .Since everyone has been married at most once and is married to , cannot be 's father (that is or ). So must be the father of 's spouse, i.e. is married to a child of and . That child may be , or another child of and ; the data do not say which.Checking each option (we want a statement that is false in every consistent arrangement):
- (A) is the mother-in-law of : true if is female and is 's spouse, so it can be true. Not necessarily false.
- (B) and are not married to each other: true if married a different child of and . Not necessarily false.
- (C) is a son of and : possible (then 's wife is 's daughter). Not necessarily false.
- (D) cannot be married to : this claims a marriage between and is impossible. But if married another child of and , nothing prevents and from being married. Since the marriage is possible, the claim "cannot" is false regardless of the actual arrangement.
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