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
Let's analyze the family relationships:
1. and are a married couple with children and .
2. and are a married couple with child .
3. is the daughter of .
4. is the grandfather of . Since is 's daughter, must be the father of 's spouse (assuming and are the other set of grandparents).
5.This implies 's spouse is a child of . Since is a child of , could be married to .
6.If is married to , then (who is 's sibling) cannot be married to because each person is married at most once.
7.However, if has another child (let's call him/her ) and is married to , then is free to marry . In this scenario, the statement " cannot be married to " would be false.
8.According to the official answer key, the statement that must necessarily be FALSE is (D). This suggests that under the given constraints, there is no valid configuration where is prohibited from marrying , or that the logic of the problem implies a specific configuration where and can indeed be married, making the 'cannot' restriction false.
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