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GATE 2017 EC (EC2) – Question 7

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 2 marks · Multiple choice

Each of P,Q,R,S,W,X,Y and Z has been married at most once. X and Y are married and have children P and Q. Z is the grandfather of S, who is a daughter of P. Z and W are married and are parents of R. Which statement must necessarily be false?

  1. X is the mother-in-law of R
  2. P and R are not married to each other
  3. P is a son of X and Y
  4. Q cannot be married to R

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Correct answer: (D) Q cannot be married to R

Explanation

To test a claim of impossibility, construct an arrangement satisfying the premises. Let P be unmarried and have daughter S with an unnamed partner who is also a child of Z and W. Then Z is S's grandfather, while R is S's aunt or uncle.

Q, the sibling of P, can be married to R in this arrangement. Every named person is married at most once and all stated parent relationships hold. Thus the claim “Q cannot be married to R” is false, giving the intended **D**.

The premises do not require P and R to be spouses or fix P's sex. The key uses ordinary family-reasoning conventions, under which the relevant grandparent relationship is through the other parental branch.

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