GATE CS 2025 Set 1 Q.4: Analytical and Logical Reasoning

Consider the relationships among P, Q, R, S, and T:

The following statements are made based on the relationships given above.

(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.

Which one of the following options is correct?

Both (1) and (2) are true.

Both (1) and (3) are true.

Only (3) is true.

Only (4) is true.

Official answer and solution

Solution

Construct the family tree across the three generations (R -> P, Q -> S, T) and note whose gender is known versus unknown.

From the given statements:

Generation 1: $R$ (female) is the mother of $Q$ and $P$ .
Generation 2: $P$ (male) is the brother of $Q$ (whose gender is not specified).
Generation 3: $S$ (female) is the daughter of $Q$ , and $T$ is the sister of $S$ (so $T$ is also a daughter of $Q$ ).

Evaluating the four statements:

(1) True: $R$ is the mother of $Q$ , and $Q$ is a parent of $S$ , so $R$ is the grandmother of $S$ .
(2) True: $P$ is the brother of $Q$ , so $P$ is the uncle of $Q$ 's children $S$ and $T$ .
(3) Not necessarily true: $Q$ 's gender is unknown ( $Q$ could be male, giving $R$ two sons $P$ and $Q$ ).
(4) False: Both $S$ and $T$ are daughters of $Q$ .

Therefore, both (1) and (2) are true.

Final answer

Option (A)

Common trap

Assuming Q is female and concluding that R has only one son.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Paper: GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question: 4 of 65
Section: General Aptitude

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