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P is the brother of Q and R. S is R's mother. T is P's father. Which of the following statements cannot be definitely true?

Difficulty: Medium

Correct Answer: Q is T's son

Explanation:


Introduction / Context:

This reasoning question asks you to identify which one of the given statements cannot be definitely concluded from the information provided. It is not about which statement is impossible, but rather which statement is not guaranteed to be true in every valid family arrangement consistent with the given clues. Understanding the difference between “possible” and “definitely true” is the key here.


Given Data / Assumptions:

  • P is the brother of Q and R, so P, Q and R are siblings and P is male.
  • S is R's mother.
  • T is P's father.
  • Standard exam convention assumes siblings share the same parents unless stated otherwise, so P, Q and R typically have the same mother and father.
  • We must decide which of the given four statements cannot be asserted as definitely true.


Concept / Approach:

First, we interpret “brother of Q and R” in the usual exam sense: P, Q and R are children of the same parents S (mother) and T (father). Then we check each option to see whether it must follow in all such cases or whether, in at least one consistent interpretation, it might fail. The subtle point is about the gender of Q, which is not specified.


Step-by-Step Solution:

Step 1: If S is R's mother and P is the brother of R, then in standard reasoning puzzles S is also the mother of P and Q. Step 2: Similarly, if T is P's father and P is the brother of Q and R, T is also taken as the father of Q and R. Step 3: Under these assumptions, T is Q's father. So the statement “T is Q's father” must be true. Step 4: Since S is the mother of R and siblings typically share parents, S is also P's mother. So “S is P's mother” is definitely true as well. Step 5: P is explicitly stated to be male (“brother”), and S is his mother, so “P is S's son” is also definitely true. Step 6: However, the statement “Q is T's son” assumes that Q is male. The question does not specify Q's gender; Q could be either a son or a daughter of T. Step 7: Because we cannot be certain that Q is male, we cannot say with certainty that “Q is T's son” is true. Q might instead be T's daughter.


Verification / Alternative check:

Consider two possible family configurations consistent with the clues. In one, Q is male; then the statement “Q is T's son” is true. In another, Q is female; then the statement becomes false and the correct description would be “Q is T's daughter”. Since both configurations are consistent with the question stem, the statement about Q being T's son is not definitely true.


Why Other Options Are Wrong:

Each of the other three options follows directly from the standard assumption that P, Q and R are full siblings with common parents S and T. There is no scenario under that convention in which T is not Q's father, S is not P's mother, or P is not S's son.


Common Pitfalls:

Many students mistakenly look for logical impossibility instead of “not definitely true”. Others overlook unspecified gender and assume that every child mentioned without a label is male. Always pay close attention to which individuals have clearly stated genders (like “brother”) and which do not.


Final Answer:

The statement that cannot be definitely true is “Q is T's son.”

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