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Texas Instruments technical mcq question, verified with a worked answer. Free to practise - no sign-up.
The oldest sister** There are four sisters P, S, R, and T. P is younger than S, and R is older than T. Which of the given data will allow you to find out the oldest among the four sisters? Statement 1: R is older than P Statement 2: S is older than R Statement 3: T is the youngest of all
Show answer & explanation
To find the oldest sister, we need a definitive upper bound. Given P < S and T < R, Statement 2 (S > R) establishes that S is older than both P and R, and since R is older than T, S is the oldest of all four.
Step-by-step Derivation:
Step 1: Analyze the initial constraints provided in the question stem:
- P < S (S is older than P)
- T < R (R is older than T)
Step 2: Evaluate Statement 1 (R > P):
- Combining with initial constraints: S > P, R > T, R > P.
- We cannot determine if S > R or R > S. Therefore, the oldest could be either S or R. Statement 1 is insufficient.
Step 3: Evaluate Statement 2 (S > R):
- Combining with initial constraints:
- S > P (from stem)
- S > R (from Statement 2)
- R > T (from stem)
- Since S is older than P and S is older than R, and R is older than T, it follows that S > R > T and S > P.
- S is definitively the oldest. Statement 2 is sufficient.
Step 4: Evaluate Statement 3 (T is the youngest):
- This confirms T < P, T < S, and T < R.
- We still only know S > P and R > T. We do not know the relationship between S and R. Statement 3 is insufficient.
Conclusion: Only Statement 2 allows us to uniquely identify S as the oldest sister.