Five people, P, Q, R, S and T, are standing in a line; who is in the middle?
Statements:
1. Q is to the left of T.
2. S is in between P and T.
The question asks to identify the person standing in the middle of a line of five people (P, Q, R, S, T).
Analyzing Statement 1
Statement 1: "Q is to the left of T."
This implies the relative order is Q ... T. It does not specify the positions of P, R, S, or their positions relative to Q and T.
Possible arrangements satisfying this condition:
- Q R S T P (Middle person: S)
- P Q R T S (Middle person: R)
Since different people (S or R) can be in the middle, Statement 1 alone is not sufficient.
Analyzing Statement 2
Statement 2: "S is in between P and T."
This implies the relative order is either P ... S ... T or T ... S ... P. It does not fix the positions of Q and R or the exact location of S, P, and T.
Possible arrangements satisfying this condition:
- Q R P S T (Middle person: P)
- R Q T S P (Middle person: T)
Since different people (P or T) can be in the middle, Statement 2 alone is not sufficient.
Analyzing Both Statements Together
Statement 1: Q ... T
Statement 2: P ... S ... T or T ... S ... P
Case A: Combining Q ... T with T ... S ... P gives Q ... T ... S ... P.
- Possible arrangement: Q T S P R (Middle person: S)
- Possible arrangement: Q R T S P (Middle person: T)
Case B: Combining Q ... T with P ... S ... T gives possibilities like P ... S ... T and Q ... T.
- Possible arrangement: Q P S T R (Middle person: S)
- Possible arrangement: P Q S T R (Middle person: S)
- Possible arrangement: P S Q T R (Middle person: Q)
Combining both cases, the middle person could be S, T, or Q.
Since combining both statements does not lead to a unique answer, the data is insufficient.
Conclusion
Neither Statement 1 nor Statement 2 alone is sufficient to determine who is in the middle. Combining both statements also does not provide a definite answer.
Therefore, the correct option is that neither statement is sufficient.
Similar Questions
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- Read the following question and decide which of the given statements is/are sufficient.
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Statements:
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Important Questions from Linear Arrangement
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How many people sit between R and V?
