In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statement/s are sufficient to answer the question. Read both the statements and choose your answer carefully. Question: P, Q, R, S, T, U and V are 7 people standing in a row all facing North (not necessarily in the same order). Who is standing second to the right of T? Statements: (I) U is standing 3rd from the right end and 2nd to the left of R. (II) Q is standing to the immediate right of T. Q is standing 2nd to the left of P
The data in both the Statements (I) and (II) together are NOT sufficient to answer the question.
Analyzing the Seating Arrangement Question
This question asks us to determine who is standing second to the right of person T, based on the information provided in two statements about a row of 7 people (P, Q, R, S, T, U, V) all facing North.
Evaluating Statement (I) for Seating Arrangement
Statement (I) gives us two pieces of information:
- U is standing 3rd from the right end. In a row of 7 people, if we number the positions from left to right as 1, 2, 3, 4, 5, 6, 7, then the 3rd position from the right end is the 5th position from the left end. So, U is at position 5.
- U is standing 2nd to the left of R. This means there is one person between U and R, and U is to the left of R. If U is at position 5, then R must be at position ${5 + 2 = 7}$.
Based on Statement (I), we know the positions of U and R in the 7-person row:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | ? | ? | ? | ? | U | ? | R |
We know U is at position 5 and R is at position 7. However, we have no information about the position of T or any other person (P, Q, S, V). Since T's position is unknown, we cannot determine who is standing second to the right of T using only Statement (I).
Conclusion: Statement (I) alone is not sufficient to answer the question.
Evaluating Statement (II) for Seating Arrangement
Statement (II) gives us two pieces of information about the relative positions of T, Q, and P:
- Q is standing to the immediate right of T. This tells us that T and Q are adjacent, with Q on the right side of T. We can represent this as T Q.
- Q is standing 2nd to the left of P. This tells us there is exactly one person between Q and P, and Q is on the left side of P. We can represent this as Q _ P.
Combining these two parts of Statement (II), we get a block of people in relative positions: T Q _ P. This block involves T, Q, one unknown person, and P.
This block of four people must stand together in the row of 7. However, Statement (II) does not specify where this block is located in the row (e.g., it could be positions 1-4, 2-5, 3-6, or 4-7). Also, the identity of the person standing between Q and P is not revealed by this statement alone. We are looking for the person second to the right of T. In the T Q _ P sequence, the person immediately to the right of T is Q. The person second to the right of T is the person in the '_' position.
Since the position of the T Q _ P block is not fixed in the 7-person row, and the person in the '_' position is unknown from this statement alone, we cannot determine who is second to the right of T using only Statement (II).
Conclusion: Statement (II) alone is not sufficient to answer the question.
Combining Statement (I) and Statement (II) for Seating Arrangement
Now, let's combine the information from both statements to see if we can find a unique seating arrangement and identify the person second to the right of T.
- From Statement (I): U is at position 5 and R is at position 7. The arrangement is _ _ _ _ U _ R.
- From Statement (II): We have the relative arrangement T Q _ P.
We need to fit the block T Q _ P into the remaining positions (1, 2, 3, 4, and 6) in the structure _ _ _ _ U _ R.
The T Q _ P block requires 4 consecutive positions. Looking at the available slots (1, 2, 3, 4, 6), the only set of 4 consecutive positions is (1, 2, 3, 4).
So, the block T Q _ P must occupy positions 1, 2, 3, and 4. The person at position 1 is T, at position 2 is Q, at position 4 is P. The person at position 3 is the unknown person from the T Q _ P block.
The arrangement so far is: T (Pos 1), Q (Pos 2), _ (Pos 3), P (Pos 4), U (Pos 5), _ (Pos 6), R (Pos 7).
The two empty positions are 3 and 6. The remaining people from the group P, Q, R, S, T, U, V are S and V. So, the person at position 3 and the person at position 6 must be S and V, in some order.
Let's fill in the arrangement:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | Q | ? | P | U | ? | R |
The persons at positions 3 and 6 are S and V. So, position 3 is either S or V, and position 6 is the other person (V or S).
The question asks: Who is standing second to the right of T?
T is at position 1. The person immediately to the right of T (1st to the right) is at position 2, which is Q.
The person second to the right of T (2nd to the right) is at position 3.
According to the combined information, the person at position 3 is either S or V. We cannot definitively determine whether it is S or V.
Since the identity of the person second to the right of T is not unique (it could be S or V), the data in both Statements (I) and (II) together is not sufficient to answer the question.
Conclusion: Both Statements (I) and (II) together are NOT sufficient.
Final Sufficiency Assessment for the Seating Puzzle
We analyzed Statement (I) alone and found it insufficient. We analyzed Statement (II) alone and found it insufficient. Finally, we combined both statements and deduced that while we could place most people, the person second to the right of T could still be one of two possibilities (S or V). Since the answer is not unique, the combined data is not sufficient.
Therefore, the data in both the Statements (I) and (II) together are NOT sufficient to answer the question.
Revision Table: Seating Puzzle Clues
| Statement | Key Information Given | Inference from Statement | Sufficiency |
|---|---|---|---|
| (I) | U is 3rd from right end (Pos 5). U is 2nd to left of R. | U at pos 5, R at pos 7. | Not sufficient (T's position unknown) |
| (II) | Q immediate right of T (T Q). Q 2nd left of P (Q _ P). | Relative arrangement: T Q _ P. | Not sufficient (Block position unknown) |
| Combined (I & II) | U at pos 5, R at pos 7 and relative T Q _ P. | Arrangement is T Q (S/V) P U (V/S) R. Person at pos 3 is S or V. | Not sufficient (Person second to right of T (at pos 3) is not unique) |
Additional Information on Data Sufficiency Questions
Data sufficiency questions are common in logical reasoning sections of competitive exams like SBI PO. They test your ability to determine if the given data is adequate to answer a specific question, not necessarily to find the answer itself.
- You must evaluate each statement individually first.
- If neither statement alone is sufficient, combine them and evaluate the combined information.
- If even the combined data does not lead to a unique answer for the question asked, then the data is not sufficient.
- Pay close attention to keywords like "immediate," "to the left/right," "from the end," and "between."
- For seating arrangements, drawing diagrams can be very helpful to visualize the constraints and potential arrangements.
In this seating arrangement puzzle, the goal was not to find *a* possible arrangement, but to determine if the person second to the right of T could be uniquely identified. Since it could be one of two people even after combining the statements, the data is insufficient.
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