Direction: The question given below consists of two statements numbered I and…

2024

Direction: The question given below consists of two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give the answer:

In a row, there are 5 poles - P, Q, R, S and T, which pole is at the penultimate position?

Statements:

I. Poles S and Q are at the two extreme ends of the row respectively from left to right.

II. Pole T is to the right of pole R.

  1. A.

    I alone is sufficient while II alone is not sufficient

  2. B.

    II alone is sufficient while I alone is not sufficient

  3. C.

    Either I or II is sufficient

  4. D.

    Neither I nor II is sufficient

Attempted by 17 students.

Show answer & explanation

Correct answer: D

Concept: In a data-sufficiency question, a statement (or a combination of statements) is sufficient only if it pins down one single, unique answer. If more than one valid arrangement remains consistent with the given information, the data is not sufficient.

Application:

  1. From Statement I: Poles S and Q occupy the two extreme ends of the row, respectively from left to right, so S is at position 1 and Q is at position 5. This still leaves P, R and T free to sit in positions 2, 3 and 4 in any order, so Statement I alone cannot fix the second-last (4th) position.

  2. From Statement II: Pole T is to the right of pole R - only a relative order between R and T, with no information about S, Q or P. Statement II alone gives no fixed positions at all, so it cannot determine the second-last position either.

  3. Combining both: with S fixed at position 1 and Q at position 5, P, R and T must fill positions 2, 3 and 4 in some order that keeps R to the left of T. Checking every arrangement of P, R and T in these three slots:

Positions 2-3-4

Resulting row

Second-last pole (position 4)

P, R, T

S, P, R, T, Q

T

R, P, T

S, R, P, T, Q

T

R, T, P

S, R, T, P, Q

P

Cross-check: all three rows satisfy both statements (S at the left end, Q at the right end, and R to the left of T), yet the second-last pole comes out as T in two of them and P in the third. Even after combining Statement I and Statement II, the second-last position is not uniquely fixed.

Since neither statement alone, nor the two together, pin down a single second-last pole, the correct choice is that neither statement is sufficient.

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