Directions: The question below consists of a question and two statements…

2025

Directions: The question below consists of a question and two statements numbered I and II are 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 answer.

Find the total number of people sitting in the row?

I. If A is 12th from the left end. B is 15th from the right end and the number of people sitting between them is 8.

II. The positions of A and B are interchanged then the new position of B is 6th from the right

  1. A.

    Data in statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

  2. B.

    Data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

  3. C.

    Data in statements I alone or in Statement II alone are sufficient to answer the question.

  4. D.

    Data in both the Statements I and II together are necessary to answer the question.

Show answer & explanation

Correct answer: D

Concept:

For a straight row, position from the left end + position from the right end minus 1 gives the total number of people (N), once the number of people strictly between two individuals is known. However, the same people-between count can arise from two different total lengths -- one where the counting from each end does not overlap and one where it does -- so a lone between-count can leave N ambiguous until a second, independent condition rules out one of the two cases. In data sufficiency, each statement is tested ALONE first, and only checked TOGETHER when neither alone settles the question.

Statement I:

  1. A is 12th from the left end, so position(A) = 12.

  2. B is 15th from the right end, so position(B) = N minus 14.

  3. 8 people sit between A and B, so |position(A) minus position(B)| minus 1 = 8, which gives |26 minus N| = 9.

  4. This equation has two solutions, N = 35 or N = 17, so the total is not yet fixed.

Statement I alone leaves two candidate totals, so it is not sufficient by itself.

Statement II:

  1. Interchanging A and B's positions means B's new position equals A's original position.

  2. B's new position is given as 6th from the right, so A's original position = N minus 5.

  3. This single relation connects two unknown quantities -- A's position and N -- without fixing either one on its own.

Statement II alone therefore does not determine the total number of people.

Combining both statements:

  1. Statement I already fixes A's position at 12.

  2. Substituting into Statement II's relation, 12 = N minus 5, so N = 17.

  3. N = 17 is exactly one of the two values Statement I allowed, so it stays consistent with Statement I, while the other candidate (N = 35) would require A at position 30, contradicting the given position of 12.

Combining the two statements removes the case-ambiguity left by Statement I and fixes a single, unique total. Since neither statement alone determines the total but both together do, the data in Statements I and II together are necessary to answer the question.

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