Question

What is the position of A from the beginning in a row of 17 students? Statements: (I) There are three students between A and B. (II) B is behind A.

• A. Statement (I) alone is sufficient to answer the question, but (II) alone is not sufficient.
• B. Statement (II) alone is sufficient to answer the question, but (I) alone is not sufficient.
• C. Both the statements (I) and (II) are sufficient to answer the question, but neither statement alone is sufficient.
• D. Both the statements (I) and (II) together are not sufficient to answer the question and additional data are required.

Hint:

In arrangement problems, relative position gives order, but exact position needs at least one fixed reference point.

Answer 1

The Correct Option is D

Concept: To find the exact position of A from the beginning, we need enough fixed positional information. Relative positions alone may not determine the exact place.

Step 1: Checking Statement (I).
Given: \[ \text{There are 3 students between A and B} \] So the gap between A and B is: \[ 4 \] Possible arrangements: \[ A \; \_ \; \_ \; \_ \; B \] or \[ B \; \_ \; \_ \; \_ \; A. \] But their exact starting position in the row is unknown. Thus, Statement (I) alone is not sufficient.

Step 2: Checking Statement (II).
Given: \[ B \text{ is behind A} \] This only tells us: \[ A \text{ is before } B \] But no exact position is known. Thus, Statement (II) alone is not sufficient.

Step 3: Checking both statements together.
From Statement (I): \[ A \text{ and } B \text{ are 4 places apart} \] From Statement (II): \[ B \text{ is behind A} \] So arrangement becomes: \[ A \; \_ \; \_ \; \_ \; B \] Still, A can be in many positions: \[ 1,2,3,\dots,13 \] since total students are 17. Thus, A’s exact position cannot be uniquely determined. Hence, additional data are required.