Question: What is the length of the line segment AC?

Reasoning ·Previously asked in JKSSB Sub Inspector (Executive) 2022

View the full solved paper: JKSSB Sub Inspector (Executive) 2022

Question

Given below is a question followed by 2 statements numbered I and II. Choose the statement(s) required to answer the question.

Question: What is the length of the line segment AC?

I. Length of line segment AB is 10 cms

II. Length of line segment BC is 10 cms

  1. A. Statement (I) ALONE is sufficient, but statement (II) ALONE is NOT sufficient
  2. B. Statement (II) ALONE is sufficient, but statement (I) ALONE is NOT sufficient
  3. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
  4. D. Statements (I) and (II) TOGETHER are NOT sufficient (Correct answer)

Correct Answer

Option D — Statements (I) and (II) TOGETHER are NOT sufficient

Detailed Solution & Explanation

The correct answer is Statements (I) and (II) TOGETHER are NOT sufficient.

Key Points

  • To find the length of AC, we would need to know that B lies on line segment AC (i.e., A, B, C are collinear with B between A and C).
  • Statement I gives AB = 10 cm and Statement II gives BC = 10 cm. Even together, we cannot determine AC because we do not know the configuration: B might not be between A and C (they could form a triangle, or B could be outside AC).
  • Without knowing the geometric arrangement, AC cannot be determined.
  • Hence, statements I and II together are NOT sufficient.