Question

How many different triangles can be formed?
I. There are 16 coplanar, straight lines.
II. No two lines are parallel.

• A. The question cannot be answered even with the help of both the statements taken together.
• B. The question can be answered by any one of the statements
• C. Each statement alone is sufficient to answer the question, but not the other one.
• D. Both statements I and II together are needed to answer the question

Hint:

To find the number of triangles from lines, both the number of lines and conditions about parallelism/concurrency are required.

Answer 1

The Correct Option is D

I: Knowing only the number of lines does not guarantee they are not parallel or concurrent, so cannot ensure triangles can be formed.
II: Knowing only that no two lines are parallel does not tell the total number of lines.
Together: From 16 lines, with no two parallel and no three concurrent, number of triangles = $\binom{16}{3}$ = 560. %Quick tip