2IIM - CAT Discussion Forum

The following data sufficiency question is a question that tests your knowledge about circles in geometry.

Directions to answer the DS question

1. Statement (A) ALONE is sufficient, but statement (B) alone is not sufficient to answer the question asked.
2. Statement (B) ALONE is sufficient, but statement (A) alone is not sufficient to answer the question asked.
3. BOTH statements (A) and (B) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (A) and (B) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Question

Does the circle A with radius ‘a’ touch circle B with radius ‘b’ internally?
A. The two circles touch each other at only 1 point
B. The distance between centers of A and B is a-b

Correct Answer
Choice (2). Statement B alone is sufficient while statement A is not sufficient.

Explanatory Answer

Statement A: The two circles touch each other at only 1 point. If two circles touch each other at only one point, they could touch each other either externally or internally. Hence, this statement is not sufficient to answer the question.

Statement B: The distance between the centers of A and B is a-b. If two circles touch each other internally, then the distance between their centers is the difference between their radii. If they touch each other externally, then the distance between their centers is a+ b.

As statement B clearly states that the distance between the centers is a - b, the two circles touch each other internally.

Choice (2) is the correct answer.