Data Sufficiency : Geometry

Data Sufficiency questions appear either in the Quantitative reasoning section or in the Data Interpretation and LR section of the CAT test.

Usually 5 to 10 questions appear in DS depending upon how many total questions are there in the section.

A data sufficiency question comes with the following set of instructions.

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

Here is a DS question from Geometry.

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.

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.

Some basics about Circles that Touch and Intersect
(i) If two circles touch each other externally, then the distance between their centers is a+ b. There will just be one point at which the circumference of the two circles touch each other.

(ii) If two touch each other internally, then the distance between their centers is a - b, where a > b. There will be only one point at which the circumference of the two circles touch each other.

(iii) If two circles intersect, then there will be two points at which the circumference of the two circles meet. We will not be able to determine the distance between their centers using the information about the radii of the two circles.

Geometry, Coordinate geometry and mensuration are favourite areas in which questions in DS typically appear. Practice with adequate number of questions from your CAT Preparation Material to get familiar with these questions.