GMAT by the Numbers: Data Sufficiency

Now that you’ve learned how to approach Data Sufficiency questions on the GMAT, let’s add one more dimension to your understanding of how they work.

Take a moment to try this question. Following is performance data from thousands of people who have studied with Kaplan over the decades. Through analyzing this data, we will show you how to approach questions like this one most effectively and how to avoid similarly tempting wrong answer choice types on Test Day.

  1. A circle is inscribed inside square ABCD.  Side AB contains point E and line segments connect point E with C and D, forming a triangle.
    In the figure above, a circle is inscribed in square ABCD. What is the area of ∆CDE?
    1. The circle has a radius of length 3.
    2. CDE is isosceles.
    1. Statement (1) ALONE is sufficient, but Statement (2) is not sufficient.
    2. Statement (2) ALONE is sufficient, but Statement (1) is not sufficient.
    3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    4. EACH statement ALONE is sufficient.
    5. Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation

You’re asked to find the area of triangle CDE. The area of a triangle is equal to Base × Height. You can use CD as a base, and the height would be the length of a perpendicular drawn from point E to CD. Since that perpendicular line would be equal in length to BC, you only need to learn the length of the sides of square ABCD to know the length of both the base (CD) and the height (equal to BC) of triangle CDE.

Statement (1) says that the radius of the inscribed circle is 3, so its diameter is 6. That diameter equals the length of the sides of the square, which is what you need to answer the question. So Statement (1) is sufficient. Statement (2) gives no measurements to work with. It does allow you to figure out that point E bisects AB, but that’s irrelevant to the question. Statement (2) is insufficient. Since Statement (1) is sufficient but Statement (2) is not, the correct answer is (A).

The question statistics reveal two very common habits that lead to wrong answers. Many test takers select (C), believing that the statements are sufficient only when combined. Statement (1) alone does not tell you the placement of point E, but you don’t need that information to find the triangle’s area. You don’t always need to know everything to be able to answer the question that’s asked.

Also, some people struggle to relate the data about the circle to the square and then to the triangle. They look at Statement (1) and think, “I don’t know how to solve with this,” so they treat the statement as insufficient, leading in this question to (E). But to do so is to equate “I don’t know how to solve this” with “This can’t be solved”—not the same thing at all! You can see from the question statistics that this is a common line of thinking—and not one that the GMAT likes to reward. Be wary of guessing that a statement is insufficient unless you can see exactly why it doesn’t lead to a clear answer. 

More GMAT by the Numbers . . .

To see more questions with answer choice statistics, be sure to review the full-length CATs in your online resources.