In the figure above, if the area of square region B is 4, what is the

Given: In the figure above, the area of square region B is 4.

Asked: What is the area of triangular region D?

Area of triangular region D = \(\frac{1}{2}\) * side of square region B * side of square region C
= \(\frac{1}{2}\) * 2 * side of square region C = side of square region C

(1) The area of square region C is 9.
Side of square region C = 3
SUFFICIENT

(2) The area of square region A is 13.
13 = 2^2 + x^2
x = 3 = Side of square region C
SUFFICIENT

IMO D

Official Explanation

In this figure, we appear have three squares and a right triangle, although the question itself prior to the data statements only identifies B as a square. We want the area of triangle D, so we will need a valid base-height pair. But since D is a right triangle, we can find the length of any third side given the other two sides, with the Pythagorean Theorem. Therefore, any two lengths along the triangle will be sufficient. And since the area of square B is 4, we have a length of 2 on that side. We need only one more length of the triangle for sufficiency.

Statement (1) tells us another side of the triangle (it's 3), so it is sufficient.

Statement (2) also tells us another side of the triangle (it's \(\sqrt{13}\), so it is sufficient. The correct answer is (D).

By the way, if this figure looks familiar to you from your early education, you may have seen it as part of a proof of the Pythagorean Theorem. Keep in mind, however, that trigonometry (that is, sines, cosines, tangents, and so on) are not tested on the GMAT. Of special note on the GMAT is that the distance formula in the coordinate plane is essentially an application of the Pythagorean Theorem, and that fact will come up on some questions.

Again, the correct answer is (D).