Target Test Prep Sample Triangle Data Sufficiency Question

Example 1

medium

Image027

In the triangle above, is the length of side XY > the length of side WZ?

1) Angle WXY = 2n

2) Side XY = 4

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Confirm your answer
Show solutionHide solution

Solution:

Question Stem Analysis:

We can start by assigning values to some of the angles in the given triangles.

Image028

Statement One Alone:

⇒ Angle WXY = 2n

Using the information from statement one, we can assign values to angle WXY in the diagram as well as to the other angles.

Image026

In our new diagram, we should realize that because side XY and side WY of triangle WXY are both across from angles of 2n (within the same triangle), it follows that side XY = side WY. Similarly, because side WZ and side WY of triangle WYZ are both across from angles of 4n (within the same triangle), it follows that side WY = side WZ. Therefore, side XY = side WY = side WZ. We can answer the question: no, side XY is not greater than side WZ. Statement one alone is sufficient.

Eliminate answer choices B, C, and E.

Statement Two Alone:

⇒ Side XY = 4

Statement two merely provides the length of side XY. Because we are not given any information about the length of side WZ, we do not have enough information to compare the two sides. Statement two alone is not sufficient.

Correct answer:A