GMAT OFFICIAL GUIDE PS

Solution:

We are given that the graph is SYMMETRIC along the vertical line x = 2. We are also given that when x = 1, y = 1. We are asked to determine the value of y when x is 3. Keep in mind that when x = 1, it is ONE UNIT away from the line x = 2, and when x = 3, it is also ONE UNIT away from the line x = 2.

Since the y-coordinate is 1, when x is 1, the y-coordinate is ALSO 1 when x is 3. Again, this is because the graph is symmetric with the line x = 2.

Another way to look at this problem is to see that the point (1,1) is actually being reflected over the line x = 2.

We see that the point (1,1) is exactly 1 unit from the line x = 2. In fact the point (2,1) is on the line x = 2 which is exactly 1 unit from (1,1). However, (1,1) is exactly 1 unit on the LEFT of (2,1), so by symmetry, the point that is exactly 1 unit on the RIGHT of (2,1) is (3,1). Thus the y-coordinate is 1.

Answer: E

About The Author

Scott Woodbury-Stewart is the founder & CEO of Target Test Prep. A passionate teacher who is deeply invested in the success of his students, Scott began his career teaching physics, chemistry, math, and biology. Since then, he has spent more than a decade helping students gain entry into the world’s top business schools, logging 10,000+ hours of GMAT, EA, GRE and SAT instruction. Scott also served as lead content developer and curriculum architect for the revolutionary courses Target Test Prep GMAT, Target Test Prep EA, Target Test Prep GRE and Target Test Prep SAT Quant.