Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE PS – On the graph above, when x = 1/2…

On the graph above, when x = 1/2…

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