Question

In the figure above, what is the value of x+ y?
(1) x= 70
(2) $△ABC$ and $△ADC$ are both isosceles triangles.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

1. Even if x = 70, the location of point D can vary. As the location of D varies, the value of y will vary, and hence the value of x + y will vary. Therefore, the value of x + y cannot be determined; NOT sufficient.
2. If and are isosceles triangles, then and have the same measure, and and have the same measure. However, since no values are given for any of the angles, there is no way to evaluate x + y; NOT sufficient.

• Taking (1) and (2) together, x = 70 and and have the same measure. Since the sum of the measures of the angles of a triangle is 180 degrees, both and have measure 55 degree (70 + 55 + 55 = 180), but there is still no information about the value of y. Therefore, the value of x+ y cannot be determined. The correct answer is E; both statements together are still not sufficient.