Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine whether the area of the triangular region is less than 20.
Statement One Alone:
x^2 + y^2 ≠ z^2
Because we don’t know anything about the values of x, y, and z, statement one alone is not enough information to answer the question.
Statement Two Alone:
x + y < 13
Again, we can’t determine the values of x and y (and z), so statement two alone is not enough information to answer the question.
Statements One and Two Together:
Using both statements, we still can’t determine the value of x and y (and z). For example, if we take y as the base of the triangle, we see that the height of the triangle, h, has to be less than x. So, let’s say y = 10, x = 2.5, and h = 2; then, the area of the triangle is ½ x 10 x 2 = 10, which is less than 20. However, let’s say y = 6.4, x = 6.5, and h = 6.4; then, the area of the triangle is ½ x 6.4 x 6.4 = 20.48, which is greater than 20.
Answer: E
