Gmat_mission wrote: ↑

Sun Sep 19, 2021 11:53 am

2017-06-26_1314.png

Is the area of the triangular region above less than \(20?\)

(1) \(x^2 + y^2\ne z^2\)
(2) \(x + y < 13\)

Answer: E

Source: Official Guide

Target question: Is the area of the triangular region above less than 20?

I'm going to head straight to....

Statements 1 and 2 combined
Consider the following two scenarios, each of which satisfies BOTH statements.

case a: The triangles is an equilateral triangles and each side has length 0.001. As you can imagine, we need not find the area of this triangle since it's clear that the area is LESS THAN 20

case b: Even though statement 1 tells us that x and y cannot be the legs of a right triangle, let's see what would happen if those sides WERE the legs of a right triangle. Also, let's say that x and y are both equal to 6.5. In this case, the base has length 6.5 and the height has length 6.5. So, the area = (base)/(height)/2 = (6.5)(6.5)/2 = 21.125
Granted this scenario breaks both of the given conditions (x and y ARE the legs of a right triangle AND x+y is NOT less than 13, HOWEVER, we need only recognize that if were were to reduce the angle between x and y from 90 degrees to 89.9999999 degrees, then the area of the triangle would be a teeeeny bit less than 21.125. This would mean that x and y are NOT the legs of a right triangle, so statement 1 is satisfied.
Likewise, if we were to reduce the length of x from 6.5 to 6.49999999, then the area of the triangle would be a teeeeny bit less than 21.125. This would mean that x+y < 13, so statement 2 is satisfied.
As we can see, we can make it so that case b satisfies both conditions, and have it so that the area of the triangle is GREATER THAN 20
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E