McGraw-Hill Education GRE 2019

Thus

3 x +4x +5x = 180

12 x = 180

x = 15

The measurement of the smallest angle is 3(15) = 45.

Quantitative Comparison Questions

1. B Based on the triangle inequality theorem,
   (9 – 7) < x < (7 + 9)
   2 < x < 16
   Since x < 16, Quantity B is greater. The correct answer is B.


2. D Since the triangle is isosceles, the third side can have a length of 7 or 12. If
   the length of the third side is 7, then the perimeter is 7 + 7 + 12 = 26. In this
   case, the two quantities are equal. If the third side is 12, then the perimeter is
   7 + 12 + 12 = 31. In this case, Quantity A is greater. The relationship cannot be
   determined.


3. A Recall that the relationship of the sides in an obtuse triangle is a^2 + b^2 < c^2.
   In the triangle, this inequality is satisfied: 3^2 + 4^2 < 6^2. Thus triangle ABC is
   obtuse and the measure of angle ABC > 90.


4. A To determine a relationship between the areas, determine the relationship
   between the side lengths. If the altitude in the triangle in Quantity A is 8, then
   the side length must be more than 8. To understand why, see the following
   figure.

60°

30°

8

A D C

B

Side AB is the hypotenuse of triangle ABD, which means that AB > 8. Thus

the side length of the triangle in Quantity A is greater than the side length of

the triangle in Quantity B. Therefore, the area of the triangle in Quantity A is

greater.

5. D From the diagram, you can infer that
   x + (x + 30) + y = 180
   2 x + y = 150
   However, without any other relationships, the relationship between x and y
   cannot be determined.

396 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 396 12/05/17 12:04 pm