McGraw-Hill Education GRE 2019

triangle are 5 and 12, the hypotenuse OPQ and thus the radius of the circle

must be 13.

3. D Test Choice B against the conditions in the prompt. If the radius of the
   circle is 19, then the circumference of the circle is 38π. Since you are told that
   the circumference is less than 40π, a radius greater than 19 or smaller than
   19 would satisfy the given conditions. Thus the relationship between the two
   quantities cannot be determined.


4. A Since circumference = π × diameter, Quantity A can be expressed as
   π × diameter
   diameter = π. π is approximately 3.14, which is greater than 3. Thus Quantity
   A is greater.


5. A Each time the wheel revolves, it travels the equivalent of its circumference.
   Thus the wheel travels 3π × 2 = 6π feet per second. Set up a proportion:
   distance
   time =

6π feet

second =

x feet

60 seconds^ →^ x = 360π. Quantity A is greater.

6. B Since triangle ABC is equilateral, the rays of each angle intersect^13 of the
   circle’s circumference. Thus, arc ABC represents^23 of the circle’s circumference.
   If arc ABC is^23 of the circle’s circumference, it follows that 36 =^23 × y, where
   y = the circle’s circumference. Thus y = 36 ×^32 = 54. Quantity B is greater.


7. B Since AC is the radius of the larger circle and the diameter of the smaller
   circle, it follows that the diameter of the larger circle is double the diameter
   of the smaller circle. To determine the ratio, plug in numbers. Let AC = 4 and
   BC = 2. If AC = 4, the area of the larger circle is π4^2 = 16π and the area of the
   smaller circle is π2^2 = 4π. The ratio of the area of the smaller circle to the area
   of the larger circle is thus 16π4π = 164 =^14. Quantity B is greater.

Solids and Cylinders

So far, you have only looked at two-dimensional shapes. The GRE will occasionally

test your knowledge of three-dimensional shapes. You will need to know how to

calculate the surface area and volume of rectangular solids, cubes, and cylinders.

A cube is a type of rectangular solid, so let’s consider cubes and rectangular solids

together.

If your test date is very close, you should focus on memorizing the

formulas in bold.

CHAPTER 13 ■ GEOMETRY 421

04-GRE-Test-2018_313-462.indd 421 12/05/17 12:05 pm