McGraw-Hill Education GRE 2019

9. 24 The volume of the box is 10 × 15 × 20 = 3,000. Each of the small cubes
   being placed into the box has a volume of 5^3 = 125. The number of cubes that
   can fit into the box = 3,000 125 = 24.


10. D Each metal cube has a volume of 2^3 = 8. Since there are three metal cubes,
    their combined volume is 8 × 3 = 24. The volume of the cylinder is π(r^2 )h =
    π(3^2 )(8) = 72π. 72π^24 =^13 π.

Quantitative Comparison Questions

1. B The formula for the diagonal of a cube is e√3. The value in Quantity A is
   thus 3√ 3. The formula for the diagonal of a rectangular solid is √l^2 + w^2 + h^2.
   The value in Quantity B is thus √4 + 9 + 16 = √ 29. √ 29 > 3√ 3. Thus Quantity B
   is greater because squaring both sides of the equation will show that 29 > 9 × 3.


2. B The value in Quantity A is 4 × 5 × 6 = 120. The value in Quantity B is
   π(3^2 )6= 54π. 54π > 120. Quantity B is greater.


3. A Let e = the edge of the cube. You are thus comparing e^3 to 6e^2. To simplify
   the comparison, divide both sides by e^2 (you can do this since e^2 is positive).
   The new comparison is thus:
   QUANTITY A QUANTITY B
   e 6
   Since you are told that e > 6, Quantity A is greater.

The Coordinate Plane

The coordinate plane is used to designate points in a two-dimensional plane. It is

created by two perpendicular lines that meet at the origin. The horizontal line is

called the x-axis and the vertical line is called the y-axis. These lines split the plane

into four quadrants: I, II, III, and IV.

y

x

IV

II I

III

Points on the coordinate plane are designated by assigning two numbers: an

x-coordinate and a y-coordinate. A point is written in the form (x,y).

430 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 430 12/05/17 12:06 pm