McGraw-Hill Education GRE 2019

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C B
QUANTITY A QUANTITY B


  1. The area of trapezoid ABCD 40 A B C D


Exercise Answers


Discrete Quantitative Questions



  1. D ADC is a right triangle with sides 30, 40, and 50 (this is a multiple of the
    3-4-5 triangle). Thus AD = 30. If AD = 30, the area of ABCD = lw = 30(40) =
    1,200. Since the area of MNOP = 1,200:
    0 × (MN) = 1,200
    MN = 60

  2. 60 Recall that the sum of the angles of a polygon = (n – 2)180, where n =
    number of sides. Thus the sum of the angles in a six-sided polygon is (6 − 2)180
    = 4(180) = 720. Use the unknown multiplier to represent the quantities of the
    angles as 2x, 3 x, 4 x, 4x, 5x, and 6x. The sum of these quantities = 720:
    2 x + 3 x + 4x + 4x + 5x + 6x = 720
    24 x = 720
    x = 30
    The smallest angle = 2x = 2(30) = 60.

  3. C Let l = length of the rectangle and w = width of the rectangle:
    Area = lw = 36
    Perimeter = 2(l + w) = 26
    l + w = 13
    Use substitution to solve for l: w = 13 – l. Substitute (13 – l) for w in the first
    equation:
    l(13 – l) = 36
    13 l – l^2 = 36
    l^2 – 13l + 36 = 0
    (l – 4)(l – 9) = 0
    l =4 or l = 9
    If l = 4, then w = 9. If l = 9, then w = 4. Since you are told that l > w, l = 9.
    The correct answer is C.


CHAPTER 13 ■ GEOMETRY 405

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