GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag173

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67. (D) Without additional information (such as lines m and n are parallel), the relation-
ship cannot be determined from the information given. Select (D). Tip: The lines m and n 
appear parallel, but the question does not state that is the case.
68. (C) Because angles b and c are supplementary, lines l and m are parallel. Therefore, 
∠ ≅ ∠a d (because corresponding angles of parallel lines are congruent) and their measures 
are equal. The two quantities are equal. Select (C).
69. (A) The sides of the two triangles are in the ratio 3:1, so the areas of the two triangles 
are in the ratio 32 : 12 = 9:1. Thus, the area of the larger triangle is ×9 (25 square inches) = 
225 square inches. Quantity A is greater.
70. (A) The measure of ACB 180 65 70 45∠ = ° − ° − ° = ° and the measure of 
DCA 60 45 105∠ = ° + ° = °. The measure of an exterior angle of a triangle equals the sum of 
the measures of the remote interior angles. Thus, the measure of DCA 105 30∠ = ° = ° + the 
measure of ∠E. Hence, the measure of E∠ = ° − °105 30 = °75 . The measure of B∠ = °70 . 
Thus, the measure of B∠ is less than the measure of E∠ . Quantity A is greater.
71. (D) ∠A is a common angle in the two right triangles ABC and ADE. Thus, the two 
triangles are similar (because corresponding angles are congruent). However, without 
further information, you cannot determine AD. Therefore, the relationship cannot be 
determined from the information given. Select (D).
72. (C) Sketch a figure.
P
Q
R
Y
Z
X
 In the two triangles, two pairs of corresponding sides are proportional, and the included 
angles are congruent. Therefore, the triangles are similar. ∠m R equals ∠m Z (because cor-
responding angles of similar triangles are congruent). The two quantities are equal. Select (C).
73. (D) Let l = the length and w = the width of the rectangular region. Then, its area = 
=lw 24 and its perimeter = +l w2( ). If l = 24 and w = 1, then = ⋅ =lw 24 1 24 and perimeter 
= +l w2( ) = +2(24 1) = 50. In this case, Quantity A is greater. If l = 12 and w = 2, then 
= ⋅ =lw 12 2 24 and perimeter = +l w2( ) = +2(12 2) = 28. In this case, Quantity B is greater. 
Because you found different results (one where Quantity A was greater and one where 
Quantity B was greater), the relationship cannot be determined from the information given. 
Select (D).
06_McCune_Answer.indd 164 2/21/22 4:44 PM