McGraw-Hill Education GRE 2019

8. C Since a and c are the two angles above l, their sum must equal 180: a + c =
   180. Add the two equations to solve for a:
   a – c = 20
   
   
   • a + c = 180
     2 a = 200 → a = 100
     Since a and b are the larger angles formed by the transversal, they must be
     equal. Thus b = 100.
   
   
   
   


9. 30 Si nce (3a + b) and d are the larger angles formed by the transversal,
   3 a + b = 100. Combine this equation with a + b = 40:
   3 a + b = 100
   a + b = 40
   To solve for a, express b in terms of a: b = 40 – a. Substitute 40 – a for b in the
   first equation:
   3 a + (40 – a) = 100
   2 a + 40 = 100
   2 a = 60
   a = 30

Quantitative Comparison Questions

1. B Since a > 90, a must be the larger angle created by the transversal. Thus b
   and d must be the smaller angles created by the transversal. The smaller angles
   created by the transversal are always less than 90 degrees. Thus Quantity B is
   greater.


2. B Since a and b create line l, they must be supplementary. If a > 90, then
   b < 90.


3. A The angles above line l must add to 180. Thus 2x + a = 180. The angles
   below line l must add to 180. Thus 2a + x = 180. Add these equations:
   2 x + a = 180
   
   
   • x + 2a = 180
     3 x + 3a = 360
     Divide both sides by 3: x + a = 120. Since x > 60, a < 60.
   
   
   
   


4. D Although a and z are the larger angles formed by a transversal, the
   transversals forming these angles are different. Thus you can only infer that
   a and x are each greater than 90. No information can be deduced about their
   relationship. The correct answer is D.

CHAPTER 13 ■ GEOMETRY 375

04-GRE-Test-2018_313-462.indd 375 12/05/17 12:04 pm