GMAT考试-Testprep数学精解2(19)

网络资源 Freekaoyan.com/2008-04-10

  7. The set S of numbers has the following properties:

  I) If x is in S, then 1/x is in S.

  II) If both x and y are in S, then so is x + y.

  Is 3 in S?

  (1) 1/3 is in S.

  (2) 1 is in S.

  Consider (1) alone. Since 1/3 is in S, we know from Property I that 1/(1/3)

  = 3 is in S. Hence, (1) is sufficient.

  Consider (2) alone. Since 1 is in S, we know from Property II that 1 + 1 = 2

  (Note, nothing in Property II prevents x and y from standing for the same n

  umber. In this case both stand for 1.) is in S. Applying Property II again s

  hows that 1 + 2 = 3 is in S. Hence, (2) is also sufficient. The answer is D.

  8. What is the area of the triangle above?

  (1) a = x, b = 2x, and c = 3x.

  (2) The side opposite a is 4 and the side opposite b is 3.

  From (1) we can determine the measures of the angles: a + b + c = x + 2x + 3

  x = 6x = 180

  Dividing the last equation by 6 gives: x = 30

  Hence, a = 30, b = 60, and c = 90. However, different size triangles can hav

  e these angle measures, as the diagram below illus


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