Practice GMAT Problem Solving Question

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f(x) = Figure 1; f(-1)=
Correct Answer: A
  1. To determine f(-1), we must first know (-1)59, (-1)57, and (-1)56. You should never multiply out hundreds of numbers.
  2. Instead, look for a pattern:
    (-1)1=-1
    (-1)2=+1
    (-1)3=-1
    (-1)4=+1
    ...
    (-1)(odd number)=-1
    (-1)(even number)=+1
  3. This means (-1)56=+1 since 56 is an even number, (-1)57=-1 since 57 is an odd number, and (-1)59=-1.
  4. This simplifies the numerator to:
    5(-1) - 3(-1) + 4(1)
    -5 + 3 + 4 = 2
  5. Plugging in -1 for x in the denominator yields:
    2(-1 )+ 1
    -2 + 1 = -1
  6. Combining the top and bottom of the fraction yields an answer of f(-1)=2/-1 = -2. The correct answer is A.

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