Practice GMAT Problem Solving Question
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f(x) =

; f(-1)=
Correct Answer: A
- To determine f(-1), we must first know (-1)59, (-1)57, and (-1)56. You should never multiply out hundreds of numbers.
- 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
- This means (-1)56=+1 since 56 is an even number, (-1)57=-1 since 57 is an odd number, and (-1)59=-1.
- This simplifies the numerator to:
5(-1) - 3(-1) + 4(1)
-5 + 3 + 4 = 2
- Plugging in -1 for x in the denominator yields:
2(-1 )+ 1
-2 + 1 = -1
- 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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