# Practice GMAT Problem Solving Question

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f(x) = -5x

^{197}-8x^{248}+1; f(-1) = ?Correct Answer:

**C**- To determine f(-1), we must first know (-1)
^{197}and (-1)^{248}. You should never multiply out lots 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)
^{197}=-1 since 197 is odd and (-1)^{248}=+1 since 248 is even. - This pattern simplifies the equation to:

-5(-1) - 8(1) + 1, which equals 5 - 8 + 1, or -2.

Thus, C is the correct answer.

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