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Problem Solving (PS) | Set T consists of 100 consecutive odd integers. If k is an integer

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GMATPrepNow wrote:

Set T consists of 100 consecutive odd integers. If k is an integer, which of the following CANNOT equal the median of set T?

A) k² - k - 6
B) k² + 8k + 15
C) 4k² + 4k + 1
D) k³ - 4k² - k
E) 3k³ - 27k²

*Kudos for all correct solutions

GMATPrepNow , if it's any consolation, I hit a brain freeze at the options check. Boo.

The median of an even number of consecutive odd integers is even. (E.g. 1, 3, 5, 7. Median is 6.)

Options: which one CANNOT be even?

C did not "announce itself"
...

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