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Here is this week’s problem:

If n is a prime number greater than 2, is 1/x > 1?

(1) xn < x < x(1/n)

(2) x(n“1) > x(2n“2)

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#### Tom Williams

Tom Williams is a Marketing Associate at Manhattan Prep. His background and interests are primarily within New Media and Online Marketing. As such, he spends approximately 18 hours a day in front of a computer. When heâ€™s not interacting with Manhattan Prep students on Facebook and Twitter, Tom can be found listening to records, rooting for the Mets and Jets, and reading history books.

### 6 responses to Challenge Problem Showdown – November 19, 2012

1. ans: both 1 and 2 can answer the problem

Since n > 2, n can only be odd. Also for 1/x to be greater than 1, x should be a proper fraction.

From statement 1 we know that x is a proper fraction since x^n < x1
eg: If x = 1/2 and n = 3 ; x^n = 1/8; x^1/n = 1/1.41

From statement 2 we know that x is a proper fraction again, therefore 1/x>1
eg: x=1/2 and n = 3 ; x^(n-1) = 1/4 and x^(2n-2) = 1/16

3. As we know that x is a prime number greater than 2, 1/x is definitely less than 1. So no matter what choice 1 and 2 are saying, we’ve got the answer. It’s d. Rather tricky!

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