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# From MGMAT If x is a prime number, what is the value of x?

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From MGMAT If x is a prime number, what is the value of x? [#permalink]  29 Oct 2006, 04:10
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From MGMAT

If x is a prime number, what is the value of x?

(1) 2x+2 is a cube of a positive integer

(2) The average of any x consecutive integer is an integer
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Senior Manager
Joined: 08 Jun 2006
Posts: 342
Location: Washington DC
Followers: 1

Kudos [?]: 23 [0], given: 0

Getting E

From 1
2x + 2 is even and cube of an integer
All the even integerâ€™s cube is even and odd integerâ€™s cube is odd
(2x+2)^ 1/3 has to be even ... 8 (2^3) or 64 (4^3) or 216 (6^3) ....
So x could be 3 or 31 or 107...x is odd
Insufficient

From 2
Average of any x consecutive integer is an integer, only when x is odd
Insufficient

Together
So x could be 3 or 31 or 107..........
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