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

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Manager
Joined: 05 May 2005
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If x is a prime number, what is the value of x? [#permalink]

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17 May 2007, 18:07
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How would you solve?

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

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

(2) The average of any x consecutive integers is an integer.
Director
Joined: 26 Feb 2006
Posts: 901
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Re: Prime numbers - DS [#permalink]

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17 May 2007, 18:30
above720 wrote:
How would you solve?

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

(1) 2x + 2 is the cube of a positive integer.
(2) The average of any x consecutive integers is an integer.

from i, x could be 3 or 31 or so on ==> nsf
from ii, x is not 2. so x is odd==> nsf.
togather also nsf because x is odd..

E
VP
Joined: 03 Apr 2007
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Re: Prime numbers - DS [#permalink]

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17 May 2007, 19:04
above720 wrote:
How would you solve?

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

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

(2) The average of any x consecutive integers is an integer.

Stat 1:
x can be 2,3,5,7....

2x+2 ->even

-that implies x =2

A is sufficient

Stat 2:
x is a odd number

eg : avg of 3 integers is an integer.
avg of 5 integers is an integer.

B is suff

Ans :C
VP
Joined: 08 Jun 2005
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Re: Prime numbers - DS [#permalink]

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17 May 2007, 23:22
as Himalayan wisely wrote !

statement 1

2x + 2 is the cube of a positive integer.

f(2) = 2*2 + 2 = 6
cube(6) = not an integer

f(3) = 2*3 + 2 = 8
cube(8) = 2

f(5) = 2*5 + 2 = 12
cube(12) = not an integer

f(7) = 2*7 + 2 = 16
cube(16) = not an integer

f(31) = 2*31 + 2 = 64
cube(64) = 4

insufficient

statement 2

The average of any x consecutive integers is an integer

means only that x can't be 2 !

for (6,7) = (6+7)/2 = not an integer

insufficient

statement 1&2

still insufficient

Re: Prime numbers - DS   [#permalink] 17 May 2007, 23:22
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