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

Question

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.

Himalayan · Answer

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

goalsnr · Answer

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

KillerSquirrel · Answer

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

so the answer is (E)

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

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