(1)2 x + 2 is the cube of a positive integer
2(x+1) = n^3

2 times any integer gives an even number, therefore n^3 is even and x is odd
If n^3 = 8, x=3
If n^3 = 64,x=31
Because we have two values for x, statement is insufficient

(2) The average of any x consecutive integers is an integer
Average of odd consecutive integers = integer
Average of even consecutive integers = non-integer
Therefore x is odd
Average of 1,2,3 is different from average of 1,2,3,4,5
Statement is insufficient

Combining both
From 1) x = odd
From 2) x = odd
Therefore this is also insufficient since x could have any odd values

Answer = E

Hi ,

Thanks for the reply, but I still don't get the statement 2.

Given that x is a prime numbers so x must be 2,3,5,7,11.....so on

now what should do after this, should I try the cases?

Please advise.

Thanks

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

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

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

Statement 1: 2x + 2 is the cube of an integer
Make a list of options for 2x+2:
2x+2 = 1, 8, 27, 64...

Subtracting 2 from each side, we get:
2x = -1, 6, 25, 62

Dividing each side by 2, we get:
x = -1/2, 3, 25/2, 31...

The values in red are prime.
Since it's possible that x=3 or that x=31, INSUFFICIENT.

Statement 2: The average of any x consecutive integers is an integer.
The average of an EVEN number of consecutive integers will always be a NON-INTEGER.
The average of an ODD number of consecutive integers will always be an INTEGER.
Thus:
It's possible that x=3, since the average of 3 consecutive integers will always be an integer.
It's possible that x=31, since the average of 31 consecutive integers will always be an integer.
INSUFFICIENT.

Statements combined:
Both statements are satisfied if x=3.
Both statements are satisfied if x=31.
Since x can be different values, INSUFFICIENT.

The correct answer is E.