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.
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