prime number

[GmatKiss]

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

[Stuart@KaplanGMAT]

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

Hi!

Very open question, but we see it's about primes. Whenever you see a DS question about primes, always think about 2, the only even prime!

Pretty straightforward question, so let's dive right into the statements. (2) seems simpler, so let's start there.

The only way that (2) could be sufficient is if it narrowed x down to an even number. So, let's check: if x=2, then we have 2 consecutive integers. The average of two consecutive integers will always have a ".5" at the end. so (2) means that x cannot be even. Any odd value of x will make (2) true, so (2) doesn't help us find a specific value of x. Insufficient, eliminate B and D.

(1) We can quickly test 2 and see that it doesn't work (4+2=6 which is not a perfect cube). Making a quick list of perfect cubes:

1, 8, 27, 64

and checking for possible x values:

if x=3, then 2x+2 = 8.. so x could be 3;
if x=31, then 2x+2 = 64.. so x could be 31.

We already have 2 possible values for x, so (1) is also insufficient: eliminate A.

Since 3 and 31 satisfy both statements, even combined we can't find just 1 value: insufficient, eliminate C, choose E!

[Anurag@Gurome]

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

(1) 2x + 2 is the cube of a positive integer.
Let 2x + 2 = N^3, N is even.

If N = 2 then 2x + 2 = n^3 = 8 or x = 2 = prime
If N = 4 then 2x + 2 = n^3 = 4^3 or x = 31 = prime
If N = 6 then 2x + 2 = n^3 = 6^3 or x = 107 = prime

No definite answer for x; NOT sufficient.

(2) The average of any x consecutive integers is an integer.
Now average of even consecutive integers gives a fraction and that of odd consecutive integers gives an integer value. So, x is odd but x can be any prime number.
No definite answer for x; NOT sufficient.

Combining (1) and (2), x is an odd prime number
x can be 31 or 107.
No definite answer for x; NOT sufficient.

The correct answer is E.