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.

what is the value of x? The answer is 3.

Step-by-step explanation:

2x + 2 = y^3 where y is a positive integer. One possible answer for this is 3, because 2*3 + 2 is 8, that is 2^3, so 2 * 2 * 2 = 8. Also the second restrictions says that x consecutive numbers added and then divided by x will give an integer. So 2 + 3 + 4 = 9 and 9/3 = 3, that is an integer, and we have 3 consecutive numbers, therefore the answer is 3, as 3 is prime as well.