If x = (y)(y + 1) and y is a prime number less than 11, which of the f

Since y is a prime number less than 11, there are only 4 possible vales for y.
y COULD equal 2, 3, 5 or 7

This also means there are only 4 possible vales for x.

x = (y)(y + 1)

If y = 2, then x = (2)(2 + 1) = 6
If y = 3, then x = (3)(3 + 1) = 12
If y = 5, then x = (5)(5 + 1) = 30
If y = 7, then x = (7)(7 + 1) = 56

Now let's check each answer choice...
a) Can 5x be the product of 2 consecutive integers?
Yes. When x = 6, then 5x = 5(6) = 30
So, 5x CAN BE the product of 2 consecutive integers (5 and 6)
ELIMINATE A

b) Can 11x be the product of 2 consecutive integers?
Yes. When x = 12, then 11x = 11(12)
So, 11x CAN BE the product of 2 consecutive integers (11 and 12)
ELIMINATE B

c) 13x
When x = 12, then 13x = 13(12)
So, clearly, 13x CAN BE the product of 2 consecutive integers (12 and 13)
ELIMINATE C

e) 57x
When x = 56, then 57x = 57(56)
So, clearly, 57x CAN BE the product of 2 consecutive integers (56 and 57)
ELIMINATE E

By the process of elimination, the correct answer is D

Cheers,
Brent