Sqaure of an integer

i think with 2 we can know that k is not a square of an integer

1. 8 vs 16
2. k = p1 * p2 * p3 * ... * pK

p1, p2, .., pK are prime numbers in prime factorization
"exactly different prime numbers" -> p1 through pK are different (to my understanding)

hence k cannot be square of integer. Square of integers must have even numver of each prime number in its prime factorization

B is the answer

A cnt answer the question.. But in "B", i didnt understand ..

Does K should be divisible by all different prime numbers?

obviously, 1 Is not sufficient. Since both 8 and 16 are divisible by 4 but 8 is not a square of an integer whereas 16 is.

From statement 2 we can deduce that K/2, K/3, K/5, K/7,..., If K = 14, 2 and 7 divide K, If K = 15, 3 and 5 divide k, if k = 21 3 and 7 divide k, If k is 30, 2, 3 and 5 divide K. We can go on and on. But it's worth noting here that K = 14, 15, 21, 30 are all not square of an integer.Hence, we can say No with statement 2. Therefore, Statement 2 is sufficient (B)

This is GMAT Prep question. I was also going with B. However the OA is E. Also as Ian mentioned there was a typo which I have fixed.

Thanks Ian, I understand your explanation. My reasoning was that 4 different prime numbers means 2x3x5x7 I did not think that they can appear twice.