Not sure if this is the easiest way but this is one way

Stmt I)

k is divisible by 4

8 div by 4 not a sqaure of an integer

16 div by 4 square if an integer

INSUFF

Stmt II

2*3*5*7 has 4 different prime factors but not square of an integer

2^2 * 3 ^ 2 * 5 ^2 * 7 ^2 has 4 different prime factors but is the square of n integer

INSUFF

Stmt I and Stmt II
2^2 * 3 ^ 2 * 5 ^2 * 7 ^2 satisfies both statements and is sqaure of an integer

2^3 3 ^2 5 ^2 7 ^2 satisfies both statements and is not square of an
integer

E)

Hope I have not missed something! Let me know if u still have questions

cramya wrote:Not sure if this is the easiest way but this is one way

Stmt I)

k is divisible by 4

8 div by 4 not a sqaure of an integer

16 div by 4 square if an integer

INSUFF

Stmt II

2*3*5*7 has 4 different prime factors but not square of an integer

2^2 * 3 ^ 2 * 5 ^2 * 7 ^2 has 4 different prime factors but is the square of n integer

INSUFF

Stmt I and Stmt II
2^2 * 3 ^ 2 * 5 ^2 * 7 ^2 satisfies both statements and is sqaure of an integer

2^3 3 ^2 5 ^2 7 ^2 satisfies both statements and is not square of an
integer

E)

Hope I have not missed something! Let me know if u still have questions

Cramya, your method is the easiest and fastest one. All we need to do is to prove the statement with a number and move forward.