Statement 1) The greatest common factor of k and n is 4.

Assuming some values we get
k = 8 and n = 12, remainder = 4
k = 8 and n = 16, remainder = 0

Not Sufficient!!!

Statement 2) The least common multiple of k and n is 84.

Assuming some values we get
k = 7 and n = 12, remainder = 5
k = 12 and n = 28, remainder = 4
k = 28 and n = 42, remainder = 14

Remainder is always > 2.

Sufficient!!!

Answer B.

Can someone explain this in detail?

As both statements together we get, 4*a * 4*b = 84 * 4, solving we get a*b = 21 and only values that satisfy this keeping 4<k<n in mind are k = 4*3 = 12 and n = 4*7 = 28.

If we divide n by k we get a remainder as 4, which is greater than 2. Hence we are certain.

But can we answer the question with such certainty by taking into account only Statement 2(shown in my previous reply to this thread).

Thanks

Puneet

I think the correct answer is D.
in your explanation:
+ Statement 1: The greatest common factor of k and n is 4.
Assuming some values we get
k = 8 and n = 12, remainder = 4
k = 8 and n = 16, remainder = 0 (8 is the factor of 16, but the stem is that k is not a factor of n)
--> statement 1 is sufficient
--> correct answer is D

Thanks Tranhang, I missed that and Answer should be D.

Statement I:

If gcd(n,k)=4, let n=4a, k=4b

We have 4a = 4bx + R => R must be a multiple of 4. Hence, Statement 1 is sufficient.

Statement II:

LCM(n,k)= 84

If(n,k)= (12,7) => R=5

If(n,k)= (14,12) => R=2

So, statement II is not sufficient.

Hence, choice A is correct