Data Sufficiency

Pls explain the answer

If figures M and N are circles, what is the circumference of N?

(1) If the radius of N were 4 times as long, the areas of M and N would be equal.
(2) The difference between the diameter of M and the diameter of N is 12.


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT SUFFICIENT

Is the answer C?

(1) If we call m the radius of circle M and n the radius of circle N, then from (1) we have that 4n = m, which is clearly not sufficient to know the circumference of N since we know nothing about the actual values of m and n.

(2) This gives us that |2m-2n|=12, but again, nothing about the values of either radius (they could be 13 and 1 or 90 and 77). In addition we don't even know which circle is the bigger of the two.

(1)&(2) From (1) we know that M is the bigger circle, that 4n = m, and from (2) we know that 2m-2n=12. Substituting the first equation into the second we can solve for

n = 2
m = 8

So the circumference of N is 4(pi).

Yes the answer is C..Thank u very much..