IMO : A
As the distance between two centers is lesser than the sum of the radius. That means the circles would overlap.

rupsk wrote:C is a circle with center D and radius 2. E is a circle with center F and radius R. Are there any point on both E and C?

(1) distance from D to F is 1+R
(2) R=3

I know st 1 & 2 alone is not sufficient. But together how they are please explain me that

Hi -- I think Statement 1 itself is SUFFICIENT to answer this question.

Even if the two circles touch each other, the distance between their centers comes out to be 2+R
But, it is given that the distance is 1+R.. Clearly, the two circles must be overlapping to make this case possible.

What is the OA. Please do put the OE as well.

thanks but in exam it is given C as correct answer though i had picked a as an ans.

Which exam? Then I think I am missing something. Can you copy paste the explanation given in that exam?
Or, the best thing to do is to ping an expert here. They know the best.

If R is very small, Circle E could fit entirely inside of Circle C, such that they wouldn't intersect. Try R=0.0001 and you'll see this is easy to do. Circle E is centered just over half-way between D and the circumference of Circle C, but it's this tiny little dot. Tricky, eh? But it's a possibility that makes Statement (1) Insufficient.

If we know that R=3, then obviously Circle E can't fit inside Circle C, the distance between the radii is 4 but the sum of the radii is 5, so they must intersect, as everyone else here has already logically concluded.

Neat question! Never neglect the extreme examples; sometimes really weird things happen if you think of really tiny (or really huge) numbers on unusual DS question stems.

yeah ..tricky little DS

Thanks Adam, I am at fault -- i did not consider the case when one circle is inside the other... silly mistake..!

As adam pointed out,we can have a case when circle E is inside C.

The distance between two circles is 1+R. So 1+2R < 2.

So if R < 0.5 we can have a case when circles don't intersect.

Statement 1 and 2 not sufficient ..

Hence c because we can conclude that r is 4