Is the perimeter of square S greater than the circumference

[ShahidB174]

Source: Gmat Hacks

Is the perimeter of square S greater than the circumference of
circle C ?
(1) The area of S is equal to the area of C.
(2) The length of a side of S is greater than the length of
the radius of C.


How do we scrutinize statement 2 more flawlessly to not reach D.
For example if S=2 Perimeter is 8
If R=1 C=6.something.
P>C yes

If S= 5 Perimeter =20
if R=4 C= 25
P<C
No.

It isn't very intuitive and prone to error; where as OA is A. Is there another approach to this prb?

[StaceyKoprince]

Please remember to read (and follow!) the forum guidelines before posting. This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources). I'll answer you briefly here, but if you want to discuss anything further, please post in the relevant folder for this source (General GMAT Math).

The method you showed is what we call Testing Cases and that's exactly what I would do myself for statement 2. The trick is to study this technique well enough that you get a good idea of what kinds of numbers to test for different kinds of problems.

Once you test the first case, you'll get either a yes or no answer. Next, ask yourself what kinds of numbers are most likely to give you the opposite answer.

Q: Is 4s > 2pi*r?
(2) s > r
Case #1: s = 2, r = 1. Perim of square = 8, circum of circle = 2*3.14. In this case, yes, perim > circum.
How to get a No? Make the circum bigger, and make r essentially "closer" to s. (In the first case, r is only half of s.)
Case #2: s = 20, r = 19. Perim = 20*4. Circum = 2*3.14*19. So 20*4 vs. 6.28*19. The second one is bigger. Done! (Don't do calculations you don't need to do...)