before i begin the solution, a very useful,general tip for DS ; ALWAYS write simplified DS question with constraints.

you need to find circumference=2*pi*R or i can say you need "R"

i) Area=pi*R*R=36pi...... so you can find R (suff.)
ii) Area of square region in circle=72
diagonal of square will be diameter because angle drawn from 2 end-points of a diameter make 90 degrees angle on the circle. since diagonalof square=2R.. you can find side of square and hence area of square in terms of R. That means you can find R.(suff.)

Ans = D

In (1), R^2=36, R could be 6 or -6. Why -6 is not being considered in this case?

Hi,

When you have a square, then the square root of that is always positive on the GMAT.

for example, x^2, when square rooted is mod x which is always positive.

But if you have a number that is being square rooted, for example 9, then it has 2 options - positive 3 and negative 3.

Plus quite honestly, I understand the usage of the above principle for number theory but there is never going to a circle with a negative radius.

Regards
Anup

anuprajan5 wrote: But if you have a number that is being square rooted, for example 9, then it has 2 options - positive 3 and negative 3.

Above statement is wrong as it implies sq.rt.(9) = +3, -3 BUT
sq.rt.(9) = +3 only
and, x^2=9 ==>> x = +3,-3


To greenwich ,Answer is your question is given correctly by anupranjan5 and is quoted below

there is never going to a circle with a negative radius.

Experts,

Can you please share your insights on this problem?