The goal is to determine if the shape is in fact a square.

Statement 1) P = 4/3*(A)

If true, then P=4x and A = x^2

4x = 4/3*(x^2)
x = x^2/3
x = 3

Only true if the side is length 3. We don't know if the side of the shape has length 3, so the statement is insufficient.

Statement 2) P = 4sqrt(A)

4x = 4sqrt(x^2)
4x=4x
x = x

This statement is true, so the statement is sufficient.

This question raises very important point on DS questions.

First of all it is a YES/NO question.

When you plug in numbers statement (2) becomes YES. And when you plug numbers in statement (2) the answer is almost always no. Theoretically both statements give you concrete YES or NO, therefore each alone must be sufficient.

But two statements must both either say YES or NO. If one statement yields YES but the other NO, then the statement that you know for 100% is sufficient is the correct answer. And there must be at least on set of numbers that would give YES answer for statement one. But you should not bother to find that set of numbers.

Hey dabaobao ,

You did a very BIG mistake of not reading the question properly.

Question says "If a rectangular region" but you took it a square.

For a rectangle, Perimeter = 2(l+b) and area = l * b.

Now, try substituting the values in statement A, you won't be able to determine whether l = b for the region to be a square. Hence, A is insufficient.

Does that make sense?
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I have a question:

Even without seeing the (1) or (2), we can prove that this equation needs to be true: \(P = 4\sqrt{A}\).
Proof: If the shape is a square,

The length of one side should be: \(\sqrt{A}\),
The perimeter should be: \(P = 4\sqrt{A}\)

We know that the shape can be a square only if the equation above holds. If we are given the information in (1), we could definitely conclude that the shape is NOT a square, since it contradicts the equation above.

So I would think the answer should be D. Can anyone illuminate me about what is wrong in my rationale?
(I know the official answer is not D.)