If a rectangular region has perimeter P...

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by GMATGuruNY » Fri Dec 06, 2013 6:35 pm
Zach.J.Dragone wrote:If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A

B
Statement 1: P = (4/3)A
Case 1: A=9
If the rectangle is a square with an area of 9, then s=3 and P = 4s = 12.
This works, since statement 1 requires that P = (4/3)(A) = (4/3)(9) = 12.
Thus:
In Case 1, the rectangle is a square with a side of 3.

Case 2: A=81
If the rectangle is a square with an area of 81, then s=9 and P = 4s = 36.
This doesn't work, since statement 1 requires that P = (4/3)(A) = (4/3)(81) = 108.
Thus:
In Case 2, the rectangle is NOT a square.
INSUFFICIENT.

Statement 2: P = 4√A
Case 1: A=9
If the rectangle is a square with an area of 9, then s=3 and P = 4s = 12.
This works, since statement 2 requires that P = 4√A = 4√9 = 12.
Thus:
In Case 1, the rectangle is a square with a side of 3.

Case 2: A=81
If the rectangle is a square with an area of 81, then s=9 and P = 4s = 36.
This works, since statement 2 requires that P = 4√A = 4√81 = 36.
Thus:
In Case 2, the rectangle is a square with a side of 9.

The cases above illustrate that, in statement 2, the rectangle must be a square.
SUFFICIENT.

The correct answer is B.
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by Uva@90 » Fri Dec 06, 2013 6:59 pm
Zach.J.Dragone wrote:If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A

B
Hi Zach,
Let's find the relation between Area and Perimeter of the Square.
Let it's side be a.
So A= a*a
P= 4*a => a= P/4
A = P^2/16 => P = 4√A
Which is statement 2.

hence answer is B

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Uva.
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by Milovan » Thu Dec 19, 2013 1:19 pm
Hi Zach,

Area of square is A = a^2 and perimeter is P = 4a where a is a side of a square.

Statement 1: P = 4/3 A

4a = 4/3 * a^2; 4 = 4/3 a; a = 3
What this means is that a can take value of 3 and then it is a square but for any other value of side a it is not a square. Therefore, the statement 1 is not sufficient.

Statement 2: P = 4 √A

4a = 4 √a^2; 4a = 4a; 4 = 4;
This statement is always correct no matter on the value of the side a. Therefore, this statement is sufficient.

The correct answer is B
Milovan Arnaut