Vincen wrote: ↑

Mon Mar 22, 2021 8:10 am

If a rectangular region has perimeter \(P\) inches and area \(A\) square inches, is the region square?

(1) \(P = \dfrac43 A\)
(2) \(P = 4\sqrt{A}\)

Answer: B

Source: GMAT Prep

Given: A rectangular region has perimeter P inches and area A square inches

Target question: Is the region square?
This is a good candidate for rephrasing the target question.

So, what kind of relationship between P and A do we need in order for the rectangular region to be a SQUARE?
Well, if the region is a square, then all 4 sides will be the same length
So, if P = the perimeter (sum of all 4 sides), then P/4 = the length of each side
If P/4 = the length of each side, then the AREA = (P/4)(P/4)
In other words: A = (P/4)(P/4)
Simplify: A = P²/16
Multiply both sides by 16 to get: 16A = P²
Take square root of both sides to get: 4√A = P
So, if 4√A = P, then we can be certain that the region is a square.
REPHRASED target question: Does 4√A = P?

Statement 1: P = (4/3)(A)
Let's TEST some values.
There are several values of P and A that satisfy statement 1. Here are two:
Case a: P = 12 and A = 9. In this case, the answer to the REPHRASED target question is YES, 4√A DOES EQUAL P
Case b: P = 4 and A = 3. In this case, the answer to the REPHRASED target question is NO, 4√A does NOT equal P
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: P = 4√A
Perfect!!
The answer to the REPHRASED target question is YES, 4√A DOES EQUAL P
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B