swerve wrote:
In the figure above, what is the perimeter of rectangle ABPQ?
(1) The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
(2) The perimeter of rectangle ABCD is 54.
The OA is
E.
Source: Official Guide
Target question: What is the perimeter of rectangle ABPQ?
Statement 1: The area of rectangular region ABCD is 3 times the area of rectangular region ABPQ.
Since we aren't given any information regarding ACTUAL lengths,
we cannot determine the perimeter of rectangle ABPQ
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The perimeter of rectangle ABCD is 54
There are many possible cases in which ABCD's perimeter is 54, yet the
perimeter of rectangle ABPQ is not fixed (see diagrams below)
Statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: The measurements are as follows:
Notice that the area of ABCD (72 square units) is 3 times the area of rectangular region ABPQ (24 square units)
Also notice that ABCD has perimeter 54
In this case,
the perimeter of rectangle ABPQ = 1 + 24 + 1 + 24 = 50
Case b: The measurements are as follows:
Notice that the area of ABCD (126 square units) is 3 times the area of rectangular region ABPQ (42 square units)
Also notice that ABCD has perimeter 54
In this case,
the perimeter of rectangle ABPQ = 2 + 21 + 2 + 21 = 46
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
