In the figure above, what is the perimeter of rectangle ABPQ?

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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

OA E

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AAPL wrote:
Sun Oct 17, 2021 7:53 am
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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

OA E
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:
Image
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:
Image
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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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