**Official Guide**

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

00:00

**A**

**B**

**C**

**D**

**E**

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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00:00

**A**

**B**

**C**

**D**

**E**

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

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

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