In the figure above, PQR and STU are identical equilateral

[BTGmoderatorDC]

In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6. What is the perimeter of polygon PQWTUVR?

(1) Triangle SWV has perimeter 9.
(2) VW has length 3.5.



OA A

Source: Official Guide

[Scott@TargetTestPrep]

In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6. What is the perimeter of polygon PQWTUVR?

(1) Triangle SWV has perimeter 9.
(2) VW has length 3.5.



OA A

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the perimeter of polygon PQWTUVR. We see that is the sum of the perimeters of triangles PQR and STU minus the perimeter of triangle SWV. Since the perimeters of PQR and STU are each 6 x 3 = 18, the perimeter of polygon PQWTUVR = 18 + 18 - perimeter of triangle SWV. That is, if we know the perimeter of triangle SWV, then we can determine the perimeter of polygon PQWTUVR.

Statement One Alone:

Since we know that the perimeter of triangle SWV is 9, the perimeter of polygon PQWTUVR is 18 + 18 - 9 = 27. Statement one alone is sufficient.

Statement Two Alone:

Since we don’t know the lengths of SW and SV, knowing the length of VW does not allow us to determine the perimeter of polygon PQWTUVR. Statement two alone is not sufficient.

Answer: A