besos wrote: ↑

Sat May 28, 2016 11:28 am

Can someone help me understand why the answer is A?

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

Target question: What is the perimeter of polygon PQWTUVR?
This is a great candidate for rephrasing the target question.

Let x, y and z represent the lengths below.


Since each side of the equilateral triangle has lengths 6, we can label the sides as follows:


Finally, let's let QW have length a and let VR have length b


We know that a + z + b = 6.
So, it follows that: a + b = 6 - z

At this point we are ready to calculate the perimeter of PQWTUVR
The perimeter = 6 + a + (6 - x) + 6 + (6 - y) + b + 6
= 30 - x - y + a + b

Since a + b = 6 - z, we can substitute to get:
Perimeter = 30 - x - y + 6 - z

Simplify to get:
Perimeter = 36 - (x + y + z)

In other words, to find the perimeter of PQWTUVR, we need to know the value of x + y + z.

REPHRASED target question: What is the value of x + y + z?

Statement 1: Triangle SWV has perimeter 9.
In other words, x + y + z = 9
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: VW has length 3.5
In other words, z = 3.5
We still don't have enough information to find the value of x + y + z.
Since we can’t answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent