In the figure above, PQR and STU are identical equilateral triangles,

In this value-type DS question, we can rephrase this question to ask for the values of WV, SW, and SV.

1) Perimeter of SWV = 9
Even though we don't have the individual values of WV, SW, and SV, this is enough to calculate the perimeter of the polygon: perimeter of the two triangles less the perimeter of SWV = perimeter of polygon. There can only be ONE possible value of the polygon's perimeter.
SUFFICIENT

2) WV = 3.5
We don't have the values of SW and/or SV. We cannot assume that SWV is an equilateral triangle.
Consequently, we are unable to calculate the polygon's perimeter.
INSUFFICIENT

Am slightly confused. How are we counting perimeter of triangle swv?

perimeter of triangle pqr includes only wv.
perimeter of triangle stv includes st and wv.

Hi,

Perimeter of polygon PQWTUVR = PQ + QW + WT + TU + UV + VR + RP --(1)

We know the value of PQ, TU, and RP.

We can write QW + VR = QR - WV --(2)

Similarly,

WT = ST - SW --(3)

UV = US - VS --(4)

Substitute (2), (3), and (4) in equation (1), we have following

Perimeter = PQ + TU + RP + QR + TS + SU - (WV+VS+SW)

Hope this helps.

Thanks.

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.

PQ+ PR+ QR-WV + ST - WS + TU + US- VS

= Perimeter of PQR + STU - perimeter of SWV

Suff.
(2) VW has length 3.5.
What about SW, SV ?
NS.

Check out our detailed video solution to this problem here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#-soluti ... ciency_380

Kinshook ,
Hello ,Can you please tell why we need to subtract the perimeter and not only the side VW from the perimeter of 2 big triangles.
Why we are counting the sides which are inside the triangle as its not affecting perimeter of asked quad.

my assumption to solve was this :
2* perimeter of big triangle - side WV = perimeter of quad.

Once we add the perimeters of 2 equilateral triangles, all three unwanted sides are added in the result.
The perimeter of the desired figure does not include all these 3 sides. Therefore, Perimeter of the triangle containing all the 3 sides need to be subtracted.
If we simply subtract VW, then unwanted 2 sides inside equilateral triangle are also included in the perimeter which is incorrect.

Given: In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6.

Asked: What is the perimeter of polygon PQWTUVR?

Perimeter of polygon PQWTUVR = PQ + QW + WT + TU + UV + VR + PR (1)
Perimeter of equilateral triangle PQR = PQ + QW + WV + VR + PR = 18 (2)
Perimeter of equilateral triangle STU = WT + TU + VU + SV + SW = 18 (3)
Sum (2) & (3)
PQ + QW + WV + VR + PR + WT + TU + VU + SV + SW = 36
Rearranging terms
PQ + QW + WT + TU + UV + VR + PR + (WV + SV + SW) = 36
Perimeter of polygon PQWTUVR = 36 - Perimeter of triangle SWV (4)


(1) Triangle SWV has perimeter 9.
Perimeter of polygon PQWTUVR = 36 - Perimeter of triangle SWV
Perimeter of polygon PQWTUVR = 36 - 9 = 27
SUFFICIENT

(2) VW has length 3.5.
PQ + QW + WT + TU + UV + VR + PR + (WV + SV + SW) = 36
Perimeter of polygon PQWTUVR = 36 - (WV + SV + SW) = 36 - 3.5 - (SV + SW) = 32.5 - (SV + SW)
Since SV & SW are unknown.
NOT SUFFICIENT

IMO A

Here, the question says that the 2 triangles are identical.
Does that mean that they are congruent? That is their sides are equal
or
Does it mean that they are similar? Both are Equilateral triangles.
I just want to be assured about the use of word "Identical"

Bunuel chetan2u

_______________________
Identical = Congruent

The polygon pretty much looks like this:

Bunuel I think statement 2 is also suffient. Because there is only 1 type of triangle(since it both are equilateral) that can be drawn with a given base VW (length 3.5)

That is, The length of SW & SV will have only 1 value for VW=3.5. So it sufficient. Isn't it Bunuel.

Please let me know what am i missing here!

Yeah, I also think Statement 2 is sufficient. Because it is gven that these are two identical equilateral triangles. So practically speaking there is only 1 type of Triangle SVW that can be formed with base VW = 3.5. Think Practically!!

Bunuel Can you pls comment on this.

There are more than one way to angle triangle STU so that it goes through the same points W and V. For example check the images below:

Target question: What is the perimeter of polygon PQWTUVR?

This is a great candidate for rephrasing the target question.
The video below has tips on 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

VIDEO ON REPHRASING THE TARGET QUESTION:

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

There are two ways you can solve this question and you can view any solution and understand it. The most important takeaway for this question is the "common mistakes people make" resulting in getting this question incorrect. Why? Because you have to aware of traps and mistakes so that you can avoid those mistakes in other questions, especially in the exam.

Take a moment to view this step-by-step video solution to understand all nuances of solving questions like this:



Questions? Please leave a comment, I personally respond to all comments.

Cheers!