OG 16: DS 137

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OG 16: DS 137

by besos » Sat May 28, 2016 11:28 am

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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?

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by OptimusPrep » Sun May 29, 2016 8:18 pm

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besos wrote: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?
Hi besos,

Please ensure that you upload the diagram and write the full question. This is a DS question and you have missed both the statements here.

Coming to the question:

Given: PQR and STU are identical equilateral triangles and PQ = 6
This means both the triangles have the same sides and angles

Required: Perimeter of PQWTUVR

Statement 1: Triangle SWV has perimeter 9
Perimeter of PQWTUVR = sum of perimeters of both the triangles - the perimeter of SWV
SUFFICIENT

Statement 2: VW has length 3.5.
This does not tell us anything about the triangle SVW
INSUFFICIENT

Correct Option: A
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Identical triangles.png

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Re: OG 16: DS 137

by gmatbyexample » Mon Feb 21, 2022 1:44 pm

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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.

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

Solution & Common Mistakes people make here: Solution to GMAT OG (700+) Find the Perimeter of PQWTUVR DS06861 Q481: Official Guide Solutions for Beginners
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Re: OG 16: DS 137

by Brent@GMATPrepNow » Mon Feb 21, 2022 4:58 pm

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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.
Image

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

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

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
Brent Hanneson - Creator of GMATPrepNow.com
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