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?
OG 16: DS 137
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Hi besos,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?
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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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
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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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