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

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In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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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.

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-26_2103.png
2015-10-26_2103.png [ 9.81 KiB | Viewed 11890 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 26 Oct 2015, 11:01
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Bunuel wrote:
Image
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.

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-26_2103.png

(1) Triangle SWV has perimeter 9.
perimeter of polygon PQWTUVR = twice perimeter of PQR - the perimeter of SWV

We can know the perimeter of PQR and of SWV => Sufficient

(2) VW has length 3.5

We do now know the perimeter of SWV if we just have the length of VW
=> Insufficient

Ans: A

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 27 Oct 2015, 08:00
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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

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 02 Jul 2016, 07:01
Hi, I have a doubt regarding this question. We are adding the perimeters of triangles pqr and stuff which means the perimeter of triangle swv is getting counted twice. Why do we only subtract perimeter of swv only once from the sum of the perimeters of pqr and stu?

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 02 Jul 2016, 10:27
I think statement 1 alone is sufficient as the perimeter of polygon PQWTUVR would be length PQ + length QW + length WT + length TU + length UV + length VR
Which can be calculated as perimeter of triangle PQR + perimeter of triangle TSU and since triangle WSV is only a part of TSU we subtract its perimeter.

knowing length VW we still would need to know the other two sides of triangle WSV, for which no information is available in the question and its insufficient to derive the perimeter of triangle WSV which we require to calculate the perimeter of the polygon under consideration as per the above logic.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 02 Jul 2016, 23:54
1. Sufficient !!
Perimeter of the required figure = perimeter of both the triangles - smaller one
= 36-9= 27

2.Insufficient.
Therefore A

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 14 Nov 2016, 10:57
Bunuel wrote:
Image
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.

Statement 1 says that SW+SV+WV=9. If I put the value of WV=3, the summation of SW and SV will be 6. Suppose SW=3 and SV=3. If SW=3 then WT=3. If SV=3, then VU=3.
I already let WV=3. So, if WV=3, then the summation of QW and VR must be 3. Now let the value QW=1 and VR=2. So, PQ+QW+WT+TU+UV+VR=6+1+3+6+3+2
--> PQ+QW+WT+TU+UV+VR=21
Again,
Let, Statement 1 says that SW+SV+WV=9. If I put the value of WV=2, the summation of SW and SV will be 7. Suppose SW=3 and SV=4. If SW=3 then WT=3. If SV=4, then VU=2.
I already let WV=3. So, if WV=3, then the summation of QW and VR must be 3. Now let the value QW=1 and VR=2. So, PQ+QW+WT+TU+UV+VR=6+1+3+6+2+2
PQ+QW+WT+TU+UV+VR=20.
The statement 1 gives 2 values (like 21 and 20) of the perimeter of this polygon.
Actually, I am confused. Is there any mistake in my calculation or in my understanding?
Thank you.
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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 13 Jan 2017, 03:05
iMyself wrote:
Bunuel wrote:
Image
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.

Statement 1 says that SW+SV+WV=9. If I put the value of WV=3, the summation of SW and SV will be 6. Suppose SW=3 and SV=3. If SW=3 then WT=3. If SV=3, then VU=3.
I already let WV=3. So, if WV=3, then the summation of QW and VR must be 3. Now let the value QW=1 and VR=2. So, PQ+QW+WT+TU+UV+VR=6+1+3+6+3+2
--> PQ+QW+WT+TU+UV+VR=21
Again,
Let, Statement 1 says that SW+SV+WV=9. If I put the value of WV=2, the summation of SW and SV will be 7. Suppose SW=3 and SV=4. If SW=3 then WT=3. If SV=4, then VU=2.
I already let WV=3. So, if WV=3, then the summation of QW and VR must be 3. Now let the value QW=1 and VR=2. So, PQ+QW+WT+TU+UV+VR=6+1+3+6+2+2
PQ+QW+WT+TU+UV+VR=20.
The statement 1 gives 2 values (like 21 and 20) of the perimeter of this polygon.
Actually, I am confused. Is there any mistake in my calculation or in my understanding?
Thank you.


Hi,

Please check highlighted part; there is an error. Moreover, you need to add the length of PR in both cases.

Thanks

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 19 Jan 2017, 08:56
Purrple wrote:
Hi, I have a doubt regarding this question. We are adding the perimeters of triangles pqr and stuff which means the perimeter of triangle swv is getting counted twice. Why do we only subtract perimeter of swv only once from the sum of the perimeters of pqr and stu?

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.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 19 Jan 2017, 09:23
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malavika1 wrote:
Purrple wrote:
Hi, I have a doubt regarding this question. We are adding the perimeters of triangles pqr and stuff which means the perimeter of triangle swv is getting counted twice. Why do we only subtract perimeter of swv only once from the sum of the perimeters of pqr and stu?

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.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 19 Jan 2017, 20:54
Yes that's what I was trying to state. We are not double counting.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 05 Apr 2017, 19:55
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.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 17 May 2017, 07:42
Given triangle PQR and STU are identical and equilateral triangle. PQ= 6.
So perimeter of triangle PQR=Perimeter of triangle STU= 18
perimeter of polygon PQWTUVR = perimeter of triangle PQR + perimeter of triangle STU- perimeter of triangle SVW

We already know perimeter of triangle PQR & perimeter of triangle STU. We need to find out perimeter of triangle SVW.

1. first statement provides perimeter of triangle SVW. -- Sufficient
2. second Statement tells only about VW length. What about SW and SV. we do not know SW and SV so we cant find out perimeter of triangle SVW. --- Not Sufficient.

Answer : A

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 17 May 2017, 23:46
pdxyj wrote:
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

Thanks !! That was exactly the explanation I was looking for.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 20 May 2017, 13:15
perimeter of polygon PQWTUVR = Perimeter of PQR + Perimeter of STU - Perimeter of SWV

1) above equation is solvable with the information given in option 1
2) we are not sure of actual value of SW and SV , as it is not given . It means option 2 is not sufficient.

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Re: In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 27 Sep 2017, 02:29
ganand wrote:
malavika1 wrote:
Purrple wrote:
Hi, I have a doubt regarding this question. We are adding the perimeters of triangles pqr and stuff which means the perimeter of triangle swv is getting counted twice. Why do we only subtract perimeter of swv only once from the sum of the perimeters of pqr and stu?

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.



Hi,
Thanks for the same. I believe WV gets only accounted in PQR and SW & SV get accounted only in STU. Hence, no repetition as such. However, if the question had asked us to calculate the area of the same region, then i think it would have got accounted twice. What would be our approach in that case?
Thanks.

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In the figure above, PQR and STU are identical equilateral triangles, [#permalink]

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New post 27 Sep 2017, 03:24
Bunuel wrote:
Image
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.

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-26_2103.png


The answer is A
This is a tricky problem
Statement 1 gives the perimeter of the smaller triangle formed by the intersection of the two identical triangle .
We do not know what kind of triangle is the smaller triangle .
Now we know that the two big triangle are identical so calculate the perimeter of the two triangle .
Notice that to compute the perimeter of the polygon we have subtract the perimeter of the smaller triangle from the perimeter of the two triangle .
Hence sufficient

Statement 2 is insufficient as we do not know what kind of triangle is the smaller triangle .
Merely giving us a side length will not help us to compute the perimeter of the polygon

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In the figure above, PQR and STU are identical equilateral triangles,   [#permalink] 27 Sep 2017, 03:24
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In the figure above, PQR and STU are identical equilateral triangles,

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