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Math Expert V
Joined: 02 Sep 2009
Posts: 59720
In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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4
103 00:00

Difficulty:   85% (hard)

Question Stats: 53% (01:47) correct 47% (02:07) wrong based on 1797 sessions

### HideShow timer Statistics 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.

Attachment: 2015-10-26_2103.png [ 9.81 KiB | Viewed 30621 times ]

Attachment: DS06861_f001.png [ 3.83 KiB | Viewed 13789 times ]

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Manager  Joined: 11 Sep 2013
Posts: 104
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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16
3
Bunuel wrote: 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.

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
##### General Discussion
Intern  Joined: 04 Sep 2015
Posts: 2
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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1
3
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
Intern  Joined: 20 Aug 2015
Posts: 4
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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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?

Posted from my mobile device
Intern  Joined: 06 Jul 2015
Posts: 18
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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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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Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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1
1
1. Sufficient !!
Perimeter of the required figure = perimeter of both the triangles - smaller one
= 36-9= 27

2.Insufficient.
Therefore A
VP  V
Joined: 23 Feb 2015
Posts: 1350
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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Bunuel wrote: 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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Manager  D
Joined: 17 May 2015
Posts: 245
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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iMyself wrote:
Bunuel wrote: 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
Intern  B
Joined: 18 Jan 2017
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Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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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.
Manager  D
Joined: 17 May 2015
Posts: 245
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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5
1
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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Joined: 18 Jan 2017
Posts: 31
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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Yes that's what I was trying to state. We are not double counting.
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Joined: 10 Apr 2015
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Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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2
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.
NS.
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Posts: 426
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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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.

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

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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.
Wharton Moderator B
Joined: 30 May 2015
Posts: 34
Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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

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Bunuel wrote: 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.

Attachment:
2015-10-26_2103.png

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

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2
2
Bunuel wrote: 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.

Attachment:
2015-10-26_2103.png

Check out our detailed video solution to this problem here:
https://www.veritasprep.com/gmat-soluti ... ciency_380
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Intern  B
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Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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I got this one in under 2 minutes! Big breakthrough for me on my triangle problems, as I've been struggling to find answers within the time limit.

Essentially the total perimeter is going to be the perimeter of the two triangles minus whatever parts of the triangles are overlapping, which is SW, WV, and SV. So if we know the perimeter of SWV, it doesn't matter what the measure of each side is, we could just subtract SWV from 36
Intern  B
Joined: 26 Aug 2018
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Re: In the figure above, PQR and STU are identical equilateral triangles,  [#permalink]

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Hi
I have been struggling with this question not because i could not get that it is smaller triangle's perimeter that is to be subtracted in order to get the desired area but because i could not decipher that side of other triangle is also 6 cms. The triangles are mentioned as identical equilateral which means their sides will be in proportion and not necessarily equal i.e. triangle 1 can have all sides as 6 while second can have sides of any measure, 12 cms/13/ 14 or any other unit? Re: In the figure above, PQR and STU are identical equilateral triangles,   [#permalink] 13 Aug 2019, 03:55

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