Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47918

In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
26 Oct 2015, 10:04
Question Stats:
54% (01:14) correct 46% (01:32) wrong based on 1293 sessions
HideShow timer Statistics




Manager
Joined: 11 Sep 2013
Posts: 110

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
26 Oct 2015, 12:01
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: 20151026_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




Intern
Joined: 04 Sep 2015
Posts: 2

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
27 Oct 2015, 09:00
In this valuetype 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: 3

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
02 Jul 2016, 08:01
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?
Posted from my mobile device



Intern
Joined: 06 Jul 2015
Posts: 21

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
02 Jul 2016, 11:27
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.



Director
Joined: 20 Feb 2015
Posts: 511
Concentration: Strategy, General Management

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
03 Jul 2016, 00:54
1. Sufficient !! Perimeter of the required figure = perimeter of both the triangles  smaller one = 369= 27
2.Insufficient. Therefore A



Senior Manager
Joined: 23 Feb 2015
Posts: 428

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
14 Nov 2016, 11:57
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= 21Again, 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.
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow



Manager
Joined: 17 May 2015
Posts: 237

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
13 Jan 2017, 04:05
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= 21Again, 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
Joined: 18 Jan 2017
Posts: 36

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
19 Jan 2017, 09:56
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.



Manager
Joined: 17 May 2015
Posts: 237

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
19 Jan 2017, 10:23
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.



Intern
Joined: 18 Jan 2017
Posts: 36

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
19 Jan 2017, 21:54
Yes that's what I was trying to state. We are not double counting.



Manager
Joined: 10 Apr 2015
Posts: 196
GPA: 3.31

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
05 Apr 2017, 20:55
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+ QRWV + ST  WS + TU + US VS
= Perimeter of PQR + STU  perimeter of SWV
Suff.(2) VW has length 3.5. What about SW, SV ? NS.
_________________
In case you find my posts helpful, give me Kudos. Thank you.



Senior Manager
Joined: 17 Mar 2014
Posts: 353

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
17 May 2017, 08:42
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



Manager
Joined: 14 May 2017
Posts: 66
Location: India
GPA: 3.5
WE: Business Development (Education)

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
18 May 2017, 00:46
pdxyj wrote: In this valuetype 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 Thread Master
Joined: 30 May 2015
Posts: 40

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
20 May 2017, 14:15
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.



Intern
Joined: 29 Dec 2016
Posts: 3

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
27 Sep 2017, 03:29
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.



VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1219
Location: India
Concentration: Operations, Marketing
GPA: 3.4
WE: Engineering (Manufacturing)

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
27 Sep 2017, 04:24
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: 20151026_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
_________________
Please give kudos if you found my answers useful



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
21 Dec 2017, 06:46
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: 20151026_2103.png Check out our detailed video solution to this problem here: https://www.veritasprep.com/gmatsoluti ... ciency_380
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 28 Mar 2018
Posts: 48

Re: In the figure above, PQR and STU are identical equilateral triangles,
[#permalink]
Show Tags
13 Apr 2018, 11:29
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




Re: In the figure above, PQR and STU are identical equilateral triangles, &nbs
[#permalink]
13 Apr 2018, 11:29






