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similar triangles...

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by goyalsau » Sun Dec 19, 2010 11:51 pm
Help Guys,,,,,,,,,

6/7

7/6

5/6

6/5

7/5
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Source: — Problem Solving |

by prachich1987 » Mon Dec 20, 2010 1:45 am
goyalsau wrote:Help Guys,,,,,,,,,

6/7

7/6

5/6

6/5

7/5
Is this a GMAT question
I tried hard But couldn't do
someone plz help
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by frank1 » Mon Dec 20, 2010 1:45 am
I think answer is 6/5

Permimeter of Triangle 1 =10+12+8=30

perimeter of second is 10+15(found)+25/2(found)=50/2

that means

30/(50/2)

(30x 2)/50= 6/5

Now if i separate the figure it will be more clear

thanks
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by Night reader » Mon Dec 20, 2010 1:52 am
prachich1987 wrote:
goyalsau wrote:Help Guys,,,,,,,,,

6/7

7/6

5/6

6/5

7/5
Is this a GMAT question
I tried hard But couldn't do
someone plz help
this question is drawn from CAT administered in India. The CAT exam content is broad and not being limited to the topics embraced in GMAT quantitative curriculum. Having said this, I believe this is not GMAT question, and it tests knowledge of 'similar & congruent triangle' properties.
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by prachich1987 » Mon Dec 20, 2010 2:04 am
frank1 wrote:I think answer is 6/5

Permimeter of Triangle 1 =10+12+8=30

perimeter of second is 10+15(found)+25/2(found)=50/2..I didn't understand this calculation The third side would be 12.5.So So perimeter is 37.5

that means.
30/(50/2)

(30x 2)/50= 6/5

Now if i separate the figure it will be more clear

thanks
The above explanation is valid provided the triangles are similar which is not proved.
secondly even if the triangles are similar the perimeter won't be the one you have found
See my comments in red above.
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by Rahul@gurome » Mon Dec 20, 2010 2:05 am
∆PQS and ∆PQR are similar triangles.
Thus,
  • 1. PQ/QS = PR/PQ = 12/8 => PR = (12/8)PQ = (12/8)*12 = 18
    2. PQ/QS = PR/QR = 12/10 => QR = (10/12)PR = (10/12)*18 = 15
    3. SR = PR - PS = 18 - 8 = 10
Perimeter of ∆QSR = (QS + SR + QR) = (10 + 10 + 15) = 35
Perimeter of ∆PQS = (PQ + QS + PS) = (12 + 10 + 18) = 30

Required ratio = 30/35 = 6/7

The correct answer is A.

Edit: (Proof of the similarity)
In ∆PQS and ∆PQR,
  • 1. angle PQS = angle PRQ (Given)
    2. angle QPS = angle QPR (Common angle)
Thus they are similar by angle-angle similarity.
Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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by prachich1987 » Mon Dec 20, 2010 2:32 am
Rahul@gurome wrote:∆PQS and ∆PQR are similar triangles.
Thus,
  • 1. PQ/QS = PR/PQ = 12/8 => PR = (12/8)PQ = (12/8)*12 = 18
    2. PQ/QS = PR/QR = 12/10 => QR = (10/12)PR = (10/12)*18 = 15
    3. SR = PR - PS = 18 - 8 = 10
Perimeter of ∆QSR = (QS + SR + QR) = (10 + 10 + 15) = 35
Perimeter of ∆PQS = (PQ + QS + PS) = (12 + 10 + 18) = 30

Required ratio = 30/35 = 6/7

The correct answer is A.

Edit: (Proof of the similarity)
In ∆PQS and ∆PQR,
  • 1. angle PQS = angle PRQ (Given)
    2. angle QPS = angle QPR (Common angle)
Thus they are similar by angle-angle similarity.
I am not clear on the above
how can ∆PQS and ∆PQR be similar
∆PQS can be similar to ∆PRQ but not to ∆PQR
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by goyalsau » Mon Dec 20, 2010 2:38 am
Night reader wrote: this question is drawn from CAT administered in India. The CAT exam content is broad and not being limited to the topics embraced in GMAT quantitative curriculum. Having said this, I believe this is not GMAT question, and it tests knowledge of 'similar & congruent triangle' properties.
The Source of this question is www.time4education.com.
I am a member of the institute and they have uploaded the Gmat Quant material on the website. And it is Gmat Quant Section... Night reader Its always good to be smart with the syllabus,,,But saying that question is out of syllabus is not a great response,.......... If you have seen the interview of jyoti with Eric,,,, They said couple of times that preparing for Gmat is like marathon training........

Marathon is of 26 miles and people tend to run 52 miles before the race so when it comes to the real test, They can give there best. Now its up to the person ,, How much preparation one needs to do.........???????
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
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by Rahul@gurome » Mon Dec 20, 2010 2:39 am
prachich1987 wrote:I am not clear on the above
how can ∆PQS and ∆PQR be similar
∆PQS can be similar to ∆PRQ but not to ∆PQR
∆PRQ is essentially same as ∆PQR.
Only difference between them is the order of vertexes.
While considering the similarity the order of vertexes as well as as order of sides matters but while mentioning a triangle the order plays no role.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Join the discussion

by goyalsau » Mon Dec 20, 2010 2:41 am
prachich1987 wrote: I am not clear on the above
how can ∆PQS and ∆PQR be similar
∆PQS can be similar to ∆PRQ but not to ∆PQR
Prachi I will suggest you to Draw Three different Triangles on your scratch paper,, I m sure it will help in understanding.....

& Rahul's Solution is Absolutely Correct , Answer is 6/7
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
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by Night reader » Mon Dec 20, 2010 2:50 am
goyalsau wrote:
Night reader wrote: this question is drawn from CAT administered in India. The CAT exam content is broad and not being limited to the topics embraced in GMAT quantitative curriculum. Having said this, I believe this is not GMAT question, and it tests knowledge of 'similar & congruent triangle' properties.
The Source of this question is www.time4education.com.
I am a member of the institute and they have uploaded the Gmat Quant material on the website. And it is Gmat Quant Section... Night reader Its always good to be smart with the syllabus,,,But saying that question is out of syllabus is not a great response,.......... If you have seen the interview of jyoti with Eric,,,, They said couple of times that preparing for Gmat is like marathon training........

Marathon is of 26 miles and people tend to run 52 miles before the race so when it comes to the real test, They can give there best. Now its up to the person ,, How much preparation one needs to do.........???????
As far as I know the GMAT Quant is intellectual domain of GMAC and the institute mentioned by you is not affiliated with GMAC, correct? When it comes to preparation, I agree with you that GMAT is like marathon in terms of testing one's endurance. I might try to solve matrix by Gauss, or prove (disprove) theorem in Geo, yet GMAT is quite different story...
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by lukester » Mon Dec 20, 2010 7:42 am
prachich1987 wrote:
Rahul@gurome wrote:∆PQS and ∆PQR are similar triangles.
Thus,
  • 1. PQ/QS = PR/PQ = 12/8 => PR = (12/8)PQ = (12/8)*12 = 18
    2. PQ/QS = PR/QR = 12/10 => QR = (10/12)PR = (10/12)*18 = 15
    3. SR = PR - PS = 18 - 8 = 10
Perimeter of ∆QSR = (QS + SR + QR) = (10 + 10 + 15) = 35
Perimeter of ∆PQS = (PQ + QS + PS) = (12 + 10 + 18) = 30

Required ratio = 30/35 = 6/7

The correct answer is A.

Edit: (Proof of the similarity)
In ∆PQS and ∆PQR,
  • 1. angle PQS = angle PRQ (Given)
    2. angle QPS = angle QPR (Common angle)
Thus they are similar by angle-angle similarity.
I am not clear on the above
how can ∆PQS and ∆PQR be similar
∆PQS can be similar to ∆PRQ but not to ∆PQR
You'll need to flip the triangle.

Try flipping the smaller one. Flip in the way that essentially QSP will be the same as RQP.
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by Woozler » Mon Dec 20, 2010 9:20 pm
Jesus, Rahul, you're brilliant. I completely ignored PQR. How could I? How could I *not* do it on the actual test? How do I grow a brain - quick - before the test? Ah, the eternal questions.
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by Balrog1978 » Mon Jan 03, 2011 8:44 am
Rahul@gurome wrote:∆PQS and ∆PQR are similar triangles.
Thus,
  • 1. PQ/QS = PR/PQ = 12/8 => PR = (12/8)PQ = (12/8)*12 = 18
    2. PQ/QS = PR/QR = 12/10 => QR = (10/12)PR = (10/12)*18 = 15
    3. SR = PR - PS = 18 - 8 = 10
Perimeter of ∆QSR = (QS + SR + QR) = (10 + 10 + 15) = 35
Perimeter of ∆PQS = (PQ + QS + PS) = (12 + 10 + 18) = 30

Required ratio = 30/35 = 6/7

The correct answer is A.

Edit: (Proof of the similarity)
In ∆PQS and ∆PQR,
  • 1. angle PQS = angle PRQ (Given)
    2. angle QPS = angle QPR (Common angle)
Thus they are similar by angle-angle similarity.

After flipping the triangles (to get a better picture of the similar triangles) - I end up getting the following

Image
by taking opposite sides of equal angles as measures for determining the ratio :
(Opposite side to Angle QPS : Opposite side to Angle QRP)

I get
PS/QP = QS/PR !! And I end up getting the final ratio as 2:3!! What am I doing wrong?
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