Problem Solving

Help Guys,,,,,,,,,

6/7

7/6

5/6

6/5

7/5

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

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

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.

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.

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

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.........???????

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

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...

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.

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.

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


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?