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# I know this is about similar triangles but not exactly sure

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I know this is about similar triangles but not exactly sure [#permalink]

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15 May 2008, 15:14
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I know this is about similar triangles but not exactly sure how.Is angle QPS=RPS?
Thank you!!

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16 May 2008, 06:13
No the angels are not equal.

need to go for any mathematical calculations. just check the slope of the lines. the two lines PQ and PR are not parallel so the angels should be different
hope you got my idea.

correct me if i am wrong.

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16 May 2008, 06:52
ventivish wrote:
I know this is about similar triangles but not exactly sure how.Is angle QPS=RPS?
Thank you!!

I don't think it's about similar triangles. It is about relationships of angles within triangles.

The stem first tells you that you are comparing angle PQR with PRS. It is essentially asking you, what information is required to be able to compute the difference in measurement of the angles.

First, you are told that QPR is 30 and you know that QSP & RSP are right angles.

The degree of PQS = 180 - 30 [given in 1)] - RPS - 90[RSP]. I assigned variables to the angles like the following:

a = PQS (unknown)
b = PSR (90 degrees)
x = RPS (unknown)
d = PRS (unknown)

Don't ask my why I chose those letters. It's kind of random, but all you need is some way to make it easier to do the math.

So we are trying to figure out if we can compare "d" with "a" when we know that QPS = 30 degrees.

Statement 1 is sufficient and here is why.

Using the variables assigned above you get the following equation:

a = 180 - 30 - x - 90 [180 for all interior angles of a triangle. 30 is already told to us, 90 for the right angle, and x for the unknown portion].

d = 180 - 90 - x. We can go right to answering "how many degrees greater is PRS [d] than PQR[a]".

d - a answers this question, but substituting in for the equation above we get:

(180 - 90 - x) - (180 - 30 - x -90) = V [V for value. I find it easier than just leaving = ____]

90 - x - 60 - x = V

30 - 2x = V

30 = 2x

15 = x

Now plug 15 for x back into the picture and we only have a & d left to solve.

QPS = 45 (30 given in statement 1 and 15 from our solution above)

Angle d = 180 - 90 - 15 = 75

Angle a = 180 - 90 - 30 - 15 = 45

So d - a = 30 degrees. We've done more than is truly required. You coudl stop once you realize statement 1 is sufficient.

Statement 2 is essentially telling you the same thing as Statement one, in a different way.

If you know PQR + PRQ = 150, that is 2 of 3 interior angles. so the 3rd angle has to be 180 - the sum of those 2 (180 - 150 = 30). So you just got through solving when QPR = 30 so you know statement 2 itself is sufficient.

Hope this helps
_________________

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a\$\$.

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Kudos [?]: 623 [0], given: 32

Senior Manager
Joined: 20 Feb 2008
Posts: 295

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16 May 2008, 23:05

I also found a shorter way of doing this for stat A

angleQPR=30
anglePQR+angleQPR+180-anglePRQ=180;
anglePQR+30-anglePRQ=0
anglePRQ-anglePQR=30
So stat 1 sufficient!!

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Joined: 30 Apr 2008
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17 May 2008, 00:44
ventivish wrote:

I also found a shorter way of doing this for stat A

angleQPR=30
anglePQR+angleQPR+180-anglePRQ=180;
anglePQR+30-anglePRQ=0
anglePRQ-anglePQR=30
So stat 1 sufficient!!

Can you explain your answer? It will help others (and me) to see the shorter way, but it will only help really if you explain why you use the figures you do. The reason my answer was so "long" is that often answers to questions on here state the answer but don't walk a person through the entire process to let that person truly grasp the solution to the problem. It's great to see what the answer is, but it's better to understand how we get there because those same principles that show how will help other, similar questions in on the real GMAT.
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a\$\$.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 623 [0], given: 32

Senior Manager
Joined: 20 Feb 2008
Posts: 295

Kudos [?]: 51 [0], given: 0

Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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17 May 2008, 07:09
jallenmorris wrote:
ventivish wrote:
I know this is about similar triangles but not exactly sure how.Is angle QPS=RPS?
Thank you!!

I don't think it's about similar triangles. It is about relationships of angles within triangles.

The stem first tells you that you are comparing angle PQR with PRS. It is essentially asking you, what information is required to be able to compute the difference in measurement of the angles.

First, you are told that QPR is 30 and you know that QSP & RSP are right angles.

The degree of PQS = 180 - 30 [given in 1)] - RPS - 90[RSP]. I assigned variables to the angles like the following:

a = PQS (unknown)
b = PSR (90 degrees)
x = RPS (unknown)
d = PRS (unknown)

Don't ask my why I chose those letters. It's kind of random, but all you need is some way to make it easier to do the math.

So we are trying to figure out if we can compare "d" with "a" when we know that QPS = 30 degrees.

Statement 1 is sufficient and here is why.

Using the variables assigned above you get the following equation:

a = 180 - 30 - x - 90 [180 for all interior angles of a triangle. 30 is already told to us, 90 for the right angle, and x for the unknown portion].

d = 180 - 90 - x. We can go right to answering "how many degrees greater is PRS [d] than PQR[a]".

d - a answers this question, but substituting in for the equation above we get:

(180 - 90 - x) - (180 - 30 - x -90) = V [V for value. I find it easier than just leaving = ____]

90 - x - 60 - x = V

30 - 2x = V

30 = 2x

15 = x

Now plug 15 for x back into the picture and we only have a & d left to solve.

QPS = 45 (30 given in statement 1 and 15 from our solution above)

Angle d = 180 - 90 - 15 = 75

Angle a = 180 - 90 - 30 - 15 = 45

So d - a = 30 degrees. We've done more than is truly required. You coudl stop once you realize statement 1 is sufficient.

Statement 2 is essentially telling you the same thing as Statement one, in a different way.

If you know PQR + PRQ = 150, that is 2 of 3 interior angles. so the 3rd angle has to be 180 - the sum of those 2 (180 - 150 = 30). So you just got through solving when QPR = 30 so you know statement 2 itself is sufficient.

Hope this helps

Hi Jallenmorris,
Thank you for your explanation. I just realised that your method is the same as mine and I did not exactly follow through whereas you did.Sorry my mistake just missed that sentence where you said we can go right to answering the question. The highlighted portion above is pretty much where I left the answer at. I do appreciate your explanation and I agree it makes the solutions alot easier for others to comprehend.

I also found a shorter way of doing this for stat A

angleQPR=30
anglePQR+angleQPR+180-anglePRQ=180;
anglePQR+30-anglePRQ=0
anglePRQ-anglePQR=30 This corressponds to d-a in your explanation above
So stat 1 sufficient!!

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Re: GmatprepGeometry DS   [#permalink] 17 May 2008, 07:09
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