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# Triangles

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27 May 2009, 10:10
00:00

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (00:02) wrong based on 1 sessions

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I'm stuck on this one.. Thanks.
Manager
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27 May 2009, 14:08
I would say E.

In order to answer the question, you would have to know the measure of angles PRS and PQR

(1) Measure of Angle QPR - gives us some insight into what angles PRS and PQR may be, as they are in a triangle, but not enough to answer the question. (insufficient)

(2) Measure of Angles PRQ and PQR together - gives us nothing, we already know this information with (1). (insufficient)

What we really need to know in order to answer this question is the measure of angle PRS or PRQ alone, because 180-PRQ = PRS and vice versa. Or if we had some other information, such as PQR alone, or QPS, since we could get PQR from that. but nothing gives us what we need to know so it is E.
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27 May 2009, 20:36
1
KUDOS
A. QPR = 30

QPR + PQR +QRP = 180
==> 30 + PQR + (180-PRS) = 180
==> PRS - PQR = 30 ..........sufficient

B. PQR+ PRQ =150

==> PQR + (1800-PRS) =150
==> PRS - PQR =30..........sufficient

Manager
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28 May 2009, 09:40
Property of triangle : Sum of Angle of Triangle = 180

let assume RPS = P1 & QPS = p2, PRQ = R1 , PRS = R2

Now from triangle
Q + p2 = 90 ---- (a)
R2 + p1 = 90 ---- (b)

From 1st Statement:
p2 - p1 = 30

subtract (a) from (b)
R2 - Q + p1 - p2 = 0 =>
R2 - Q = p2 - p1 = 30

Hence 1st statemnet alone is suff.

From 2nd statement

R1 + Q = 150

Now R1 + R2 = 180 ...its clear

So 180 - R2 + Q = 150 =>
R2 - Q = 30

2nd statemnet alone is also suff

So for me Answer should be (D)
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28 May 2009, 10:29
Stmt 1 = Stmt 2, it's the same thing. So, it has to either be D or E

D

Last edited by pm4553 on 06 Aug 2009, 06:43, edited 1 time in total.
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28 May 2009, 13:38
This is a great answer. Most of us (including me) try to figure out what value PRS and PQR actually have in order to find the difference, but that's not always required. Once we get an equation that tells us the answer it doesn't matter if that answer actually has values filled in because the values do not matter, the answer is 30, and that means the data provided is sufficient.

traveller10 wrote:
A. QPR = 30

QPR + PQR +QRP = 180
==> 30 + PQR + (180-PRS) = 180
==> PRS - PQR = 30 ..........sufficient

B. PQR+ PRQ =150

==> PQR + (1800-PRS) =150
==> PRS - PQR =30..........sufficient

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Manager
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28 May 2009, 14:01
yes I never thought to just put them all into formulas, was thinking graphically I suppose. Very tricky question, you dont have to know the measure of either angle, just how much larger it is than the other. Good job traveler.
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24 Jul 2009, 22:57
Excellent question!
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Re: Triangles   [#permalink] 24 Jul 2009, 22:57
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