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In the figure shown, what is the value of x?

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by DanaJ » Mon Jun 29, 2009 1:39 am
Hey there,

If you have problems attaching pictures, then feel free to PM me with the document and I'll see to it that it's attached.
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by alexdallas » Mon Jun 29, 2009 5:13 pm
thanks bro..i think i got it this time:
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by Gelopzwewr » Mon Jun 29, 2009 6:19 pm
I got E, spending a lot more than 2 minutes to figure it out
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by alexdallas » Mon Jun 29, 2009 6:26 pm
could u maybe explain it, if u have the time?
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by GMATQuantCoach » Mon Jun 29, 2009 10:30 pm
This is a quite difficult geometry problem.

I will use < sign to represent angles.

Statement 1 or 2 alone is not sufficient because we can move the other point around to form different angles of x.

When the two statements are combined, it gets tricky. I have two approaches. One is more robust than the other but will take more time.

Approach 1:
Assume <R = 60, then you can calculate x. You will find x = 45.
Assume <R = 10, you still find x = 45.
Assume <R = 45, you get x = 45.
Here I am just trying different values of <R to see if the value of x changes or not. With three totally different cases, it is safe to assume x = 45.

Approach 2:
Geometrically show that x = 45 no matter what <R is.
We know:
<RSQ + x + <TSU = 180
x = 180 - (<RSQ + <TSU)
We need to figure out what is <RSU + <TSU by using all the given conditions in the problem.

<R + <RSQ + <RQS = <R + 2<RSQ = 180
<T + <TSU + <TUS = <T + 2<TSU = 180

Adding the two equations yields:
<R + <T + 2(<RSQ + <TSU) = 360

We are almost there. We know RPT is a right triangle. Then
<R + <T = 90
Therefore
90 + 2(<RSQ + <TSU) = 360
<RSQ + <TSU = 135
Then
x = 180 - (<RSQ + <TSU) = 45


C is your answer.
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Answer with exact calculation and no assumption.

by struggling_guy2001 » Tue Jun 30, 2009 4:16 am
From statement 1) i.e. QR=RS

<RSQ = <RQS

From statement 2) i.e. ST=TU

<TSU = <SUT.

From big triangle PRT,

<R + <T = 90.

From statement 1) <R = 180-2 <RSQ.

From statement 2) <T = 180- 2 < TSU.

Hence (180-2 <RSQ ) + (180- 2 < TSU) = 90.

360-2( RSQ+ TSU ) =90

Now TRS forms a straight line. hence RSQ + X + TSU =180
Therefore,

RSQ + TSU = 180-X.
Therefore,
360-2 ( 180-x) =90
therefore,

x=45.

Hence from the equation it is clear that both the statements are necessary and enough to solve the problem.
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Hi GMATQuantCoach or any other senior people...

by struggling_guy2001 » Tue Jun 30, 2009 4:36 am
Hi GMATQuantCoach or any other senior people... can you provide your opinion on the way I solved it.. is it fine and refined??
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by GMATQuantCoach » Tue Jun 30, 2009 6:13 am
It's good!
In these complicated geometry problems, just be sure to use all the given information. Most likely you will need all of them to solve the question.

Here, the given information is: RSQ and STU are isosceles triangles; RPT is a right triangle.

You were able to use all the information.
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by alexdallas » Sun Jul 05, 2009 10:11 am
tks struggling guy!
ure not struggling after all! :D
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Hey...

by struggling_guy2001 » Tue Jul 14, 2009 10:45 pm
Hey.. nothing is perfect in the world.. so I need to struggle to reach perfection....
Anyone from Hyderabad or Telugu speaking community.

Searching for a serious study partner from Hyderabad or the one who work for same Company.
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by bhumika.k.shah » Tue Feb 02, 2010 7:13 am
Hi i am sowree i still dint get it!
Could someone help me explain this sum ?

I marked E coz the question is asking us to find the value of x = a solid #

How can we get a value from either or both of these statements ??

OA C
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by ajith » Tue Feb 02, 2010 8:27 am
bhumika.k.shah wrote:Hi i am sowree i still dint get it!
Could someone help me explain this sum ?

I marked E coz the question is asking us to find the value of x = a solid #

How can we get a value from either or both of these statements ??

OA C
Combining the statements

QRS+RTP =90 ---- (1)
UST+x+QSR =180 ---- (2)
QRS+2QSR =180 - (3) (QSR = RQS and sum of the angles of the triangle QSR =180)
RTP+ 2UST =180 ---(4) (UST = SUT and sum of the angles of the triangle UST=180)
QRS+RTP +2(QSR+UST) =360 ((3)+(4))
QSR+UST = 135 ---(5)
X =45 ((5) in 2)
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by Mom4MBA » Tue Feb 02, 2010 1:38 pm
after checking that each statement alone will not do any good we will check both the statements together. so use the basic properties or triangles and quadrilaterals and start working.

Image

take the big triangle:

sum of the three angles = 180
180-2a + 180-2b + 90 = 180
a+b = 135

now take the quadrilateral:

sum of the 4 angles = 360
180-a + 180-b + x + 90 = 360
x= a+b - 90
x= 135 - 90
x= 45[/img][/url]
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by bhumika.k.shah » Tue Feb 02, 2010 7:02 pm
Thanks!
finally got it this way :-)
Mom4MBA wrote:after checking that each statement alone will not do any good we will check both the statements together. so use the basic properties or triangles and quadrilaterals and start working.

Image

take the big triangle:

sum of the three angles = 180
180-2a + 180-2b + 90 = 180
a+b = 135

now take the quadrilateral:

sum of the 4 angles = 360
180-a + 180-b + x + 90 = 360
x= a+b - 90
x= 135 - 90
x= 45[/img][/url]
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