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

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In the figure shown, what is the value of x? [#permalink]

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08 Aug 2012, 07:39
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55% (hard)

Question Stats:

66% (02:24) correct 34% (01:20) wrong based on 38 sessions

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

(1) The length of line segment QR is equal to the length of line segment RS.

(2) The legnth of line segment ST is equal to the length of line segment TU.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-what-is-the-value-of-x-125923.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Aug 2012, 15:16, edited 2 times in total.
Edited the question and added the OA.
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08 Aug 2012, 09:02
thagem01 wrote:
Hi Guys,

Please find attached a question of geometry that i do not understand.

Could you please give me the explanation?

Thanks

Neither (1) nor (2) alone is sufficient.
Let's see why together they are sufficient:

(1) and (2) together: Triangle RQS isosceles, so $$\angle {RSQ}=\frac{180^o-\angle{R}}{2}$$.
Similarly, triangle TSU is asosceles, so $$\angle{TSU}=\frac{180^o-\angle{T}}{2}$$.
It follows that $$x=180-90+\frac{\angle{R}}{2}-90+\frac{\angle{T}}{2}=\frac{\angle{R}+\angle{T}}{2}=\frac{90}{2}=45$$, because triangle PRT is right angled.
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08 Aug 2012, 09:24
Thanks a lot... I got it now!

This was not an easy one... Was it?
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08 Aug 2012, 09:52
I did this by plugging 2 different sets of values.
We know PRT is a right angle triangle. So let it be 90-60-30 or 90-45-45 triangle.
Now we can find out the value of X for both this situation. In both case the value of X comes as 45 degree.
So St 1+ St 2 Sufficient.
For 90-60-30: <RST + <TSU = 135 degree, so X =45 degree
For 90-45-45: <RST + <TSU = 135/2 + 135/2 = 135 Degree, so X =45 Degree
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08 Aug 2012, 12:07
SOURH7WK wrote:
I did this by plugging 2 different sets of values.
We know PRT is a right angle triangle. So let it be 90-60-30 or 90-45-45 triangle.
Now we can find out the value of X for both this situation. In both case the value of X comes as 45 degree.
So St 1+ St 2 Sufficient.
For 90-60-30: <RST + <TSU = 135 degree, so X =45 degree
For 90-45-45: <RST + <TSU = 135/2 + 135/2 = 135 Degree, so X =45 Degree

You cannot plug in values for the angles of the right triangle.
From your computations, how can you know that you will get the same value for different angles of the right triangle? In the question, there is nothing specified about the angles of the R and T.
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Re: In the figure shown, what is the value of x? [#permalink]

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08 Aug 2012, 15:15
Expert's post
thagem01 wrote:
In the figure shown, what is the value of x?

(1) The length of line segment QR is equal to the length of line segment RS.

(2) The legnth of line segment ST is equal to the length of line segment TU.

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

x+<QSR+<UST=180 (straight line =180) and <R+<T=90 (as PRT is right angle)

(1) The length of line segment QR is equal to the length of line segment RS --> QRS is isosceles --> <RQS=<QSR=(180-R)/2 (as <RQS+<QSR+<R=180 --> 2<QSR+<R=180 --> <QSR=(180-R)/2). Not sufficient.

(2) The legnth of line segment ST is equal to the length of line segment TU --> UST is isosceles --> <SUT=<UST=(180-T)/2. Not sufficient.

(1)+(2) x+<QSR+<UST=180 --> x+(180-R)/2+(180-T)/2=180 --> x+(360-(R+T))/2=180 --> as R+T=90 --> x+(360-90)/2=180 --> x=45. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-what-is-the-value-of-x-125923.html
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Re: In the figure shown, what is the value of x?   [#permalink] 08 Aug 2012, 15:15
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