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

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

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New post 26 Aug 2018, 00:50
shorteverything wrote:
Image
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 length of line segment ST is equal to the length of line segment TU


Attachment:
Triangle.GIF
30 seconds approach
C

This is geometry DS question. I prefer to use technique mentioned in gmat prep now video.

St1) now point S and Q are fixed. So line SQ will have a fixed incline but point U is not fixed. You can move around point U and can get variable values of x

Not sufficient

St2) now point U is fixed but Q is variable.
Not sufficient

Combining
Both points are fixed. X can take only one value. No need to spend time finding the value. We know the figure is restricted now and can only assume bigger sides but the angle will remain same

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

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New post 26 Aug 2018, 03:54
ravikumarmishra wrote:
Bunuel wrote:
Image
In the figure shown, what is the value of x?

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


(1) The length of line segment QR is equal to the length of line segment RS --> triangle QRS is isosceles --> \(\angle{RQS}=\angle{QSR}=\frac{180-\angle{R}}{2}\) (as \(\angle{RQS}+\angle{QSR}+\angle{R}=180\) --> \(2*\angle{QSR}+\angle{R}=180\) --> \(\angle{QSR}=\frac{180-\angle{R}}{2}\)). Not sufficient.


(2) The length of line segment ST is equal to the length of line segment TU --> triangle UST is isosceles --> \(\angle{SUT}=\angle{UST}=\frac{180-\angle{T}}{2}\). Not sufficient.


(1)+(2) \(x+\angle{QSR}+\angle{UST}=180\) --> \(x+\frac{180-\angle{R}}{2}+\frac{180-\angle{T}}{2}=180\) --> \(x+\frac{360-(\angle{R}+\angle{T})}{2}=180\) --> since \(\angle{R}+\angle{T}=90\) --> \(x+\frac{360-90}{2}=180\) --> \(x=45\). Sufficient.

Answer: C.


Thanks Bunuel, perfect solution. For more practice, can you please provide links for similar problems, thanks.





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

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New post 26 Aug 2018, 03:55
ravikumarmishra wrote:
Bunuel wrote:
Image
In the figure shown, what is the value of x?

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


(1) The length of line segment QR is equal to the length of line segment RS --> triangle QRS is isosceles --> \(\angle{RQS}=\angle{QSR}=\frac{180-\angle{R}}{2}\) (as \(\angle{RQS}+\angle{QSR}+\angle{R}=180\) --> \(2*\angle{QSR}+\angle{R}=180\) --> \(\angle{QSR}=\frac{180-\angle{R}}{2}\)). Not sufficient.


(2) The length of line segment ST is equal to the length of line segment TU --> triangle UST is isosceles --> \(\angle{SUT}=\angle{UST}=\frac{180-\angle{T}}{2}\). Not sufficient.


(1)+(2) \(x+\angle{QSR}+\angle{UST}=180\) --> \(x+\frac{180-\angle{R}}{2}+\frac{180-\angle{T}}{2}=180\) --> \(x+\frac{360-(\angle{R}+\angle{T})}{2}=180\) --> since \(\angle{R}+\angle{T}=90\) --> \(x+\frac{360-90}{2}=180\) --> \(x=45\). Sufficient.

Answer: C.


Thanks Bunuel, perfect solution. For more practice, can you please provide links for similar problems, thanks.




23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations




For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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Re: In the figure shown, what is the value of x?  [#permalink]

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New post 21 Jul 2019, 23:57
The working out here is just too boring to follow, so I drew a diagram to make things clear.

See attached
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Capture.JPG
Capture.JPG [ 125.78 KiB | Viewed 211 times ]


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

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New post 13 Oct 2019, 08:27
I \(x+180-y+180-z=270 \implies x-y-z=-90\)
II \(x+y+z=180\)
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Screenshot 2019-10-13 at 17.32.41.png [ 83.95 KiB | Viewed 21 times ]

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In the figure shown, what is the value of x?   [#permalink] 13 Oct 2019, 08:27

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