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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 25 Aug 2018, 23:50
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

Consider kudos if that helped

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Thank you =Kudos
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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, 02:54
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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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Math Expert
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Joined: 02 Sep 2009
Posts: 52213
Re: In the figure shown, what is the value of x?  [#permalink]

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New post 26 Aug 2018, 02:55
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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: In the figure shown, what is the value of x? &nbs [#permalink] 26 Aug 2018, 02:55

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