In the ﬁgure shown, lines k and m are parallel to each other. Is x = z

Question

https://gmatclub.com/forum/download/file.php?id=27302 In the figure shown, lines k and m are parallel to each other. Is x = z ? (1) x = w (2) y = 180 - w Untitled.png

chetan2u · Answer

1) statement one tells us that X=W..
 but W=Z since both are alternate angles between two llel lines.. suff

2) y=180-w... also y=180-x as y and x are supplementary angles.. so w=x , same info as statement 1... suff
D Ans

sasyaharry · Answer

I made a mistake by discarding second statement since it did not provide any new information. Duh.
Answer is  D

iliavko · Answer

Guys can you tell me where can learn the angles stuff?

Bunuel · Answer

23. Geometry 
     Theory   
 Everything you need to know about GMAT Geometry in one slideshow 
 Common Mistakes in Geometry Questions 
 GMAT Trick: Rules about Figures in GMAT Geometry 
 INSCRIBED AND CIRCUMSCRIBED POLYGONS ON THE GMAT 
 Useful Articles and Practice Questions to ace GMAT Geometry 
 Why Does the GMAT Test Geometry? 
     Questions   
 Geometry Ability Quiz 
 GEOMETRY: Shaded Region Problems 
 Probability and Geometry Problems 
 The E-GMAT Question Series on Geometry 
 DS Questions 
 PS Questions

24. Coordinate Geometry 
     Theory   
 Math: Coordinate Geometry 
 Beauty of Coordinate geometry 
 Dealing with Tangents on the GMAT 
     Questions   
 DS Questions 
 PS Questions

25. Triangles 
     Theory   
 Math: Triangles 
 Mastering Important Concepts Tested by GMAT in Triangles - I 
 Mastering Important Concepts Tested by GMAT in Triangles - II 
 Mastering Important Concepts Tested by GMAT in Triangles - III 
 Medians, Altitudes and Angle Bisectors in Special Triangles on GMAT 
 What Austin Powers Can Teach You about Similar Triangles 
 Determining the Area of Similar Triangles on the GMAT 
 Looking for Similar Triangles on the GMAT 
 GMAT Tip of the Week: Today's Date in Geometry History - Pythagorean Triplets 
     Questions   
 DS Questions 
 PS Questions

26. Polygons 
     Theory   
 Math: Polygons 
     Questions   
 DS Questions 
 PS Questions

27. Circles 
     Theory   
 Math: Circles 
     Questions   
 DS Questions 
 PS Questions

28. Rectangular Solids and Cylinders 
     Theory   
 Math : 3-D Geometries 
     Questions   
 GEOMETRY: 3-D Geometry Questions 
 DS Questions 
 PS Questions

shashankism · Answer

Given : Figure in which k || m
DS : x = z ?
From figure, y = 180 -x

Option 1 : x = w 
SO sum of all angles of a quadrilateral = 360 
-> y + w +(180 -z) + x(alternate angle) = 360 
-> 180 -x + x + 180 - z + x = 360 
-> x = z
 SUFFICIENT

Option 2 : Y = 180 - w = 180 - x 
-> x = w which is smae as option 1 
 SUFFICIENT

Answer D

BrentGMATPrepNow · Answer

Target question :    Is x = z ?  
Before we examine the statements, let's first recognize that, since k||m, we can conclude that   angles w and z are EQUAL  
 https://i.imgur.com/83z1dX6.png

Okay, now onto the statements

Statement 1 : x = w   
We already learned that    w = z  
Statement 1 tells us that w = x
Since x and z are both equal to w,  it must also be true that x = z 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : y = 180 - w  
We can also REPHRASE this as y + w = 180
Since    w = z  , we can also replace w with z in the above equation to get:  y + z = 180  
In the diagram, we can see that since angles y and x are on the same line, then  y + x = 180 
Since both equations are set equal to 180, we can also write: y + z = y + x
From here, we can subtract y from both sides to get  z = x 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=F26uam3kmCU

hero_with_1000_faces · Answer

The Diagram really confused me, whether "W" was alternate angle of X or Z.
How do I determine this in exams, in such cases ? do i have to see the degree symbol, which was on right side

dcummins · Answer

alternate angles.

Just derive algebraically that x= w in either statement to determine that each is sufficient.

Basshead · Answer

(1) x = w

From the figure we can conclude w = z, as we're told lines k and m are parallel to each other (alternate angles are equal). From statement 1 we're told x = w. Thus x = w = z. SUFFICIENT.

(2) y = 180 - w

This statement tells us x = w. Since w = z, z = x. SUFFICIENT.

Answer is D.

MHIKER · Answer

(1) As the figure is a parallelogram;  w=z ; as they are alternate angels, Given  x=w, \ so \ x=z ; Sufficient.

(2) As  y=180-w ,  x=180-180+w=w , now for the condition described in option 1  x=z ; Sufficient.

The answer is  D

CEdward · Answer

St1 - x = w
w = z (alternating angles)

Sufficient.

St2 - y = 180 - w

180 - w = 180 - x (by rule of supplementary angles)

x = w

Sufficient.

D.

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine whether x = z. We see that x + y = 180. Furthermore, we are given that lines k and m are parallel, so w = z because they are alternate interior angles.

Statement One Alone:

Since x = w and w = z, then x = z. Statement one alone is sufficient.

Statement Two Alone:

Since y = 180 - w and w = z, then y = 180 - z or z + y = 180. Since x + y = 180 and z + y = 180, we see that x = z. Statement two alone is sufficient.

Answer: D

dylanl1218 · Answer

When a line transverses two parallel line we end up with a couple of special properties. One of which is that the corresponding acute and obtuse angles are equal to each other. So from analyzing the picture in the stem we can conclude right off the bat that W=Z.

Statement 1:  
If X = W, then X = W = Z, so X must be equal to Z

Statement 2:  
Given that the angles X and Y are supplementary, we can conclude that X+Y = 180, and furthermore with the information provided in statement two we can say that X + 180 - W = 180, so X = W. Since in the stem we concluded that W=Z then we can now conclude that X = W = Z, so it must be the case that X = Z.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the ﬁgure shown, lines k and m are parallel to each other. Is x = z

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia