GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 12:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the figure above, if z = 50, then x + y =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 173
In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

27 Dec 2012, 07:09
8
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:23) correct 11% (01:42) wrong based on 1122 sessions

### HideShow timer Statistics

Attachment:

Angles.png [ 9.95 KiB | Viewed 30003 times ]
In the figure above, if z = 50, then x + y =

(A) 230
(B) 250
(C) 260
(D) 270
(E) 290
Intern
Joined: 26 Jun 2012
Posts: 24
Location: Germany
GMAT 1: 570 Q31 V39
GMAT 2: 710 Q43 V44
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

18 Jun 2013, 23:50
5
1
My 30 second solution:

sum of angles in triangle = 180

Sum of angles in small triangle:
(180-y) + (180-x) + 90 = 180
--> x+y = 270

IMO the information z = 50 is not needed to calculate x+y if we know that the two vertical lines are parallel and hence we have a right angle in the smaller triangle.
Let me know if my reasoning is wrong.

Cheers
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 58445
In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

27 Dec 2012, 07:19
3
1
1

In the figure above, if z = 50, then x + y =

(A) 230
(B) 250
(C) 260
(D) 270
(E) 290

Look at the diagram below:
Attachment:

Angles2.png [ 10.57 KiB | Viewed 25172 times ]
Notice that red angles are equal, thus red angle in smaller triangle is 50 degrees as well: (red angle) = 50.

Now, smaller triangle is right angled, thus (red angle) + (blue angle) = 90 --> 50 + (blue angle) = 90 --> (blue angle) = 40.

Next, since x + (blue angle) = 180, then x = 140. Also, since (red angle) = 180 - y, then, y = 130.

x + y = 140 + 130 = 270.

_________________
Manager
Joined: 03 Nov 2009
Posts: 55
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

27 Dec 2012, 17:36
1
Adding on to what Bunuel has explained,

Alternate angles between two parallel lines are equal, so angle Z is equal to Red angle = 50

Sum of all angles in a Triangle = 180 so , 90+50 (Red)+Blue = 180
Blue Angle = 40, hence X = 180-40 = 140 --> A

Sum of all interior angles in a Quadrilateral is 360,

So z+y+2 Right angles = 360
50+Y+90+90 = 360
Y = 360-230 = 130 --> B

From Statement A and Statement B we get x+y = 140+130 = 270

Ans D
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 590
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

19 Jun 2013, 02:18
1
kingflo wrote:
My 30 second solution:

sum of angles in triangle = 180

Sum of angles in small triangle:
(180-y) + (180-x) + 90 = 180
--> x+y = 270

IMO the information z = 50 is not needed to calculate x+y if we know that the two vertical lines are parallel and hence we have a right angle in the smaller triangle.
Let me know if my reasoning is wrong.

Cheers

An exterior angle of a triangle ( In this case y) is always equal to the sum of the opposite interior angles [ In this case 90 degrees and (180-x)]

Thus, y = 90 + 180-x --> x+y = 270

So, yes you are correct.
Attachments

Angles.jpg [ 10.29 KiB | Viewed 24475 times ]

_________________
SVP
Joined: 14 Apr 2009
Posts: 2273
Location: New York, NY
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

29 Nov 2013, 13:17
1
Yes, the setup of y = 90 + (180 - x)

is a great way to solve this question without knowing x or y.

If you are not familiar with spotting exterior angles and prefer to do things the old school way - well, there's plenty of information in the diagram from which you can gather together to find the actual value of y. And then from there you can solve for x and then add up x and y.

Either method works fine.

Below is a video demonstration of the adding up x and y approach:

Intern
Joined: 04 Jun 2014
Posts: 46
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

25 Jul 2014, 00:06
I think I don't understand an important part in this question here.. What is meant by x + y ? I thought it is the value of the angles? (blue + red one)

So i would have calculated 40 + 130. Can anyone help me ?
Math Expert
Joined: 02 Sep 2009
Posts: 58445
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

25 Jul 2014, 03:09
lou34 wrote:
I think I don't understand an important part in this question here.. What is meant by x + y ? I thought it is the value of the angles? (blue + red one)

So i would have calculated 40 + 130. Can anyone help me ?

Yes, the question asks about the sum of the measures of angles x and y. x = 140° and y = 130°, so the sum is 270°.

Complete solution is here: in-the-figure-above-if-z-50-then-x-y-144792.html#p1161593

Hope it helps.
_________________
Senior Manager
Joined: 23 Sep 2015
Posts: 371
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

05 Nov 2015, 05:35
x + y = 360 - 90 (the right angle of the smaller triangle, which equals the other two angles of the smaller triangle). We don't need z to compute it
_________________
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

13 Jul 2016, 07:50
Attachment:
Angles.png
In the figure above, if z = 50, then x + y =

(A) 230
(B) 250
(C) 260
(D) 270
(E) 290

When looking at the diagram, we want to start with the quadrilateral that contains angles z and y. We must remember that any quadrilateral has a total of 360 degrees. We know that two angles of the given quadrilateral are 90 degrees each and that z = 50 degrees. Thus, we can set up the following equation to determine the measure of angle y.

90 + 90 + 50 + y = 360

230 + y = 360

y = 130

Now that we know the value of angle y, we can move to the triangle in the lower part of the diagram. Let’s label it triangle ABC and draw it below. We see that angle ACB and angle y are supplementary, so angle ACB = 180 – 130 = 50 degrees. We also see that the triangle is a right triangle so the remaining angle, angle ABC = 180 – (90 + 50) = 40 degrees. Finally, since angle ABC and angle x are supplementary we see that angle x = 180 – 40 = 140 degrees.

Thus, x + y = 140 + 130 = 270.

The answer is D.
_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Joined: 02 Sep 2016
Posts: 649
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

04 Sep 2017, 04:18
y= 360-(50+90+90)= 130 (straight line method and sum of angles of a quadrilateral is 360)

x is the exterior angle and hence = (180-y)+90= 140

140+130= 270

I did not use the parallel line method. Hope this is fine.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

01 Feb 2018, 13:10
Hi All,

This question requires an understanding of similar triangles, "line" rules (specifically that the angles on a line sum to 180 degrees) and that the angles in a triangle sum to 180 degrees.

We're told that Z=50. Since the two triangles have the same angles (they both have a 90 and the same angle "next" to angle X), we know that the triangles are similar. This means that Z and the angle "next" to Y are the SAME (meaning that they BOTH = 50).

By extension, Y + 50 = 180, so Y = 130.

The angles in the smaller triangle are 90, 50 and the missing angle. 90+50 = 140, so the missing angle = 40.

40 + X = 180, so X = 140

Thus, X+Y = 130+140 = 270

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
Joined: 09 Sep 2013
Posts: 13275
Re: In the figure above, if z = 50, then x + y =  [#permalink]

### Show Tags

07 May 2019, 03:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In the figure above, if z = 50, then x + y =   [#permalink] 07 May 2019, 03:25
Display posts from previous: Sort by

# In the figure above, if z = 50, then x + y =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne