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# What is the value of x + y in the figure above?

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Manager
Joined: 07 Jan 2008
Posts: 249
What is the value of x + y in the figure above?  [#permalink]

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30 Mar 2008, 09:19
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71% (01:03) correct 29% (00:01) wrong based on 43 sessions

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What is the value of x + y in the figure above?

(1) w= 95
(2) z = 125

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/what-is-the-v ... 44723.html

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Senior Manager
Joined: 20 Feb 2008
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Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
Re: What is the value of x + y in the figure above?  [#permalink]

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30 Mar 2008, 10:14
mbawaters wrote:
Q22:

<Please see attached file for the figure>

What is the value of x + y in the figure above?
(1) w = 95
(2) z = 125
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
(E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hi, I would say E the two statements are not sufficient

The relationship between x,y,w and z can only be made if either of the lines were parallel. Which in this case are not.
(A)w =95, sure you might think 180-95=85 will give you the internal angle, but this is not sufficient to find x or way
B) z= 125 again you can calculate the internal angle 180-125 =55 again this is insufficient as there is no way to calcaulate C It is tempting to add the internal angles of w+z but it is not equal to x + y since there is no relationship, eg we dont know the sum of the angles, also the lines are not parrallel so we cannot use either of those rules.
D is insufficient
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Re: What is the value of x + y in the figure above?  [#permalink]

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30 Mar 2008, 18:08
1
I'd say C.
From (1) and (2) we can find out the 2 angles of the quadrilateral next to w and z. the other two angls are 180-x and 180-y. We know the sum of the angles of a quadrilateral is 2*180 = 360. From here x+y=140
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Joined: 18 Sep 2012
Posts: 1
Re: What is the value of x + y in the figure above?  [#permalink]

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18 Sep 2012, 02:29
I think the answer would be C)

Explanation:
W=95, so interior angle W'= 180-95 = 85
Z = 125, so interior angle Z'= 180-55= 85

Summation of interior angles of the quadrilateral = 360
Therefore,
W' + Z' + X'+ Y' = 360
85 +85+ X' +Y" =360
X'+Y'= 180
since X + X' + Y+Y' =360 (the fall on a straight line as pairs of supplimentary angles)
X+Y must be equal to 360-180 = 180
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Joined: 02 Sep 2009
Posts: 55271
What is the value of x + y in the figure above?  [#permalink]

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23 Jul 2017, 04:40

What is the value of x + y in the figure above?

Sum of Interior Angles of a polygon is $$180(n-2)$$ where $$n$$ is the number of sides (so is the number of angles). So, the sum of the interior angles of a quadrilateral is 180*2=360. Look at the diagram below:

According to the above: (180-x)+(180-y)+(180-z)+(180-w)=360 --> x+y=360-w-z, so all we need to know is the values of w and z.

(1) w= 95. Not sufficient.
(2) z = 125. Not sufficient.

(1)+(2) Sufficient.

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What is the value of x + y in the figure above?   [#permalink] 23 Jul 2017, 04:40
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