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## Is there a simpler way to solve this question?

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 2 member replies
shibsriz@gmail.com Master | Next Rank: 500 Posts
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#### Is there a simpler way to solve this question?

Tue Jun 11, 2013 3:54 am

00:00

A

B

C

D

E

# Global Stats

Difficult

166. What is the value of x + y in the figure above?
(1) w = 95
(2) z = 125
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Brent@GMATPrepNow GMAT Instructor
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Tue Jun 11, 2013 5:16 am
shibsriz@gmail.com wrote:

What is the value of x + y in the figure above?
(1) w = 95
(2) z = 125
Target question: What is the value of x + y?

Statement 1: w = 95

Important: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1103

If w = 95, then the angle inside the quadrilateral must be 85.

So, those 2 angles (95 and 85) are "locked." In other words, the 2 lines that create those two angles are locked in place to create the 95- and 85-degree angles.
However, line1 is not locked into place, so we can still move it, which means we can freely alter the size of angle y.
As such, the value of x + y will vary.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z = 125
If z = 125, then the angle inside the quadrilateral must be 55.

Since line2 is not locked into place, we can still move it, which means we can freely alter the size of angle x.
As such, the value of x + y will vary.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We now have the following:

Since all angles in a quadrilateral add to 360 degrees, we know that 85 + 55 + j + k = 360
If we solve for j + k, we get: j + k = 220

Also notice that, since angles x and k are on a line, it must be true that x + k = 180.
Similarly, it must be true that y + j = 180
If we combine both of these equations, we get: x + y + j + k = 360
Since we already know that j + k = 220, we can replace j + k with 220, to get:
x + y + 220 = 360
This means x + y = 140
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

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Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 2:08 pm; edited 2 times in total

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GaneshMalkar Senior | Next Rank: 100 Posts
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Tue Jun 11, 2013 9:16 am
One more way to do this :-

Let the interior angles be a,b,c,d in the clockwise direction.

So, (180-x) + (180-y) + (180-w) + (180-z) = 360

720 - (x+y+w+z) = 360
x+y+w+z = 360

x + y = 360 - (w + z) ... We need to know the values of w and z to get x + y

(a) w = 95
Not Sufficient since we need value of z.

(b) z = 125
Not Sufficient since we need value of w.

(a) and (b)

Sufficient.

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Rohit_Prakash88@yahoo.in Newbie | Next Rank: 10 Posts
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Fri Apr 01, 2016 10:32 am
Dear All,

Request you to please guide me how can we assume it to be quadrilateral when it is not that the two lines are parallel . As we have learnt in the basic that we should not assume seeing the figure then can we infer that the two lines are parallel.

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Brent@GMATPrepNow GMAT Instructor
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Fri Apr 01, 2016 10:37 am
Rohit_Prakash88@yahoo.in wrote:
Dear All,

Request you to please guide me how can we assume it to be quadrilateral when it is not that the two lines are parallel . As we have learnt in the basic that we should not assume seeing the figure then can we infer that the two lines are parallel.
There need not be any parallel sides for a shape to be a quadrilateral.
A quadrilateral is any 4-sided polygon.

Cheers,
Brent

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ceilidh.erickson GMAT Instructor
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Sat Apr 02, 2016 12:48 pm
GaneshMalkar wrote:
One more way to do this :-

Let the interior angles be a,b,c,d in the clockwise direction.

So, (180-x) + (180-y) + (180-w) + (180-z) = 360

720 - (x+y+w+z) = 360
x+y+w+z = 360

x + y = 360 - (w + z) ... We need to know the values of w and z to get x + y

(a) w = 95
Not Sufficient since we need value of z.

(b) z = 125
Not Sufficient since we need value of w.

(a) and (b)

Sufficient.

Ganesh's solution is my recommended approach on this question!

On DS geometry questions, a lot of students get into trouble if they begin by plugging the statement information into the figure right away. If there is a given figure, it's much better to make any and all inferences you can before looking at the statements. Otherwise, you might think that you need statement information that was already inferable from the figure.

Here's an example of a DS geometry problem that student often get wrong if they don't make inferences first:
http://www.beatthegmat.com/area-of-the-circumscribed-circle-t276376.html#719010

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