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## what is the sum of angles x and y?

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 0 member replies
LulaBrazilia Master | Next Rank: 500 Posts
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#### what is the sum of angles x and y?

Thu Mar 06, 2014 9:05 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])

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

1) w=95
2) z=125

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Thu Mar 06, 2014 9:12 am
Quote:

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 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 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 not answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent

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Patrick_GMATFix GMAT Instructor
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Thu Mar 06, 2014 9:17 am
Remember that a 4-sided polygon must have (4-2)*180 = 360 degrees total. To find x+y, it would be sufficient to find the sum of interior angles opposite x and y, inside the 4-sided polygon. The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).

-Patrick

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Matt@VeritasPrep GMAT Instructor
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Thu Mar 06, 2014 5:31 pm
Here's a pretty straightforward approach:

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