Question:

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

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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. ​Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: (C)

Approach Solution : 1

We must ascertain what x + y will be. We can see that the quadrilateral's x and y are two of its exterior angles, and its w and z are the other two. The sum of the measures of the exterior angles of a polygon is always 360 degrees, so take note that x + y + w + z = 360. Therefore, we can determine the value of x + y if we know the values of both w and z or if we know the value of w + z.
Statement - 1 : w = 95
This statement alone is insufficient because the value of z is unknown.
Statement - 2 : z = 125
This statement alone is insufficient because the value of w is unknown.
Let us combine both the statements.
Note that x + y + w + z = 360. As a result, we get
=> x + y + 95 + 125 = 360
=> x + y + 220 = 360
=> x + y = 140
Therefore both the statements together are sufficient.

Approach Solution : 2

180(n-2) is the sum of a polygon's interior angles, where n is its number of sides (so is the number of angles). Therefore, 180*2=360 is the total of a quadrilateral's interior angles.
In accordance with the above diagram, we can write the following.

=> (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.
Statement - 1 : w = 95
This statement alone is insufficient because the value of z is unknown.
Statement - 2 : z = 125
This statement alone is insufficient because the value of w is unknown.
By combining both statements we can get the answer as both of them each has the values for z and w respectively. Therefore both the statements together are sufficient.

“What is the value of x + y in the figure above?” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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