Is there a simpler way to solve this question?

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

[Brent@GMATPrepNow]

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: https://www.gmatprepnow.com/module/gmat- ... cy?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

Answer = C

Cheers,
Brent

[GaneshMalkar]

One more way to do this :-

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

Then a+b+c+d = 360 ...(a closed quadrilateral adds angle to 360)

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.

Answer C

[[email protected]]

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.

[Brent@GMATPrepNow]

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

[ceilidh.erickson]

One more way to do this :-

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

Then a+b+c+d = 360 ...(a closed quadrilateral adds angle to 360)

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.

Answer C

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:
https://www.beatthegmat.com/area-of-the- ... tml#719010