What is the value of x + y in the figure above?
This topic has expert replies
-
- Legendary Member
- Posts: 1223
- Joined: Sat Feb 15, 2020 2:23 pm
- Followed by:1 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
What is the value of x + y in the figure above?
(1) w= 95
(2) z = 125
Answer: C
Source: Official Guide
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: What is the value of x + y?BTGModeratorVI wrote: ↑Sat Mar 14, 2020 7:00 am
What is the value of x + y in the figure above?
(1) w= 95
(2) z = 125
Answer: C
Source: Official Guide
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 the second video below.
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 cannot answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7294
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Solution:BTGModeratorVI wrote: ↑Sat Mar 14, 2020 7:00 am
What is the value of x + y in the figure above?
(1) w= 95
(2) z = 125
Answer: C
Source: Official Guide
We need to determine the value of x + y. We see that x and y are two of the exterior angles of the quadrilateral, and w and z are the other two exterior angles. Notice that x + y + w + z = 360 since the sum of the measures of the exterior angles of a polygon is always 360 degrees. Therefore, if we know the values of both w and z or if we know the value of w + z, then we can determine the value of x + y.
Statement One Alone:
Since we don’t know the value of z, statement one alone is not sufficient.
Statement Two Alone:
Since we don’t know the value of w, statement two alone is not sufficient.
Statements One and Two Together:
Recall that that x + y + w + z = 360; therefore, we have:
x + y + 95 + 125 = 360
x + y + 220 = 360
x + y = 140
Both statements together are sufficient.
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews