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06 Jun 2017, 10:05
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:23) correct
35%
(02:10)
wrong
based on 410
sessions
History
Date
Time
Result
Not Attempted Yet
What is a + b + c + d?
A. 110
B. 120
C. 130
D. 150
E. Cannot be determined from the information above
Attachment:
Multipoint_ABCD.png [ 8.54 KiB | Viewed 10834 times ]
06 Jun 2017, 10:44
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Bunuel
Nice question!!
I can see some triangles that include the necessary angles (a, b, c and d)
So, let's add some extra angles, x and y:
Since x, 30 and y are on a line, we know that x + y + 30 = 180
This means that x + y = 150
Now let's examine some hidden triangles. Here's one:
Since angles in a triangle add to 180 degrees, we can write: a + c + x + 30 = 180
Subtract 30 from both sides to get: a + c + x = 150
Here's another hidden triangle
Since angles in a triangle add to 180 degrees, we can write: b + d + y + 30 = 180
Subtract 30 from both sides to get: b + s + y = 150
We now have two equations:
a + c + x = 150
b + s + y = 150
ADD them to get: a + b + c + d + x + y = 300
Since x + y = 150, we can write: a + b + c + d + 150 = 300
Subtract 150 from both sides to get: a + b + c + d = 150
Answer:
Cheers,
Brent
Attachments
A3.png [ 19.68 KiB | Viewed 34508 times ]
A1.png [ 20.94 KiB | Viewed 13624 times ]
A2.png [ 19.89 KiB | Viewed 13562 times ]
18 Mar 2018, 08:05
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GMATPrepNow
Hi Brent
Sorry for using your image.
I am using it to arrive at answer using different approach.
I will try to explain using Theorem: An exterior angle of a triangle is equal to the sum of the opposite interior angles.
x=b+d
y= a+c
and x+y+30 =180.
Putting x and y value in above equation.
we get
b+d+a+c+30=180
a+b+c+d= 150
