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What is a + b + c + d?

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What is a + b + c + d?  [#permalink]

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New post 06 Jun 2017, 09:05
2
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00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (02:22) correct 31% (02:04) wrong based on 142 sessions

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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
Multipoint_ABCD.png [ 8.54 KiB | Viewed 2045 times ]

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Re: What is a + b + c + d?  [#permalink]

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New post 06 Jun 2017, 09:44
3
Top Contributor
1
Bunuel wrote:
Image
What is a + b + c + d?

A. 110
B. 120
C. 130
D. 150
E. Cannot be determined from the information above

Attachment:
The attachment Multipoint_ABCD.png is no longer available


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:
Image
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:
Image
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
Image
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
A3.png [ 19.68 KiB | Viewed 2538 times ]

A1.png
A1.png [ 20.94 KiB | Viewed 2549 times ]

A2.png
A2.png [ 19.89 KiB | Viewed 2543 times ]


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Re: What is a + b + c + d?  [#permalink]

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New post 06 Jun 2017, 10:05
b+d+30+X=180
a+c+30+Y=180
30+X+Y=180
so a+b+c+d=150
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Re: What is a + b + c + d?  [#permalink]

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New post 08 Jun 2017, 19:53
a + c + 30 + x = 180
-> x = 180 - a - c

b + d + 30 + 180 - x = 180
-> b + d - x = -30
-> b + d + a + c -180 = -30
-> a + b + c + d = 150
ANSWER D
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Re: What is a + b + c + d?  [#permalink]

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New post 18 Mar 2018, 07:05
2
GMATPrepNow wrote:
Bunuel wrote:
Image
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


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:
Image
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:
Image
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
Image
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




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.
Image

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
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Re: What is a + b + c + d?  [#permalink]

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New post 18 Mar 2018, 07:10
Top Contributor
Princ wrote:

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.
Image

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


No problem (and nice solution!)

Cheers,
Brent
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Re: What is a + b + c + d? &nbs [#permalink] 18 Mar 2018, 07:10
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