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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, 10:05
2
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (02:14) correct 32% (02:08) wrong based on 169 sessions

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

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New post 06 Jun 2017, 10:44
6
Top Contributor
2
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
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Re: What is a + b + c + d?  [#permalink]

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New post 06 Jun 2017, 11:05
1
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, 20:53
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, 08:05
4
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, 08:10
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?  [#permalink]

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New post 10 Jul 2019, 00:45
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


150 - (b+d) = a+c
a + b +c +d = 150

IMO D
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What is a + b + c + d?  [#permalink]

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New post 10 Jul 2019, 04:58
I've just imagined that the figure kind of "spread its wings" and became triangle (the 30 angle rise up and the peak turned around its axis).
We know that the sum of angles in triangle = 180. All we need is to substruct 30.
The answer is D.

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What is a + b + c + d?   [#permalink] 10 Jul 2019, 04:58
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