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What is a + b + c + d?

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Bunuel
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What is a + b + c + d? [#permalink] New post   06 Jun 2017, 10:05
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Question Stats:

65% (02:23) correct 35% (02:08) wrong based on 405 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

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Multipoint_ABCD.png
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D
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BrentGMATPrepNow
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Re: What is a + b + c + d? [#permalink] New post   06 Jun 2017, 10:44
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Bunuel wrote:

What is a + b + c + d?

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

Show Spoiler
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:

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:
Show Spoiler
D


Cheers,
Brent
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Princ
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Re: What is a + b + c + d? [#permalink] New post   18 Mar 2018, 08:05
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GMATPrepNow wrote:
Bunuel wrote:

What is a + b + c + d?

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

Show Spoiler
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:

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:
Show Spoiler
D


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.


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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vasu7900
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Re: What is a + b + c + d? [#permalink] New post   06 Jun 2017, 11:05
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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] 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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BrentGMATPrepNow
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Re: What is a + b + c + d? [#permalink] New post   18 Mar 2018, 08:10
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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.


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] New post   10 Jul 2019, 00:45
Bunuel wrote:

What is a + b + c + d?

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

Show Spoiler
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] 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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Re: What is a + b + c + d? [#permalink] New post   28 Jul 2019, 10:26
Expert Reply
Bunuel wrote:

What is a + b + c + d?

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

Show Spoiler
Attachment:
Multipoint_ABCD.png


Let the two angles adjacent to the 30-degree angle be e (on the left) and f (on the right). Notice that e + f = 180 - 30 = 150.

Now, using the two biggest triangles we can form, we have:

a + c + 30 + e = 180

and

b + d + 30 + f = 180

Adding these two equations together, we have:

a + b + c + d + e + f + 60 = 360

a + b + c + d + e + f = 300

But e + f = 150, so a + b + c + d = 150 also.

Answer: D
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Re: What is a + b + c + d? [#permalink] New post   31 Mar 2024, 21:32
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