Last visit was: 15 Sep 2026, 22:29 It is currently 15 Sep 2026, 22:29
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 15 Sep 2026
Posts: 113,566
Own Kudos:
841,535
 [26]
Given Kudos: 111,566
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,566
Kudos: 841,535
 [26]
What is a + b + c + d? 06 Jun 2017, 10:05
2
Kudos
Add Kudos
24
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
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 411 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

Show Spoiler
Attachment:
Multipoint_ABCD.png
Multipoint_ABCD.png [ 8.54 KiB | Viewed 11040 times ]
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,727
Own Kudos:
37,330
 [18]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,727
Kudos: 37,330
 [18]
What is a + b + c + d? 06 Jun 2017, 10:44
12
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
Bunuel

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
Show more

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
Attachments

A3.png
A3.png [ 19.68 KiB | Viewed 39967 times ]

A1.png
A1.png [ 20.94 KiB | Viewed 13875 times ]

A2.png
A2.png [ 19.89 KiB | Viewed 13814 times ]

User avatar
Princ
User avatar
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 349
Own Kudos:
939
 [7]
Given Kudos: 34
Posts: 349
Kudos: 939
 [7]
What is a + b + c + d? 18 Mar 2018, 08:05
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow
Bunuel

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
Show more



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
General Discussion
avatar
vasu7900
avatar
Joined: 17 Jun 2016
Last visit: 28 Nov 2023
Posts: 6
Own Kudos:
3
 [2]
Given Kudos: 240
Location: India
Concentration: Finance, Economics
Posts: 6
Kudos: 3
 [2]
What is a + b + c + d? 06 Jun 2017, 11:05
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
b+d+30+X=180
a+c+30+Y=180
30+X+Y=180
so a+b+c+d=150
User avatar
hoangphuc
User avatar
Joined: 31 Jul 2013
Last visit: 21 Jun 2018
Posts: 11
Own Kudos:
8
Given Kudos: 33
Location: Viet Nam
Concentration: General Management, Entrepreneurship
Schools: Schulich Sept 18 Intake Rotman '20 (II)
GMAT 1: 650 Q49 V28
GPA: 3.46
WE:Sales (Computer Software)
Schools: Schulich Sept 18 Intake Rotman '20 (II)
GMAT 1: 650 Q49 V28
Posts: 11
Kudos: 8
What is a + b + c + d? 08 Jun 2017, 20:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,727
Own Kudos:
37,330
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,727
Kudos: 37,330
What is a + b + c + d? 18 Mar 2018, 08:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Princ


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
Show more

No problem (and nice solution!)

Cheers,
Brent
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 15 Sep 2026
Posts: 6,131
Own Kudos:
6,105
 [1]
Given Kudos: 164
Location: India
Schools: HBS '28 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '28 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 6,131
Kudos: 6,105
 [1]
What is a + b + c + d? 10 Jul 2019, 00:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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
Show more

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

IMO D
avatar
Vigasimrair
avatar
Joined: 06 Feb 2019
Last visit: 26 Mar 2021
Posts: 36
Own Kudos:
37
Given Kudos: 370
Location: Russian Federation
Schools: INSEAD Sept'21 Intake (WL)
GMAT 1: 690 Q45 V40
Schools: INSEAD Sept'21 Intake (WL)
GMAT 1: 690 Q45 V40
Posts: 36
Kudos: 37
What is a + b + c + d? 10 Jul 2019, 04:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.

Posted from my mobile device
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 15 Sep 2026
Posts: 22,740
Own Kudos:
26,983
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,740
Kudos: 26,983
What is a + b + c + d? 28 Jul 2019, 10:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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
Show more

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
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,224
Own Kudos:
1,159
Posts: 39,224
Kudos: 1,159
What is a + b + c + d? 31 Mar 2024, 21:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113566 posts