Last visit was: 17 Jul 2025, 12:16 It is currently 17 Jul 2025, 12:16
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
805+ Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,603
Own Kudos:
742,255
 [12]
Given Kudos: 98,220
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,603
Kudos: 742,255
 [12]
In the above figure, lines AB and CD are perpendicular to one another. 21 May 2020, 01:48
1
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

30% (02:42) correct 70% (02:43) wrong based on 84 sessions

History

Date
Time
Result
Not Attempted Yet

Competition Mode Question




In the above figure, lines AB and CD are perpendicular to one another. If AD is parallel to BC and ∠CAB = 2∠ABD, what is the measure of ∠ACB?

(1) ∠CAD = 90
(2) ∠CBD = 60


Are You Up For the Challenge: 700 Level Questions


Show Spoiler
Attachment:
1.png
1.png [ 34.46 KiB | Viewed 5092 times ]
ShowHide Answer
Official Answer
A
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Jul 2025
Posts: 3,384
Own Kudos:
2,078
 [2]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,384
Kudos: 2,078
 [2]
In the above figure, lines AB and CD are perpendicular to one another. 21 May 2020, 03:33
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post

Solution


Step 1: Analyse Question Stem


    • Lines AB and CD are perpendicular to each other.
    • AD is parallel to BC.
    • ∠\(CAB = \)\(2\)∠\(ABD\)
    • Based on the above information lets’ draw the below diagram:

    • From the above diagram, we can see that \(y + z = 90 ……Eq.(i)\)
We need to find the value of ∠ACB.
    • This means we need to find the value of \((90 – 2x + y)\)

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: ∠CAD = 90
    • According to this statement: \(2x + z = 90\)
    • Substituting the value of z from Eq.(i) into the above equation, we get, \(2x + 90 -y = 90 \)
      o \(⟹ 90 -2x + y = 90\)
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2: ∠CBD = 60
    • According to this statement: \(z +x = 60\)
    • Subtracting the above equation from Eq.(i), we get, \(y – x = 30\)
    • However, we cannot find the value of \(y – 2x\) from this statement.
Hence, statement 2 is NOT sufficient.
Thus, the correct answer is Option A.
User avatar
MayankSingh
User avatar
Joined: 08 Jan 2018
Last visit: 20 Dec 2024
Posts: 289
Own Kudos:
271
 [3]
Given Kudos: 249
Location: India
Concentration: Operations, General Management
Schools: McDonough '25 (A) Marshall '25 (D) Tepper '25 (WA$) Kenan-Flagler '25 (A) ISB '25 (WL) IIMC '25 (A) Owen '26 (A$$$$)
GMAT 1: 640 Q48 V27
GMAT 2: 730 Q51 V38
GPA: 3.9
WE:Project Management (Manufacturing)
Products:
My Reviews
Schools: McDonough '25 (A) Marshall '25 (D) Tepper '25 (WA$) Kenan-Flagler '25 (A) ISB '25 (WL) IIMC '25 (A) Owen '26 (A$$$$)
GMAT 2: 730 Q51 V38
Posts: 289
Kudos: 271
 [3]
In the above figure, lines AB and CD are perpendicular to one another. 21 May 2020, 10:31
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
IMO A

lines AB and CD are perpendicular to one another. If AD is parallel to BC and ∠CAB = 2∠ABD, what is the measure of ∠ACB

(1) ∠CAD = 90

AD || CB => ∠DAB = ∠CBA
Now, ∠CAD = ∠CAB + ∠DAB = ∠CAB + ∠CBA = 90
In Triangle, CAB, ∠ACB = 180- ( ∠CAB + ∠CBA)= 90
Sufficient.

(2) ∠CBD = 60

∠CBA = 90-x
So, ∠ACB = 180- (2x+90-x) = 90-x
But we don't know x, so not sufficient
User avatar
freedom128
User avatar
Joined: 30 Sep 2017
Last visit: 01 Oct 2020
Posts: 942
Own Kudos:
1,327
 [1]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Products:
My Reviews
GMAT 1: 720 Q49 V40
Posts: 942
Kudos: 1,327
 [1]
In the above figure, lines AB and CD are perpendicular to one another. 21 May 2020, 16:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AD is parallel to CB, then ∠DAB = ∠ABC = b.
∠ABD = a, then ∠CAB = 2∠ABD = 2a.

Q. what is the measure of ∠ACB?

(1) ∠CAD = 90 = 2a + b
∠ACB = 180 - (2a+b)
= 180 - 90
= 90
SUFFICIENT

(2) ∠CBD = 60 = a + b
∠ACB = 180 - (2a+b)
= 180 - (a+b) - a
= 180 - 60 - a
= 120 - a
We need to know the value of ∠ABD or a.
NOT SUFFICIENT

FINAL ANSWER IS (A)

Posted from my mobile device
User avatar
kickmunch94
User avatar
Joined: 22 Feb 2017
Last visit: 06 Jun 2025
Posts: 18
Own Kudos:
9
Given Kudos: 3
Posts: 18
Kudos: 9
In the above figure, lines AB and CD are perpendicular to one another. 13 Feb 2023, 01:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AnthonyRitz

Statement 1)

Take triangle ACD.
Using angle sum property we get ACD +ADC = 90
ADC = DCB ( AD IS PARALLEL TO BC )
HENCE LACB = 90

Cant' we use the same approach for statement 2 ?
User avatar
AnthonyRitz
User avatar
Stacy Blackman Consulting Director of Test Prep
Joined: 21 Dec 2014
Last visit: 16 Jul 2025
Posts: 237
Own Kudos:
419
Given Kudos: 167
Affiliations: Stacy Blackman Consulting
Location: United States (DC)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
GPA: 3.11
WE:Education (Education)
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
GRE 2: Q170 V170
Posts: 237
Kudos: 419
In the above figure, lines AB and CD are perpendicular to one another. 13 Feb 2023, 08:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kickmunch94
AnthonyRitz

Statement 1)

Take triangle ACD.
Using angle sum property we get ACD +ADC = 90
ADC = DCB ( AD IS PARALLEL TO BC )
HENCE LACB = 90

Cant' we use the same approach for statement 2 ?

No, you sadly cannot.

The problem is that you don't know whether angle ACD and angle BDC are equal; those are not opposite interior angles for the parallel lines AD and BC. Rather, you'd need AC and BD parallel, and we don't have that.
Moderators:
Bunuel
Math Expert
102603 posts
kingbucky
453 posts