Last visit was: 24 Apr 2026, 10:46 It is currently 24 Apr 2026, 10:46
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
805+ (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,036
 [18]
Given Kudos: 105,873
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: 109,814
Kudos: 811,036
 [18]
In the figure shown below, the line segment AD is parallel to the line 06 Nov 2018, 01:40
1
Kudos
Add Kudos
17
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
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:

32% (02:19) correct 68% (02:06) wrong based on 243 sessions

History

Date
Time
Result
Not Attempted Yet

In the figure shown below, the line segment AD is parallel to the line segment BC. Is AC the shortest side of triangle ACD?

(1) x = 50
(2) z = 70


Show Spoiler
Attachment:
2018-11-06_1238.png
2018-11-06_1238.png [ 13.56 KiB | Viewed 9073 times ]
ShowHide Answer
Official Answer
B
User avatar
saurabh9gupta
User avatar
Joined: 10 Jan 2013
Last visit: 28 Jul 2023
Posts: 251
Own Kudos:
181
Given Kudos: 201
Location: India
Concentration: General Management, Strategy
Schools: Kenan-Flagler '24 (D)
GRE 1: Q163 V155
GPA: 3.95
Products:
My Reviews
Schools: Kenan-Flagler '24 (D)
GRE 1: Q163 V155
Posts: 251
Kudos: 181
In the figure shown below, the line segment AD is parallel to the line 06 Nov 2018, 01:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Since both statements do not by themselves tell anything and we do not know whether the figure is a parallelogram...individually insufficient


When we combine then we get to know the angles of the triangle.

Therefore C

OA?

Bunuel chetan... plz correct me
Posted from my mobile device
User avatar
roysaurabhkr
User avatar
Joined: 20 Oct 2017
Last visit: 04 Aug 2020
Posts: 5
Own Kudos:
14
 [1]
Given Kudos: 34
Location: India
Concentration: General Management, Strategy
GPA: 3.22
WE:Operations (Manufacturing)
Posts: 5
Kudos: 14
 [1]
In the figure shown below, the line segment AD is parallel to the line 07 Nov 2018, 09:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer is B

Quick trick: Side opposite to the biggest angle in a triangle is biggest. (And Side opposite to the smallest angle in a triangle is smallest)
In Triangle ACD:

Statement A
x= 50 degree. Thus, angle ACD = 50 degree. No conclusion can be drawn about the other angles and hence the relative size of the sides.

Statement B angle Z = 70 degree.
The sum of remaining angles in the triangle = 110 degree.
Thus one of the remaining two angles is definitely < 70 degree.
Thus, angle z is not the smallest angle
Thus we know for sure that the side opposite to angle Z is not the smallest.

Hence answer B.
User avatar
JanarthCj
User avatar
Joined: 05 May 2016
Last visit: 03 Sep 2023
Posts: 11
Own Kudos:
45
 [1]
Given Kudos: 1,296
Posts: 11
Kudos: 45
 [1]
In the figure shown below, the line segment AD is parallel to the line 07 Jun 2020, 10:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
roysaurabhkr
Answer is B

Quick trick: Side opposite to the biggest angle in a triangle is biggest. (And Side opposite to the smallest angle in a triangle is smallest)
In Triangle ACD:

Statement A
x= 50 degree. Thus, angle ACD = 50 degree. No conclusion can be drawn about the other angles and hence the relative size of the sides.

Statement B angle Z = 70 degree.
The sum of remaining angles in the triangle = 110 degree.
Thus one of the remaining two angles is definitely < 70 degree.
Thus, angle z is not the smallest angle
Thus we know for sure that the side opposite to angle Z is not the smallest.

Hence answer B.
Show more


It is possible that the other two angles could be 100 & 10, 90 & 20 or 80 & 30.
Can you please explain how you eliminated the above-mentioned possibilities?


Best,
Cj
User avatar
Lipun
User avatar
Joined: 05 Jan 2020
Last visit: 08 Jan 2025
Posts: 143
Own Kudos:
160
 [1]
Given Kudos: 291
Posts: 143
Kudos: 160
 [1]
In the figure shown below, the line segment AD is parallel to the line 08 Jun 2020, 08:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JanarthCj
roysaurabhkr
Answer is B

Quick trick: Side opposite to the biggest angle in a triangle is biggest. (And Side opposite to the smallest angle in a triangle is smallest)
In Triangle ACD:

Statement A
x= 50 degree. Thus, angle ACD = 50 degree. No conclusion can be drawn about the other angles and hence the relative size of the sides.

Statement B angle Z = 70 degree.
The sum of remaining angles in the triangle = 110 degree.
Thus one of the remaining two angles is definitely < 70 degree.
Thus, angle z is not the smallest angle
Thus we know for sure that the side opposite to angle Z is not the smallest.

Hence answer B.


It is possible that the other two angles could be 100 & 10, 90 & 20 or 80 & 30.
Can you please explain how you eliminated the above-mentioned possibilities?


Best,
Cj
Show more

Hi Cj,

The side opposite the smallest angle in a triangle will be the smallest side.

ST1: we know CAD=50, so ACD+ADC=130. If ADC<50, then it will be the smallest angle and thus, the side opposite to it will be the smallest.
If ADC > 50, then AC won't be the smallest. We can't determine ADC for sure, so not sufficient.

ST2: z=70 => CAD+ACD = 110. If CAD=ACD, then each angle equals to 55. If, they are not equal then for an increment of 1 in one angle, the other angle will decrease by 1, since their sum is constant. So, for sure one of the angles will be < 56. This means that z is not the smallest angle. Thus, AC is not the smallest side.
Sufficient.
User avatar
SaquibHGMATWhiz
User avatar
GMATWhiz Representative
Joined: 23 May 2022
Last visit: 12 Jun 2024
Posts: 623
Own Kudos:
777
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Expert
Expert reply
GMAT 1: 760 Q51 V40
Posts: 623
Kudos: 777
In the figure shown below, the line segment AD is parallel to the line 07 Nov 2022, 00:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the figure shown below, the line segment AD is parallel to the line segment BC. Is AC the shortest side of triangle ACD?

(1) x = 50
(2) z = 70
Show Spoiler
Attachment:
2018-11-06_1238.png
Show more

Solution:
Pre Analysis:
  • In the given figure, line AD is parallel to side BC
  • This means \(\angle CAD=\angle BCA=x^o\) (alternate angle)
  • We area sked if side AC is the shortest side of triangle ACD or not
  • For this, \(\angle ADC=z^o\) has to be the smallest angle of the three angles in triangle ACD

Statement 1: x = 50
  • If \(\angle A=x=50^o\) then sum of the rest of the two has to be 130
  • Let us take 2 cases:
    • \(\angle A=50, \angle C=50\), \(\angle D=30\)
      • In this case, \(\angle D\) is the smallest. Thus, side AC is the smallest
    • \(\angle A=50, \angle C=30\), \(\angle D=50\)
      • In this case, \(\angle D\) is not the smallest. Thus side AC is not the smallest
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: z = 70
  • If \(\angle D=z=70^o\) then sum of the rest of the two has to be 110
  • We can infer from this that rest of the two angles cannot be both greater than 70
  • Thus, we can say that side AC is not the smallest side
  • Thus, statement 2 alone is sufficient


Hence the right answer is Option B
Moderators:
Bunuel
Math Expert
109814 posts
kingbucky
498 posts
Gmat860sanskar
212 posts