GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Dec 2018, 10:06

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

Find the value of X in the given quadrilateral.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 10 Nov 2017
Posts: 12
Find the value of X in the given quadrilateral.  [#permalink]

Show Tags

New post 06 Oct 2018, 10:05
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:14) correct 49% (01:02) wrong based on 53 sessions

HideShow timer Statistics

Image
Find the value of X in the given quadrilateral.


A. 60 degrees.

B. Greater than 60 degrees.

C. Less than 60 degrees.

D. 90 degrees.

E. Can't be determined.


Attachment:
IMG_20181006_232825 - Copy.jpg
IMG_20181006_232825 - Copy.jpg [ 195.43 KiB | Viewed 441 times ]
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2205
Premium Member CAT Tests
Find the value of X in the given quadrilateral.  [#permalink]

Show Tags

New post 06 Oct 2018, 19:05
2
1
Arun1994 wrote:
Find the value of X in the given quadrilateral.

A. 60 degrees.
B. Greater than 60 degrees.
C. Less than 60 degrees.
D. 90 degrees.
E. Can't be determined.

Attachment:
anglex10.06.18.jpg
anglex10.06.18.jpg [ 32.07 KiB | Viewed 388 times ]

This question tests equilateral triangles, the triangle inequality theorem,
and the relationship between sides and angles in a triangle.

Draw a line that connects vertex A (on the diagram) to vertex C.
The larger triangle, ABC, has two equal sides.
Having seen answer choices, ask: can x = 60° or 90°?

Can x = 60°?
By definition of an equilateral triangle, if AC = 10, then x = 60°
x can = 60° if ∆ ABC is equilateral*
∆ ABC is equilateral only if AC = 10

Can side AC = 10?

Now consider ∆ ACD
Triangle inequality theorem:
The third side of a triangle should be greater than the difference between the other two sides and
less than the sum of the other two sides. So:
(9-1) < AC < (9+1)
8 < AC < 10
AC cannot = 10
AC must be less than 10

If AC must be less than 10, then
x must be less than 60°
If the length of a side of a triangle decreases, the angle measure opposite that side decreases, too.

The sides that are opposite the y angles both = 10
(AB and BC = 10)
ONLY if AC = 10, then x = 60°

AC must be less than 10. Therefore
x must be less than 60°

Answer C


* Or plug in.
If x = 60, then the other two angles, y, must also each be 60°
x + 2y = 180°
60 + 2y = 180
2y = 120
y = 60
GMAT Club Bot
Find the value of X in the given quadrilateral. &nbs [#permalink] 06 Oct 2018, 19:05
Display posts from previous: Sort by

Find the value of X in the given quadrilateral.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.