NEW HERE? LEARN MORE
closeclose
Last visit was: 14 May 2024, 14:19 It is currently 14 May 2024, 14:19
Decision Tracker
My Rewards
New posts
New comers' posts

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

In the figure above, if MP bisects ∠NMR, then x =

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93260
Own Kudos [?]: 623768 [0]
Given Kudos: 81863
Send PM
CAT Tests Forum Quiz Mode
In the figure above, if MP bisects ∠NMR, then x = [#permalink] New post   06 May 2020, 09:30
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

92% (00:45) correct 8% (00:46) wrong based on 37 sessions
Hide Show timer Statistics

In the figure above, if MP bisects ∠NMR, then x =

(A) 80
(B) 90
(C) 100
(D) 110
(E) 120

Show Spoiler
Attachment:
1.jpg
1.jpg [ 16.42 KiB | Viewed 3552 times ]
ShowHide Answer
Official Answer
D
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30190 [1]
Given Kudos: 799
Location: Canada
Send PM
In the figure above, if MP bisects ∠NMR, then x = [#permalink] New post   06 May 2020, 10:23
1
Kudos
Expert Reply
Top Contributor
Bunuel wrote:

In the figure above, if MP bisects ∠NMR, then x =

(A) 80
(B) 90
(C) 100
(D) 110
(E) 120

Show Spoiler
Attachment:
1.jpg


Let's first focus on the red triangle below.
Since angles in a triangle must add to 180°, we know that the missing angle must be 60°



Next, since we're told that MP bisects ∠NMR, we know that each angle must be 30°



Finally, we'll focus on the red triangle below.

Since angles in a triangle must add to 180°, we can write: x + 30 + 40 = 180

Solve, to get: x = 110

Answer: D

RELATED VIDEO
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5975
Own Kudos [?]: 13471 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge Forum Quiz Mode
Re: In the figure above, if MP bisects ∠NMR, then x = [#permalink] New post   06 May 2020, 09:33
Expert Reply
Bunuel wrote:

In the figure above, if MP bisects ∠NMR, then x =

(A) 80
(B) 90
(C) 100
(D) 110
(E) 120

Show Spoiler
Attachment:
1.jpg


Angle NMR = 180 - (40+80) = 60

Angle PMR = (1/3)*60 = 30

Now, in triangle PMR, 30+x+40 = 180

i.e. x = 110

Answer: Option D
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5346
Own Kudos [?]: 4000 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge Forum Quiz Mode
Re: In the figure above, if MP bisects ∠NMR, then x = [#permalink] New post   06 May 2020, 09:37
Bunuel wrote:

In the figure above, if MP bisects ∠NMR, then x =

(A) 80
(B) 90
(C) 100
(D) 110
(E) 120

Show Spoiler
Attachment:
1.jpg


Asked: In the figure above, if MP bisects ∠NMR, then x =

∠NMR = 180 - (80+40) = 60

∠RMP = 60/2 = 30

x = ∠MPR = 180 - (40 + 30) = 110

IMO D
User avatar
D
lacktutor
Director
Director
Joined: 25 Jul 2018
Posts: 668
Own Kudos [?]: 1120 [0]
Given Kudos: 69
Send PM
Re: In the figure above, if MP bisects ∠NMR, then x = [#permalink] New post   06 May 2020, 09:39
Let \(y\) be the angle of < NMR
\(\frac{y}{2 }+ x + 40 = 180 \)
\(\frac{y}{2 }+ 180 —x + 80 = 180 \)

\(\frac{y}{2 }+ x = 140\)
\(x —\frac{ y}{2 }= 80\)
—>\( 2x = 220 \)
—>\( x = 110 \)

Answer ( D)

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: In the figure above, if MP bisects ∠NMR, then x = [#permalink]
06 May 2020, 09:39
Moderators:
Bunuel
Math Expert
93260 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions