GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Aug 2020, 18:58

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

In the figure, LM and PN are both perpendicular to MN such that LM=3 c

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

Hide Tags

Find Similar Topics 
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 2053
Location: India
Premium Member
In the figure, LM and PN are both perpendicular to MN such that LM=3 c  [#permalink]

Show Tags

New post 06 Jul 2020, 19:35
1
5
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (03:32) correct 31% (03:24) wrong based on 16 sessions

HideShow timer Statistics

Attachment:
Untitled.png
Untitled.png [ 6.05 KiB | Viewed 422 times ]

In the figure, LM and PN are both perpendicular to MN such that LM=3 cm, MN=6 cm and PN= 5cm . Point O lies somewhere on the line MN. Find the least possible value of the sum of the length of 'LO' and 'OP'

A. 6
B. 7
C. 8
D. 9
E. 10
Senior Manager
Senior Manager
avatar
S
Joined: 18 Dec 2017
Posts: 307
Re: In the figure, LM and PN are both perpendicular to MN such that LM=3 c  [#permalink]

Show Tags

New post 06 Jul 2020, 19:54
3
Am I missing that LM and PN are perpendicular to MN or sum is like this..

Posted from my mobile device
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 2053
Location: India
Premium Member
Re: In the figure, LM and PN are both perpendicular to MN such that LM=3 c  [#permalink]

Show Tags

New post 06 Jul 2020, 20:14
1
Edited! Thanks
gurmukh wrote:
Am I missing that LM and PN are perpendicular to MN or sum is like this..

Posted from my mobile device
Manager
Manager
avatar
G
Joined: 05 Jan 2020
Posts: 142
Re: In the figure, LM and PN are both perpendicular to MN such that LM=3 c  [#permalink]

Show Tags

New post 06 Jul 2020, 21:28
1
1
Min length of LO > 3
Min length of PO > 5

=> Min length of LO + PO > 8
=> options A, B, and C can be discarded.

Check for option E.

\(\sqrt{x^2+9} + \sqrt{(6-x)^2+25} = 10\)
=> \(10 - \sqrt{x^2+9} = \sqrt{(6-x)^2+25}\)
=> \(100 + x^2 + 9 -20\sqrt{x^2+9} = (6-x)^2 + 25 = 61 + x^2 - 12x\)
=> \(5\sqrt{x^2+9} = 12 + 3x\)
=> \(25(x^2+9) = 144 + 72x + 9x^2\)
=> \(16x^2 - 72x + 81 = 0\)
=> \((4x-9)^2 = 0\)
=> \(x = 2.25\)

Option D will result in x < 0 (-ve value not possible) and x > 6 (not possible).

Ans: E

nick1816, the above solution takes a good amount of time. I'm sure you can share a much more logical approach.
Awaiting your solution. :)

Lipun
DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 2053
Location: India
Premium Member
Re: In the figure, LM and PN are both perpendicular to MN such that LM=3 c  [#permalink]

Show Tags

New post 07 Jul 2020, 18:08
3
1
Attachment:
Untitled.png
Untitled.png [ 5.81 KiB | Viewed 240 times ]
Invert the NP as shown in figure. Shortest distance between 2 points is a straight line. Hence, LO+OP is least when LOP is a straight line.

Now apply pythagoras theorem

\((LP)^2 = (LM+NP)^2 + (MN)^2\)

\(LP^2 = 8^2 +6^2 = 100\)

LP = 10
GMAT Club Bot
Re: In the figure, LM and PN are both perpendicular to MN such that LM=3 c   [#permalink] 07 Jul 2020, 18:08

In the figure, LM and PN are both perpendicular to MN such that LM=3 c

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





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