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

It is currently 26 Jun 2019, 05:13

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

Numbers x and y are chosen independently and uniformly at random from

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55802
Numbers x and y are chosen independently and uniformly at random from  [#permalink]

Show Tags

New post 13 May 2019, 23:30
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (01:49) correct 68% (02:18) wrong based on 50 sessions

HideShow timer Statistics


Director
Director
avatar
P
Joined: 19 Oct 2018
Posts: 564
Location: India
Re: Numbers x and y are chosen independently and uniformly at random from  [#permalink]

Show Tags

New post 24 May 2019, 18:33
2
We need the obtuse triangle whose sides are x,y and 1
As x and y lies in the interval of [0,1], the longest side of triangle must be 1
x^2 + y^2 < 1 {inequality holds for obtuse triangles)
Also we know that sum of two sides of triangle must be greater than the third side
x+y>1

We can use geometric probability to get our desired results.

Desired area is the area lie between two curves x^2 + y^2 < 1(circle of radius 1) and x+y>1(straight line)
Total area= square of side length 1

As we can see in the figure, Desired area(red portion)= {1/4(pi*1^2)}-(1/2*1*1)=pi/4-1/2
Total area= 1*1=1
The probability that x, y, and 1 are the side lengths of an obtuse triangle= (pi/4-1/2)/1=(pi/4-1/2)

Bunuel wrote:
________________________
BUMPING FOR DISCUSSION.

Attachments

prob.png
prob.png [ 8.16 KiB | Viewed 492 times ]

Intern
Intern
avatar
Joined: 11 May 2014
Posts: 4
Re: Numbers x and y are chosen independently and uniformly at random from  [#permalink]

Show Tags

New post 30 May 2019, 03:37
Can someone explain me the solution of this question. Not able to get the anser.
Intern
Intern
avatar
B
Joined: 16 Feb 2019
Posts: 4
Re: Numbers x and y are chosen independently and uniformly at random from  [#permalink]

Show Tags

New post 30 May 2019, 12:10
What is geometric probability ? Never heard of this term before .

Posted from my mobile device
Director
Director
avatar
P
Joined: 19 Oct 2018
Posts: 564
Location: India
Re: Numbers x and y are chosen independently and uniformly at random from  [#permalink]

Show Tags

New post 30 May 2019, 12:23
Okay i'll give you an example. There is dart circular board of radius 4cm. If you hit inside a concentric circle of radius 0.5 cm, that lies inside the dart board, you will score 25. What is the probability that you will score 25 on the first shot, if you hit the dart board.

Probability=Area of smaller circle/Area of bigger circle= (pi/4)/(16pi)=1/64

geometric probability is used when you can measure the outcomes in length, area or volume.

Ayushkumar2294 wrote:
What is geometric probability ? Never heard of this term before .

Posted from my mobile device
GMAT Club Bot
Re: Numbers x and y are chosen independently and uniformly at random from   [#permalink] 30 May 2019, 12:23
Display posts from previous: Sort by

Numbers x and y are chosen independently and uniformly at random from

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


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