Rectangle probability

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ramyaravindran: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Apr 28, 2008 5:33 am; Thanked: 2 times

by ramyaravindran » Mon Feb 08, 2010 1:21 pm

I got this question from a friend. Not sure about the source. Can someone help me with solving this?

Length of the rectangle = 16 (labelled as MS) , Width (labelled as SR) = 5. If a point P is taken on the base randomly, What is the probability that length of PR is less than 13?.

Link to the image is here.
https://img106.imageshack.us/i/ppwn2.jpg

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Last edited by ramyaravindran on Tue Feb 09, 2010 5:44 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 1:21 pm

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 1:52 pm

ramyaravindran wrote:I got this question from a friend. Not sure about the source. Can someone help me with solving this?

Length of the rectangle = 16 (labelled as MS) , Width (labelled as SR) = 5. If a point P is taken on the base randomly, What is the probability that length of PR is less than 13?.

Link to the image is here.
https://img106.imageshack.us/i/ppwn2.jpg/

I am sorry but the link seems to be broken.

Can you check the link.

Based on what i understand from the question,
The diagonal length is 17 [sqrt(289)]

length of PR is less than 13.
Now, PR = sqrt( 5^2 + PS^2) = sqrt(25 + PS^2)
since,PR < 13
=>25 + PS^2 < 169
=>PS^2 < 144
=>PS < 12

So,favorable space=PS should range from 0 to 12.

Considering total sample space = PS can range from 0 to 15.

Hence ,probability = 12/15 =4/5

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ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Mon Feb 08, 2010 2:02 pm

Without the diagram (link is broken) I would say the answer is 3/4

Heres why:

Construct a triangle PRS where PR is 13. Using Pythagorean theorem you see that PS is 12 in this case. So translate the problem.

What is the probability that PR is less than 13 is the same as saying what is the probability that PS is less than 12. Since MS is 16, P can range from 16 to zero (basically). Therefore 12/16 is the chance that P is between 12 and 0.

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ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Mon Feb 08, 2010 2:04 pm

harsh.champ wrote:
Considering total sample space = PS can range from 0 to 15.

Why can PS not be between 15 and 16?

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bln123: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Mon Jul 20, 2009 6:39 amFollowed by: 1 member; Thanked: 4 times

by bln123 » Mon Feb 08, 2010 2:07 pm

I agree with harsh.camp, a diagonal of 13 would mean other sides of lenghts 5 and 12, respectively.
i.e. the prob is 12/16 -> 3/4

OA please

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