Beat The GMAT

apoorva.srivastva · Mon Nov 16, 2009 7:19 am

In the xy- plane, a triangle has vertexes (0,0), (4,0) and (4,5). If a point (x,y) is selected at random from the triangular region, What is the probabilty that x-y>0 ?

A. 1/5
B. 1/3
c. 1/2
D. 2/3
E. 4/5

I am getting 3/5 as the answer..please explain the reasoning..

[spoiler ] OA is 4/5 [/spoiler]

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life is a test · Mon Nov 16, 2009 9:23 am

shouldn't the probability be <4/5?

probability = area of region where x-y>0 / total are of region = x/0.5*4*5 = x/10

point (4,4) is where x-y=0. point(4, <4) is where x-y>0.

x = 0.5 * 4*(<4) = <8 hence x/10 = <8/10 = <4/5

the point here is that to get 4/5 you would have to take the region where x and y = 4 in which case x-y is not >0. any value of y below 4 would give x-y>0 hence the probability should be less than 4/5...I dont think you can place an exact value on the probability as x and y can be decimals...

anyone else have any thoughts on this?

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apoorva.srivastva · Mon Nov 16, 2009 9:39 am

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apoorva.srivastva · Mon Nov 16, 2009 9:50 am

ok now i get it!!!!

The probability for x>y is nothing but = 1 - P(y>x) = 1- 1/5 = 4/5

reasoning as follows

probability = area of region where y>0 / total are of region = x/0.5*4*5 = x/10

x = 0.5 * 4* 1 = 2

so P (y>x) = 2/10= 1/5

so P(x>y) = 1- (1/5)
= 4/5

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mridul_dave · Mon Nov 16, 2009 11:22 am

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apoorva.srivastva · Mon Nov 16, 2009 11:45 am

[quote="mridul_dave]
Here is how I did it.
make a quick sketch of the triangle and make a line that represents x = y. This line joins origin (0.0) and a point (4,4) on the triangle, making another triangle inside the orginal one.
All points in the inside triangle satisfy x-y > 0. ( Think x > y )

Probability that we need is area of inner triangle / area of outer triangle.

you will get 4/5 exact. Hence the answer.

This covers integers and non integer values of x and y.
Please let me know if you have any questions.[/quote]

yeh mate thanks ..cool explanation!!