GMAT Club - Probability

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GMAT Club - Probability

by jkaustubh » Fri Nov 23, 2012 1:22 am
A circle of radius k units is drawn with (0,0) as the center. Diameters to this circle: X axis, Y axis, and |y|=|x| are drawn.
Find the probability that product of slopes of 2 diameters chosen at random is -1.

a.)1/6
b.)2/6
c.)3/6
d.)None of the above
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by Anurag@Gurome » Sat Nov 24, 2012 8:28 am
jkaustubh wrote:A circle of radius k units is drawn with (0,0) as the center. Diameters to this circle: X axis, Y axis, and |y|=|x| are drawn. Find the probability that product of slopes of 2 diameters chosen at random is -1.
The diameters are...
  • 1. X-axis --> slope = 0
    2. Y-axis --> slope = infinity
    3. x = y --> slope = 1
    4. x = -y --> slope = -1
There 4C2 = 6 possible pairs of diameter.
Among them only the product of slopes of 3 and 4 will be -1.

Hence, required probability = 1/6

The correct answer is A.
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by ihatemaths » Mon Nov 26, 2012 6:22 am
I din't understand how slopes of |x| and |y| are calculated