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Question

Given that the sum of two non-negative integers is 200, the probability that their product is not less that 34 times their greatest product value is

A
716
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B
101200
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C
916
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D
None of these
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Solution

The correct option is B 101200
Let two quantities be x and y.
Since the sum of two non-negative quantities is fixed, the product will be maximum when they are equal.
So, the greatest product =xy=10000, where x=y=100.
Now,xy(34)×10000xy(34)×10000
xy7500x(200x)7500
x2200x+75000
(x50)(x150)050x150
Thus, the favourable number of cases =15050+1=101
Total number of ways =200
Hence, required probability =101200

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