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Question

A natural number x is chosen at random from the first one hundred natural numbers. The probability that (x−20)(x−40)x−30<0 is


A

1/50

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B

3/50

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C

3/25

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D

7/25

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Solution

The correct option is D

7/25


Let E=(x20)(x40)(x30)=(x20)(x30)(x40)(x30)2
Sign of E is same as that of sign of (x-20)(x-30)(x-40)=F(say).
Note that F<0 if and only if
0<x<20 or 30<x<40.
E<0 in (0,20)(30,40)
Thus, E is negative for x=1, 2, ...., 19, 31, 32, ....., 39, that is E<0 for 28 natural numbers.
Required probability =28100=725.


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