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Question

The probability that a randomly selected three-digit number has exactly three factors will be ............

A
7900
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B
5900
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C
11900
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D
16900
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Solution

The correct option is A 7900
We need a number having only 3 factors.
For any general composite number, we have even number of factors since two numbers need to be multiplied to get the answer.
However, for square numbers, we get odd number of factors.
Also since we are in need of numbers having only 3 factors, the numbers will have to be squares of prime numbers.
The square of 10 is 100, the smallest 3 digit number whereas the square of 31 is 961, the largest square number.
Now from 10 to 31, there are 11,13,17,19,23,29,31 i.e. 7 prime numbers.
Hence, the probability comes out to be 7900

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