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If a number is selected randomly from a set of positive integers less

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New post 02 Aug 2019, 22:09
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Question Stats:

27% (01:43) correct 73% (01:51) wrong based on 37 sessions

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If a number is selected randomly from a set of positive integers less than 100, then what is the probability that the number will have either 2 or 3 factors?

A. 29/99
B. 34/99
C. 29/100
D. 35/99
E. 11/33

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New post 02 Aug 2019, 22:26
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To answer this question we have to count the prime numbers between 0 and 100 which includes 25 numbers
{2,3,5,...97}
and also the square numbers which have just three factors which includes four numbers like; {4,9,25,49}
25+4=29
29/100

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Re: If a number is selected randomly from a set of positive integers less  [#permalink]

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New post 02 Aug 2019, 23:05
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Mohammadmo wrote:
To answer this question we have to count the prime numbers between 0 and 100 which includes 25 numbers
{2,3,5,...97}
and also the square numbers which have just three factors which includes four numbers like; {4,9,25,49}
25+4=29
29/100

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It says that set of positive integers is less than 100(not inclusive) — I think answer should be 29/99 (A)
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New post 03 Aug 2019, 18:43
There are few things that we should always remember as they are often tested-

1. Only prime numbers have 2 factors - 1 and itself.
2. There are 25 prime numbers between 1 and 100.
3. Only numbers with 3 factors are the perfect squares of a prime number.


From (1) and (2) we have 25 eligible numbers.
From (3) we have 4 numbers - 4, 9, 25, 49

Thus, we have 25 + 4 = 29 positive integer less than 100 (i.e. 99) that have 2 or 3 factors.

Hence, required probability is 29/99.

Answer A

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If a number is selected randomly from a set of positive integers less   [#permalink] 03 Aug 2019, 18:43
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