Question

What percent of non – negative integers less than 30 are prime?
(a) 33.3%
(b) 20%
(c) 30%
(d) 50%

Answer 1

Hint: First understand the meaning of non – negative integers and prime numbers. Use their definitions
to find the total number of non – negative integers less than 30 and assume it as ‘x’. Find how many of
they are primes, i.e. do not have more than 2 factors, assume this as ‘y’. Finally find the required
percentage by using the relation: - \[\dfrac{y}{x}\times 100\%\], to get the answer.

Complete step by step answer:
Now, we have to find the percentage of non – negative integers less than 30 which are primes. First let
us see what is a prime and non – negative integers.
We know that integers are the set of whole numbers together with the negative of natural numbers.
Here, whole numbers are the set of natural numbers including O. Now, the basic thing is natural
numbers.
Natural numbers are the counting numbers that include: - 0, 1, 2, 3, ……. upto infinite. So, the set of
whole numbers will include: - 0, 1, 2, 3, …… upto infinite and therefore, the set of integers are: - \[-\infty
\], ……, -2, -1, 0, 1, 2,….. \[\infty \].
In the above question we have to deal with non – negative integers, that means we do not have to
consider numbers with (-) sign. So, we will have 0, 1, 2, …… as the non – negative integers.
So, number of non – negative integers less than 30, i.e. from 0 to 29 = x (say) = 30.
Now, let us know what a prime is. A prime number is a number that does not have more that 2 factors,
i.e. 1 and the number itself. For example: - 2 is a prime number because it's only factors are 1 and 2.
Similarly, 3 and 5 are other examples of prime numbers.
So, the list of prime numbers from 0 to 29 are: - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Therefore, number of
primes from 0 to 29 = y (say) = 10.
Hence, percentage of non – negative integers less than 30 which are prime = \[\dfrac{y}{x}\times
100\%\].

Substituting the values of x and y, we get,
Required percentage
\[\begin{align}
& =\dfrac{10}{30}\times 100\% \\
& =33.3\% \\
\end{align}\]

So, the correct answer is “Option A”.

Note: One must note that we have included O in the set of non – negative integers. Actually, O is neither
positive nor negative in nature but in the question we have to eliminate only negative integers which
are -1, -2, -3, …. and this is the only reason why O is there. Also, remember that the numbers which are
not primes are called composite numbers. They have more than 2 factors.