Question

Will knows that there are 73 composite natural numbers that are less than 100. Using this information, help him find the number of odd composite numbers less than 100.

• A. 27
• B. 25
• C. 24
• D. 26

Answer 1

The correct option is B 25

The nearest even number to 100 that is lower than it, is 98.

Now, as every other number is even, we can calculate the number of even numbers below 100 as:

$\frac{98}{2}=49$

So, we have:

$Numberofevennumberslessthan100=49$

As we know, all even numbers are divisible by 2.

Also, 2 is a prime number.

$\therefore \text{All even numbers,}exceptthenumber2,\text{are composite.}$

$⟹Numberofevencompositesbelow100=49-1=48$

Now, it is given that:

$Numberofcompositenumbersbelow100=73$

So,

$Evencomposites+Oddcomposites=73$

$⟹48+Oddcomposites=73$

$⟹Numberofoddcompositenumberslessthan100=73-48=25$

Therefore, there are 25 natural numbers less than 100 that are both odd and composite.