Question

Set A is formed by selecting some of the numbers from the first 100 natural numbers such that the HCF of any two numbers in the set A is 5, what is the maximum number elements that set A can have?

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is C 9

As there should be only 5 which should be common between any two number
so number may be $(5x_1,5x_2,5x_3....5x_n)$
and HFC (xi, xj) = 1
Thus, number are
$(5\times 1,5\times 2,5\times 3,5\times \mathrm{5....})$
because (xi, xj) = 1
Then only prime number will work.
$So5\times 19=95$ is biggest number.
$So5\times 1,5\times 2,5\times 3,5\times 5,5\times 7,5\times 11,5\times 13,5\times 17,5\times 19,total9numbers.$