Question

If x is a composite number which of the following is necessarily true?

• A. There is at most one factor of x (say a) such that $0<a<\sqrt{x}$
• B. There are at least two factors x (say a and b) such that $0<a<\sqrt{x}$ and $0<b<\sqrt{x}$
• C. There are at least 4 factors of x
• D. If there are 3 factors not greater than $\sqrt{x}$ then there are 3 factors not less than $\sqrt{x}$

Answer 1

Answer: (D)

If there are 3 factors not greater than $\sqrt{x}$ then there are 3 factors not less than $\sqrt{x}$

If x is a composite number then-

option A is false,

(i) because, let $x=6$, then $x=2\times 3$

$2$ & $3$ are two distinct factor, but in option say there is almost one factor

(ii) option B is false

solution :- Let $x=4$, then $x=2\times 2$

$a=2,b=2$

then $a\in (0,\sqrt{4})$ & $b\notin (0,\sqrt{4})$

$a=\sqrt{x}$ & $b=\sqrt{x}$

(iii) option C is false

because $x=6$, then $x=2\times 3$ only two factor.

so, option D is correct.