Question

Let, $x,y$ and $z$ are the natural numbers. Which of the following statements is true?
I) If $x$ is divisible by $y$ and $y$ is divisible by $z$, then $x$ must be divisible by $z$.
II) If $x$ is a factor of $y$ and $z$, then $x$ must be a factor of $y+z$.
III) If $x$ is a factor of $y$ and $z$, then $x$ must be a factor of $\frac{y}{z}$.

• A. I, II and III
• B. I only
• C. I and II
• D. II only

Answer 1

The correct option is C I and II

I. If x is divisible by y and y is divisible by z then x must be divisible by z
Let x be 12, y be 4 and z be 2.
So, here we can see that 12 is divisible by 2. Hence true.
II. If x is a factor of y and z then x must be a factor of y + z
Let x be 3, y be 6 and z be 15.
So, here we can see that 21 is divisible by 3. Hence true.
III If x is a factor of y and z then x must be a factor of $\frac{y}{z}$
Let x be 2, y be 4 and z be 6.
So, here we can see that $\frac{4}{6}$ is not divisible by 2. Hence untrue.
Therefore, option C is correct.