Which of the following statements is always true?

Question:

Which of the following statements is always true?

(a) $(x-y) / 2$ is a rational number between $x$ and $y$.

(b) $(x+y) / 2$ is a rational number between $x$ and $y$.

(c) $(x \times y) / 2$ is a rational number between $x$ and $y$.

(d) $(x \div y) / 2$ is a rational number between $x$ and $y$.

 

Solution:

(b) $(x+y) / 2$ is a rational number between $x$ and $y$ Let us assume the value of $x$ and $y$ is 6 and 9 respectively

Then,

$=(6+9) / 2$

$=14 / 2$

$=7$

Hence, the value 7 is lies between 6 and 9 .

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