Question

Choose the rational number which does not lie between rational numbers $\frac{3}{5}$ and $\frac{2}{3}$ :

• A. $\frac{46}{75}$
• B. $\frac{47}{75}$
• C. $\frac{49}{75}$
• D. $\frac{50}{75}$

Answer 1

Answer: (D)

5075 \displaystyle \frac{50}{75} 7550​

Lets make the numerator and denominator of both $\frac{3}{5}$ and $\frac{2}{5}$ as $75$ because all the given four options have their denominators as $75$.

$\therefore \frac{3\times 15}{5\times 15}=\frac{45}{75}$ and $\frac{2\times 25}{3\times 25}=\frac{50}{75}$

Now question is asking about the rational number not lying between $\frac{3}{5}$ and $\frac{2}{5}$ .

So, we need to check the numerator only that does not lie in between $45$ and $50$.
Clearly 50 does not lie between them. So, $C$ is correct.