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

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\frac{46}{75}

\frac{47}{75}

\frac{49}{75}

\frac{50}{75}

answer is D.

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Detailed Solution

Given range is

\frac{3}{5}

and

\frac{2}{3}

and the options are

\frac{46}{75}

\frac{47}{75}

\frac{49}{75}

and

\frac{50}{75}

.
All the options have a denominator of

75

.
So, let us convert

\frac{3}{5}

and

\frac{2}{3}

into equivalent fractions having denominator

75

\frac{3}{5} = \frac{3 \times 15}{5 \times 15}

\Rightarrow \frac{3}{5} = \frac{45}{75}

\frac{2}{3} = \frac{2 \times 25}{3 \times 25}

\Rightarrow \frac{2}{3} = \frac{50}{75}

Hence,

\frac{50}{75}

does not lie between the given rational numbers.
Therefore, option (4) is correct.

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