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  4. The smallest prime number satisfying the inequality (2 n-3/3) ≥ (n-1/6)+1 is

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Q. The smallest prime number satisfying the inequality $\frac{2 n-3}{3} \geq \frac{n-1}{6}+1$ is

KEAMKEAM 2020

Solution:

$n=2,3$, fails
$n=5 \Rightarrow \frac{2 \times 5-3}{3} \geq \frac{4}{6}+1$
$\frac{1}{3}>\frac{1}{6}+1$
$\frac{7}{3} \geq \frac{2}{3}+1 $
$ \frac{7}{3} \geq \frac{4}{6}+1$
$1+\frac{4}{3}>\frac{2}{3}+1$
$ 1+\frac{4}{3}>\frac{2}{3}+1$