Question 87
If $$p$$ is the smallest prime with $$7p > 5$$ and q is the largest prime with $$7q < 497$$ then the rational number $$\frac{p}{q} =$$
Solution
Given, $$7p > 5$$
$$\Rightarrow$$ $$p>\frac{5}{7}$$
$$\Rightarrow$$ $$p>0.714$$
The smallest prime number greater than 0.714 is 2
$$\Rightarrow$$ $$p=2$$
$$7q < 497$$
$$\Rightarrow$$ $$q<71$$
The largest prime number less than 71 is 67
$$\Rightarrow$$ $$q=67$$
$$\therefore\ $$ $$\frac{p}{q}=\frac{2}{67}$$
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