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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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