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If the recurring decimal number $$3.7\overline{84}$$ is equal to the rational number $$\frac{p}{q}$$ and $$GCD(p, q) = 1$$,then $$p + q =$$
Let x = $$3.7\overline{84}$$
We can write it as
x = 3.7848484...
Multiply the equation with 10 on both the sides
10x = 37.8484... equation 1
Multiply equ 1 with 100 on both the sides
1000x = 3784.8484... equation 2
Subtract equation 1 from equation 2
1000x - 10x = 3784.8484... - 37.8484...
990x = 3747
x = $$\frac{3747}{990}$$
where $$\frac{3747}{990}$$ is in $$\frac{p}{q}$$ form
For $$GCD(p, q) = 1$$
$$\frac{3747}{990}$$ = $$\frac{1249}{330}$$
p + q = 1249 + 330
= 1579
Hence, option B is correct answer.
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