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How many ordered pairs of natural numbers $(x, y)$ satisfy $\frac{1}{x} + \frac{1}{y} = \frac{1}{6}$ ?

Competition practiceNumber System, HCF & LCM

A9
B5
C8
D10

Step-by-Step Solution

Clearing fractions:

x y - 6 x - 6 y = 0

, i.e.

(x - 6) (y - 6) = 36

. Each of the 9 divisors of 36 gives one ordered pair, so there are 9.

Answer: A) 9

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