CAT 2017 Number System Question (Hard)

Question

How many different pairs of positive integers are there such that and ?

Accepted Answer

Step 1 We are given a b 9 with the condition . --- Step 2 First, eliminate denominators by multiplying everything by 9b 9a ab Rearranged ab - 9a - 9b 0 We can factor this using the method of adding and subtracting ab - 9a - 9b 81 81 This factors as a - 9 b - 9 81 --- Step 3 81 can be factorized into

CAT 2017

Quantitative

Number System

Hard

How many different pairs $(a, b)$ of positive integers are there such that $a \leq b$ and $\frac{1}{a} + \frac{1}{b} = \frac{1}{9}$ ?

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