Question
Quantitative Aptitude Question on Number Systems
How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a+1/b=1/9=?
A
1
B
3
C
5
D
4
Answer
3
Explanation
Solution
1/a+1/b = 1/9
⇒ 9(a + b) = ab
⇒ ab - 9a - 9b + 81 = 81
⇒ (a - 9) (b - 9) = 81 = 34
As a, b > 0 and a ≤ b, there are only 3 ordered pairs, given by a - 9 = 1, 3 or 9 and correspondingly b - 9 = 81, 27, 9.