TS ICET 2015 Question Paper with Solutions for online practice

Question : 94 of 200

Marks: +1, -0

The number of pairs of positive integers a and b such that a + b = 594 and gcd (a, b) = 27 is

Solution:

Given : GCD (a, b) = 27
∴ We can write,
a = 27x and b = 27y, where x and y are prime to each other.

a+b=594=27x+27y=594

⇒x+y=22

Possible pairs are (1, 21), (3, 19), (5, 17), (7, 15), (9, 13)
∴ Required answer is 5.

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