Question

How many pairs of positive integers x, y exist such that hcf of x, y = 35 and sum of x and y = 1085

Answer 1

Answer:

30

Step-by-step explanation:

• HCF of $x,y$ is 35. → 1

• $x+y=1085$ → 2

$x=35n_1$

$y=35n_2$

∵ 1

$x+y=35(n_1+n_2)=1085$

∴$n_1+n_2=31$

$(n_1,n_2)=(1,29),...,(29,1)$

∴30 pairs

Answer 2

Answer:

We can write x = 35a; y = 35b

x + y = 1085 => 35(a + b) = 1085. => (a + b) = 31.

We need to find pairs of co-prime integers that add up to 31.

Since 31 is prime. All pairs of integers that add up to 31 will be co-prime to each other.

There are totally 15 pairs that satisfy this condition.

The answer is 15.