The sum of two natural numbers is 80 and their HCF is 10. How many such pairs of numbers are possible?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 2.
k x (a + b) = Sum of the two numbers.
80 = 10 x (a + b)
⇒ a + b = 8
Now,
1. a + b = 8
2. HCF(a, b) = 1
Possible pairs of (a, b) = (1, 7), (3, 5), (5, 3), (7, 1)
Total pairs = 4 but the only pairs of coprime natural numbers
(x, y) that sum to 8 are
(1,7)open paren 1 comma 7 close paren
(1,7)and
(3, 5).