Question

suppose that a and 10 are relatively prime. Find the sum of all possible values of a that are less than 10. (a)20 (b)30 (c)40 (d)16

Answer 1

For a and 10 to be relatively prime, their HCF should be 1 .

If a = 1 , then HCF is 1

a = 2 , HCF = 2

a = 3 , HCF = 1

a = 4 , HCF = 2

a = 5 , HCF = 5

a = 6 , HCF = 2

a = 7 , HCF = 1

a = 8 , HCF = 2

a = 9 , HCF = 1

a = 10 , HCF = 10

So values of a for which HCF = 1 are, 1 , 3 , 7 , 9

Sum of values of a =1 + 3 + 7 + 9 = 20

Therefore,

Sum of all possible values of a that are less than 10 is 20

Option - A.