Let (S) denotes the number of ordered pairs (x,y) satisfying `(1)/(x)+(1)/(y)=(1)/(n),x,y,n in N`.
Q. `sum_(r=1)^(10)S(r)` equals

Options

A. 47
B. 48
C. 49
D. 50

Answer

B

Explanation

`because1^(2)toS(1)=1,2^(2)toS(2)=3,3^(2)toS(3)=3`,
`4^(2) to 2^(4)to S(4)=5,5^(2)toS(5)=3,S(6)=9`
`S(7)=3,S(8)=7,S(9)=5 and S(10)=9` [from above]
`therefore underset(r=1)overset(10(sum)S(r)=S(1)+S(2)+S(3)+S(4)+S(5)+S(6)+S(7)+S(8)+S(9)+S(10)`
`=1+3+3+5+3+9+3+7+5+9=48`