Q. Let $A=\{1,2,3,\ldots,10\}$ and $B=\left\{\frac mn:m,n\in A,\ m<n\text{ and }\gcd(m,n)=1\right\}$. Then $n(B)$ is equal to :
A) 36
B) 31
C) 37
D) 29
Explanation
[Solution by Dr. Abubacker] Distinct fractions correspond to coprime pairs $m<n\le10$: $\sum_{n=2}^{10}\varphi(n)=1+2+2+4+2+6+4+6+4=31$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.