Find the number of distinct rational numbers `x` such that `o<x<1a n dx=p//q` , where `p ,q in {1,2,3,4,5,6}` .

Question

Find the number of distinct rational numbers `x` such that `oA. 15
B. 13
C. 12
D. 11

Answer 1

Correct Answer - D
As `0 lt x lt 1`, we have `p lt q`
The number of rational numbers=5+4+3+2+1=15
When p,q have a common factor, we get some rational numbers which are not different from those already counted.
There are 4 such numbers `(2)/(4),(2)/(6),(3)/(6),(4)/(6)`.
`therefore` The required of rational numbers=15-4=11