Question

The number of distinct rational numbers x such that 0 x 1 and $x=\frac{p}{q}wherep,q\in 1,2,3,4,5,6$ is

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

The correct option is C 11

0 < x < 1 $\Rightarrow$ p < q The number of rational numbers = 5 + 4 + 3 + 2 + 1 = 15 There are some rationals which are not different from those already counted. They are $\frac{2}{4},\frac{2}{6},\frac{3}{6},\frac{4}{6},$ $\therefore$ required number = 15 – 4 = 11.