Question

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

• A. $15$
• B. $13$
• C. $12$
• D. $11$

Answer 1

Answer: (D)

$11$

Since total number of digits $=6$
So to get a number of a number of the form $\frac{p}{q}$ we will have to choose two numbers out of the 6 numbers.
There is only one way to arrange them since the number $x$ has to satisfy 0 Hence no. $x=\left(\begin{array}{c}6\\ 2\end{array}\right)\times 1=15$, but some numbers have to be removed because they are repeated.
They are :
$\frac{2}{4}=\frac{1}{2}\frac{4}{6}=\frac{2}{3}\frac{2}{6}=\frac{1}{3}\frac{3}{6}=\frac{1}{2}$
Thus the number of removed numbers$=4$
Therefore, total no. of distinct $x=15-4=11$
Hence, option 'D' is correct.