Question

If $3p+2q=25$ where $p,q$ are prime numbers, then $\frac{q}{p-1}$ is equal to

• A. $\frac{2}{3}$
• B. $\frac{5}{4}$
• C. $\frac{5}{16}$
• D. $4$

Answer 1

The correct option is B $\frac{5}{4}$

$3p+2q=25,$
Since, RHS $=25$ is odd, so either $3p$ or $2q$ is odd, since $2q$ can not be odd.
So, $3p$ is odd.

Now, $p=\frac{25-2q}{3}$
Minimum value of $q$ can be $2,$ so odd prime numbers which are not greater than $7$ will be $3,5,7$
If $p=3\Rightarrow q=8$ (not possible)
If $p=5\Rightarrow q=5$
If $p=7\Rightarrow q=2$

So, $\frac{q}{p-1}=\frac{2}{7-1}=\frac{1}{3}$
or $\frac{q}{p-1}=\frac{5}{5-1}=\frac{5}{4}$