Let, p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression $$\frac{{p - q - 1}}{{r - s}}$$  is:

A. 1 - s

B. s + 1

C. -s - 1

D. s - 1

Answer: Option C

Solution(By Examveda Team)

q > p and r > s
q > p > r > s
All number have three prime factor
One digit → s, r
s → 2         2² = 4
r → 3         3² = 9
Two digit → p, q
p → 5     5² = 25
q → 7     7² = 49
$$\eqalign{ & \frac{{p - q - 1}}{{r - s}} = \frac{{25 - 49 - 1}}{{9 - 4}} = \frac{{ - 25}}{5} = - 5 \cr & - 5 = - 4 - 1 = - s - 1 \cr} $$