If, in a pair of consecutive positive integers, both numbers are greater than 5 and their sum is less than 23, then the number of such pairs are:

Five

The correct answer is Option (4) → Five

Let the consecutive integers be $n$ and $n+1$, with $n > 5$

Condition: $n + (n+1) < 23 \Rightarrow 2n + 1 < 23 \Rightarrow 2n < 22 \Rightarrow n < 11$

So $n$ satisfies $6 \le n \le 10$

Corresponding pairs: $(6,7), (7,8), (8,9), (9,10), (10,11)$

Number of pairs = 5