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:
Answer & explanation
Correct answer: option 4
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