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 pair be n and n + 1. Both are greater than 5, so
\( n \gt 5 \)
Their sum is less than 23:
\( n + (n + 1) \lt 23 \)
\( 2n \lt 22,\quad n \lt 11 \)
So the integer n satisfies \(5 \lt n \lt 11\), that is n = 6, 7, 8, 9, 10. The pairs are
\( (6, 7),\ (7, 8),\ (8, 9),\ (9, 10),\ (10, 11) \)
There are five such pairs.