Find all pairs of consecutive **odd natural numbers** both greater than 10 such that their sum is less than 40. How many such pairs exist?
A$2$ pairs
B$4$ pairs
C$3$ pairs
D$5$ pairs
Answer & Solution
Correct answer: B. $4$ pairs
Let $x$ be the smaller of the two consecutive odd numbers. Then the other is $x + 2$, with $x > 10$ and $x + (x + 2) < 40$, i.e., $x < 19$.
Odd integers with $10 < x < 19$: $x \in \{11, 13, 15, 17\}$ — **4 values**, giving pairs $(11,13), (13,15), (15,17), (17,19)$.
Check: $17 + 19 = 36 < 40$ ✓.
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