Question

Find all pairs of consecutive odd natural numbers, both of which are larger than $10$, such that their sum is less than $40$.

• A. (11, 13), (13, 15), (15, 17), (17, 19)
• B. (11, 13), (13, 15), (15, 17)
• C. (21, 23), (23, 25), (25, 27), (27, 29)
• D. (15, 17), (17, 19), (19, 21), (21, 23)

Answer 1

Answer: (A)

Let $x$ be the smaller of the two consecutive odd natural number, so that the other
one is $x+2$
Given $x>10$ and $x+(x+2)<40$
$\Rightarrow 2x<38$
$\Rightarrow x<19$
$\therefore 10<x<19$
Since $x$ is an odd number, $x$ can take the values $11,13,15$ and 17 .
$\therefore$ Required possible pairs are $(11,13),(13,15),(15,17),(17,19)$