Find all pairs of consecutive odd positive integers, both of which are larger than 10 such that their sum is less than 40.
Answer & explanation
Correct answer: option 3
The correct answer is option (3) : 11, 13; 13, 15;15, 17; 17, 19
Let x , x+2 be the 2 consecutive odd positive integer. As are larger than 10 and their sum is less than 40, we get
$x> 10$ and $x+ (x+ 2) < 40$
$2x + 2< 40$
$10< x $ and $ x < 19$
$⇒10< x < 19$
Since x is odd positive integer and it lies between 10 and 19, the positive values of x are 11, 13, 15, 17, than the corresponding values of the other odd integer i.e x + 2 are 13, 15, 17, 19
Hence the required pairs are $11, 13; 13, 15; 15, 17; 17, 19$