Question

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

• A. $(11,13),(13,15),(15,17),(19,21)$
• B. $(9,11),(13,15),(15,17),(17,19)$
• C. $(11,13),(13,15),(15,17),(17,19)$
• D. $(11,13),(13,15),(19,21),(23,25)$

Answer 1

The correct option is C $(11,13),(13,15),(15,17),(17,19)$

Let the two consecutive odd positive integer be xx and x+2x+2.

Both number are smaller than 10 Therefore

$x+2<10$

Adding −2−2 to both sides,

$x<10-2$

$\Rightarrow x<8$

Also sum of the two integers is more than 40.

So,$x+x+2>40$

$\Rightarrow 2x+2>40$

adding −2to both sides,

$2x>40-2$

$\Rightarrow 2x>38$

Divided by 2 both sides

$x>19$

Then the number greater then 10 and less then 19 are the consecutive odd number pair

In (C) (11,13),(13,15) ,(15,17) ,(17,19) is write answer