The negative of the sum of 2 consecutive odd numbers is less than -45 , which of the following may be one of the numbers?
$B) 23 $
$C) 26 $
$D) 22 $
$ C) 24$
What will be logic to solve this problem.
Let the consecutive odd numbers be $2n-1, 2n+1$ where $n$ is any integer
So, $-(2n-1+2n+1)<-45\iff 4n>45\implies n\ge 12$
For $n=12, 2n-1=23;2n+1=25$
For $n=13, 2n-1=25;2n+1=27$ and so on
Let consecutive odd numbers be $x,x+2$
then, $-(x+(x+2))<-45\implies -(2x+2)<-45$
Multiplying both sides by $-1$; since multiplying by a negative quantity inverts the inequality, therefore
$2x+2>45\implies 2x>43\implies x>21.5$
Therefore, smaller odd number must be greater than $21.5\implies$ both odd numbers must be greater than $21.5$
Only odd number in the options are $21$ and $23$, so $23$ is the correct answer.