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The negative of the sum of 2 consecutive odd numbers is less than -45 , which of the following may be one of the numbers?

$A)21 $

$B) 23 $

$C) 26 $

$D) 22 $

$ C) 24$

What will be logic to solve this problem.

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@MartinSleziak Thank you ! I have already had in my mind .. –  SSK Jun 17 '13 at 16:24

2 Answers 2

up vote 2 down vote accepted

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

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can you elaborate how you took $12$ –  SSK Jun 16 '13 at 9:35
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@SSK, $4n>45, n>\frac{45}4=11+\frac14$ As $n$ is an integer, $n\ge 12$ –  lab bhattacharjee Jun 16 '13 at 9:36

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.

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