Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
I've noticed that you have asked about 15 questions during one week. I wanted to make sure that you are aware of the quotas 50 questions/30 days and 6 questions/24 hours, so that you can plan posting your questions accordingly. (If you try to post more questions, stackexchange software will not allow you to do so.) For more details see meta. – Martin Sleziak Jun 17 '13 at 10:33
@MartinSleziak Thank you ! I have already had in my mind .. – SSK Jun 17 '13 at 16:24
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

share|cite|improve this answer
can you elaborate how you took $12$ – SSK Jun 16 '13 at 9:35
@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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.