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Quick tips for adding numbers x to y

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Quick tips for adding numbers x to y [#permalink] New post 10 Jun 2009, 19:46
Here are some examples on adding numbers from x to y:

1) Add the numbers from 40 to 70, inclusive.
2) Add the even numbers from 40 to 70, inclusive.
3) Add the odd numbers from 40 to 70, inclusive.

4) Add the numbers from 40 to 70.
5) Add the even numbers from 40 to 70.
6) Add the odd numbers from 40 to 70.

[Reveal] Spoiler:
1) 1,705
2) 880
3) 825
4) 1,595
5) 770
6) 825

Last edited by I3igDmsu on 05 Jul 2009, 18:59, edited 7 times in total.
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Re: Quick tips for adding numbers x to y [#permalink] New post 10 Jun 2009, 21:58
1) Add the numbers from 40 to 70, inclusive.
Formula for sum of first N natural numbers is = N(N+1)/2
Sum from 1 to 70 Sa= 70*71/2
Sum from 1 to 40 Sb= 40*41/2
So sum from 40 to 70 = Sa-Sb

2) Add the even numbers from 40 to 70, inclusive.
3) Add the odd numbers from 40 to 70, inclusive.

========================

As a general solution to all these kind of problems learn the AP series.
google on Arithemic Progression series. It is kind of difficult to write the formula here but all these calculations are tooooooo simple using this series.
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Re: Quick tips for adding numbers x to y [#permalink] New post 12 Jun 2009, 13:34
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If you don't mind remembering a formula or two then yes you can.
The examples that you have given can be grouped under Arithmetic Progressions...or a finite sequence of evenly spaced numbers.

There are two formulas:

\(1. S = \frac{n}{2} [2a + (n-1)d]\)

where
\(S=\text{sum of the all the numbers in the sequence}\)
\(n=\text{total number of numbers in the sequence}\)
\(a=\text{the first number of the sequence}\)
\(d=\text{the different between any two consecutive numbers in the sequence}\)

\(2. S = \frac{n}{2} [\text{First Term}+\text{Last Term}]\)

where
\(S=\text{sum of the all the numbers in the sequence}\)
\(n=\text{total number of numbers in the sequence}\)

You can use either equation based on what is provided in the question.

Lets take your examples and solve them. For all of these we know the first and the last number so we should be fine with equation 2.

1) Add the numbers from 40 to 70, inclusive.
Solution:
Here the sequence is 40,41, 42, ...., 69, 70.
To calculate n
\(n=\text{Last number}-\text{First number} + 1\)

\(n=70-40+1 = 31\)

Using equation 1.

\(S = \frac{n}{2} [\text{First Term}+\text{Last Term}]\)

\(S = \frac{n}{2} [\text{First Term}+\text{Last Term}]\)

\(S = \frac{31}{2} [40+70]\)

\(S = \frac{31}{2} [110]\)

\(S = 31\times55\)

\(S = 1705\)

2) Add the even numbers from 40 to 70, inclusive.
Here the sequence is 40,42, 44, ...., 68, 70.
Solve using 40 as the first term and 70 as the last term
To calculate n for even (or odd) number

\(n=\frac{\text{Last number}-\text{First number}}{2} + 1\)

3) Add the odd numbers from 40 to 70, inclusive.
Here is the sequence is 41,43,....67,69
Solve using 41 as the first term and 69 as the last term

and so on...
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Re: Quick tips for adding numbers x to y [#permalink] New post 30 Jun 2009, 19:11
Could someone check my answers above please?

Thanks nookway, your help is appreciated!
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Re: Quick tips for adding numbers x to y [#permalink] New post 03 Jul 2009, 06:51
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I3igDmsu wrote:
Could someone check my answers above please?

Thanks nookway, your help is appreciated!


Don't think you need our help - this can be easily done in Excel :-D
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Re: Quick tips for adding numbers x to y [#permalink] New post 05 Jul 2009, 19:00
Done. If anyone needs practice, the answers in the spoiler are correct.
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Re: Quick tips for adding numbers x to y [#permalink] New post 02 Aug 2009, 20:30
Great stuff! Thanks!
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Re: Quick tips for adding numbers x to y [#permalink] New post 13 Oct 2011, 13:32
I did not get the logic of these.
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Re: Quick tips for adding numbers x to y [#permalink] New post 03 Feb 2015, 11:25
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Re: Quick tips for adding numbers x to y   [#permalink] 03 Feb 2015, 11:25
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