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# [Evenly spaced sets] How to find the elements given the sum ?

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Intern
Joined: 05 Nov 2013
Posts: 11
Location: Spain
GMAT Date: 03-14-2016
[Evenly spaced sets] How to find the elements given the sum ?  [#permalink]

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18 Aug 2016, 11:43
Hello guys, I have one question:

let's assume that I have an evenly spaced set of an unknown number of elements, where each element is for instance the previous + 3.
Let' assume also that I know the sum of the elements of the set, say 15

Is it possible to find the elements ?

I have the feeling that is possible but I’m struggling to demonstrate it.

Senior Manager
Joined: 23 Apr 2015
Posts: 285
Location: United States
WE: Engineering (Consulting)
Re: [Evenly spaced sets] How to find the elements given the sum ?  [#permalink]

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18 Aug 2016, 12:04
1
hellope wrote:
Hello guys, I have one question:

let's assume that I have an evenly spaced set of an unknown number of elements, where each element is for instance the previous + 3.
Let' assume also that I know the sum of the elements of the set, say 15

Is it possible to find the elements ?

I have the feeling that is possible but I’m struggling to demonstrate it.

It's not possible to find with just knowing the sum.
You need to know at least one more information, like the number of elements or starting or ending value.
for example, the set can have only {15} or {6,9} or {2,5,8}
you can generate any number of such set using the formula below :

sum = 1/2 * number of elements *(2*first element + (number of elements -1 ) *3 ) here 3 being the difference
or in simple terms, S = n/2 *( 2* a + (n-1)d)

+1 for kudos
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Concentration: Strategy, Operations
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Re: [Evenly spaced sets] How to find the elements given the sum ?  [#permalink]

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24 Aug 2016, 02:27
hellope wrote:
Hello guys, I have one question:

let's assume that I have an evenly spaced set of an unknown number of elements, where each element is for instance the previous + 3.
Let' assume also that I know the sum of the elements of the set, say 15

Is it possible to find the elements ?

I have the feeling that is possible but I’m struggling to demonstrate it.

Hi Few possible questions on GMAT based on this concept:

A = {1,2,3,4,5} . How many sets can be formed? You can use the formula 2^n = 2^5 = 32 sets including an empty set {}

If the questions specifies a non-empty set, then you need to use = 2^n-1 = 31 sets

Similarly questions can be framed based on say 1. No of sets containing even nos, odd nos and prime nos and so on.
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Re: [Evenly spaced sets] How to find the elements given the sum ?  [#permalink]

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15 Sep 2019, 21:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: [Evenly spaced sets] How to find the elements given the sum ?   [#permalink] 15 Sep 2019, 21:26
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