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Are all of the numbers in a certain list of 15 numbers equal

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Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 14 Dec 2012, 07:36
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Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 14 Dec 2012, 07:38
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Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60. Clearly insufficient.

(2) The sum of any 3 numbers in the list is 12. Since the sum of ANY 3 numbers is 12 then ALL numbers must equal to 12/3=4, because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient.

Answer: B.
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 14 Dec 2012, 07:47
because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient...

I didnt get this part bunuel can you please explain this ??
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 14 Dec 2012, 07:51
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ratinarace wrote:
because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient...

I didnt get this part bunuel can you please explain this ??


Ask yourself, if not ALL numbers are 4, can the sum of ANY 3 numbers in the list be 12?
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 23 Dec 2012, 05:54
Bunuel wrote:
ratinarace wrote:
because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient...

I didnt get this part bunuel can you please explain this ??


Ask yourself, if not ALL numbers are 4, can the sum of ANY 3 numbers in the list be 12?


Bunnel - Cant we hypothesize that there are only three elements such as :{10,1,1} ,(2,8,2}...
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 23 Dec 2012, 05:57
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vishu1414 wrote:
Bunuel wrote:
ratinarace wrote:
because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient...

I didnt get this part bunuel can you please explain this ??


Ask yourself, if not ALL numbers are 4, can the sum of ANY 3 numbers in the list be 12?


Bunnel - Cant we hypothesize that there are only three elements such as :{10,1,1} ,(2,8,2}...


Stem says: Are all of the numbers in a certain list of 15 numbers equal?

So, we know that there are 15 elements in the set.
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 26 Dec 2012, 01:44
Dear Bunnel,

I still can't understand. Would you please explain more about "list of 15 numbers"?
1. Why can't we hypothesize that there are only three elements such as :{10,1,1} ,(2,8,2}... , and the remaining elements such as {4,4,5,5,6,7......}
2. If the three elements must be 4, why the remaining elements have to be equal as well?
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 26 Dec 2012, 02:14
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violachiang wrote:
Dear Bunnel,

I still can't understand. Would you please explain more about "list of 15 numbers"?
1. Why can't we hypothesize that there are only three elements such as :{10,1,1} ,(2,8,2}... , and the remaining elements such as {4,4,5,5,6,7......}
2. If the three elements must be 4, why the remaining elements have to be equal as well?


What are you hypothesizing about? We are told that there are 15 elements. Ask yourself, if the set is {10, 1, 1, 2, 8, 2, ...}, is the sum of ANY 3 numbers in the set 12? No! 10+2+8=18.

Also, from (2) we have that ALL elements must be 4, not just 3 of them.
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 26 Dec 2012, 02:34
I finally understand what's my problem!
I didn't understand the sentence 2 clearly. It is "The sum of any 3 numbers in the list is 12. "
Thanks a lot, Bunnel!
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 29 Apr 2013, 08:32
Reducing shortcut:

After reading the question stem and noting that this is question is about lists/statistics, note that on all the numbers in the question stem are a multiples of 3. So reduce down and re-word the question:

"Are all of the numbers in a certain list of 5 numbers equal?" 15/3 = 5




1) "The sum of all the numbers in the list is 20" 60/3 = 20

Easily insufficient, as there are many ways to add up to 20.

If you wanna test numbers:

Our list:
_ _ _ _ _ = 20
4 4 4 4 4 = 20 yes, all numbers are equal
4 4 4 5 1 = 20 no, all numbers are not equal





2) "The sum of any 1 number in the list is 4?" 3/3 = 1 12/3 = 4

Sufficient, it should become apparent to you that all the numbers are now equal:

Our list: 4 4 4 4 4 = 20

How to get this:

Average = Sum/# of terms
4 = Sum/5
20 = Sum
"Any 1" number is 4
---------------
Answer is B
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 02 May 2014, 10:11
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 29 May 2014, 07:45
Hi Bunuel,
Even if st2 was "sum of any two number is 12", it would be still be sufficient, right?
Thanks!
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Re: Are all of the numbers in a certain list of 15 numbers equal [#permalink] New post 29 May 2014, 07:54
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Re: Are all of the numbers in a certain list of 15 numbers equal   [#permalink] 29 May 2014, 07:54
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