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

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Are all of the numbers in a certain list of 15 numbers [#permalink]

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26 Nov 2009, 12:28
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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26 Nov 2009, 13:27
I believe it's clear, that (1) is insufficient to answer the questions. Let's analyze (2):

We have set of 15 numbers; $$x_1, x_2, ...x_{15}$$

Any 3 numbers from this set sum up to 12. For example:

$$x_1+x_2+x_3=12$$
$$x_1+x_2+x_4=12$$
. . . . . . . . .
$$x_1+x_2+x_{15}=12$$

It is clear, that $$x_3=x_4=......=x_{15}$$. This is the way to prove that in fact all the numbers in the set are equal.

Answer: (B) - Statement 2 is sufficient
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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26 Nov 2009, 19:09
B
Let's say the list includes a,b,c,d...
According to B, a+b+c = b+c+d = 12 => a=d.
Similarly, all numbers in the list are equal.
Hence B.
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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27 Nov 2009, 21:28
let analyze satement 2

the sum of any 3 numbers is 12.

let assume 15 numbers are a,b,c,d,e,f,g,h,i,j,k,l,m,n,o

For example a+b+c= 4+4+4=12,d+e+f=4+4+4=12,if we assume like this then statement b is sufficient

but what can i do if a+b+c= 4+4+4=12,d+e+f=4+3+5=12,g+h+i=1+6+5=12......from this example all numbers couldnt be equal
so b is not sufficient .plz expain
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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27 Nov 2009, 21:33
TomB wrote:
let analyze satement 2

the sum of any 3 numbers is 12.

let assume 15 numbers are a,b,c,d,e,f,g,h,i,j,k,l,m,n,o

For example a+b+c= 4+4+4=12,d+e+f=4+4+4=12,if we assume like this then statement b is sufficient

but what can i do if a+b+c= 4+4+4=12,d+e+f=4+3+5=12,g+h+i=1+6+5=12......from this example all numbers couldnt be equal
so b is not sufficient .plz expain

if we take f,h,i from ur list the sum is not 12, from S2, any 3 numbers should total 12... so they all have to be 4
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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28 Nov 2009, 23:04
JimmyWorld wrote:
Are all the numbers in a certain list of 15 numbers equal?

1) The sum of all the numbers in the list of 60.
2) The sum of any 3 numbers in the list is 12.

Not sure on 2). Wonder if someone could explain? Thank you

Look for the clue: sum of "any three number" is 12.

Sum of any 3 numbers from a, b, c, d, e, f, g, h, i, j must be 12. That is possible only if all these numbers must be equall and integers i.e. 4.

TomB wrote:
let analyze satement 2

the sum of any 3 numbers is 12.

let assume 15 numbers are a,b,c,d,e,f,g,h,i,j,k,l,m,n,o

For example a+b+c= 4+4+4=12,d+e+f=4+4+4=12,if we assume like this then statement b is sufficient

but what can i do if a+b+c= 4+4+4=12,d+e+f=4+3+5=12,g+h+i=1+6+5=12......from this example all numbers couldnt be equal
so b is not sufficient .plz expain

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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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25 Sep 2011, 13:01
Are all the numbers in a certain list of 15 members equal?

1. Sum of all the mumbers in a list is 60
2. The sum of any three number is list is 12.

I will post OA after some discussion...
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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25 Sep 2011, 13:06
nishtil wrote:
Are all the numbers in a certain list of 15 members equal?

1. Sum of all the mumbers in a list is 60
2. The sum of any three number is list is 12.

I will post OA after some discussion...

st1: the numbers can be all 4s ot can be 14 zeros and one 60 ... hence insufficient

st2: All the numbers have to be 4 because some of any 3 has to be 12.
hence sufficient .
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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26 Sep 2011, 05:04
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JimmyWorld wrote:
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.

Its B

Data from question stem: total numbers = 15

Statement 1: If the sum of all numbers in list in 60, we can not be sure that all are equal. Lets prove it with simple examples.. If 14 numbers are 0 and 1 number is 60...the sum is still 60 but all numbers are not equal... (Answer to question NO)
or if all numbers are 4, the sum is 60 and all numbers are equal (Answer to question YES)

Hence INSUFFICIENT

Statement 2: sum of any 3 numbers is 12..all numbers have to be 4.. Hence SUFFICIENT

Time taken: 44 secs
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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27 Sep 2011, 01:44
GMATmission wrote:
JimmyWorld wrote:
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.

Its B

Data from question stem: total numbers = 15

Statement 1: If the sum of all numbers in list in 60, we can not be sure that all are equal. Lets prove it with simple examples.. If 14 numbers are 0 and 1 number is 60...the sum is still 60 but all numbers are not equal... (Answer to question NO)
or if all numbers are 4, the sum is 60 and all numbers are equal (Answer to question YES)

Hence INSUFFICIENT

Statement 2: sum of any 3 numbers is 12..all numbers have to be 4.. Hence SUFFICIENT

Time taken: 44 secs

Statement 2: sum of any 3 number is 12..there are various possiblities.. for example number 8 number 2 and number 2 can add to 12.. hence number 8, 2 ,and 2 can be part of the list... as you pointed out all three numbers can be 4.. so statement 2 is insufficient...
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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27 Sep 2011, 02:01
nishtil wrote:
GMATmission wrote:
JimmyWorld wrote:
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.

Its B

Data from question stem: total numbers = 15

Statement 1: If the sum of all numbers in list in 60, we can not be sure that all are equal. Lets prove it with simple examples.. If 14 numbers are 0 and 1 number is 60...the sum is still 60 but all numbers are not equal... (Answer to question NO)
or if all numbers are 4, the sum is 60 and all numbers are equal (Answer to question YES)

Hence INSUFFICIENT

Statement 2: sum of any 3 numbers is 12..all numbers have to be 4.. Hence SUFFICIENT

Time taken: 44 secs

Statement 2: sum of any 3 number is 12..there are various possiblities.. for example number 8 number 2 and number 2 can add to 12.. hence number 8, 2 ,and 2 can be part of the list... as you pointed out all three numbers can be 4.. so statement 2 is insufficient...

2) The sum of ANY 3 numbers in the list is 12.

Try writing a set of 15 numbers such that if you pick ANY 3 numbers randomly, the sum should be 12.

{8, 2, 2} Say these 3 of the numbers from the set. What can be the 4th number?
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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27 Sep 2011, 04:11
Thanks fluke... got it.
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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05 Oct 2011, 12:35
1 not sufficient as some numbers can be negative to make the sum as 6
2 Sufficient since to make sum of any three numbers 12 all numbers should be 4

Ans B
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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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Re: Are all of the numbers in a certain list of 15 numbers [#permalink]

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21 Feb 2016, 22:14
Expert's post
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
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Re: Are all of the numbers in a certain list of 15 numbers   [#permalink] 21 Feb 2016, 22:14
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