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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

1

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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

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

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

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26 Sep 2011, 05:04

1

This post received KUDOS

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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21 Feb 2016, 17:21

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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.

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