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

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Intern
Joined: 04 Oct 2011
Posts: 10
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

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Intern
Joined: 05 Dec 2012
Posts: 13
GMAT 1: 680 Q44 V38
Re: Are all of the numbers in a certain list of 15 numbers  [#permalink]

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04 Mar 2013, 01:02
1
Hello !

Here is how I solved it. Please correct me if I'm wrong :

(1) : Since you don't have any contraints regarding the numbers : the fifteen numbers can all equal 4 or you can have fourteen 0 and one 60. Not sufficient.

(2) : There are several ways to reach 12 by adding 3 numbers together :
4 + 4 + 4 = 12
3 + 3 + 6 = 12
8 + 2 +2 = 12
etc...

Let's consider the ways where you have at least 2 different numbers. For examples : 3 + 3 + 6. Let's say your fifteen numbers are divided in 5 groups of numbers composed by 3, 3 and 6 :

Statements 2 tells us we can pick any 3 numbers and get 12 by adding them. If you pick one full group : 3+3+6, you get 12. But if you pick 3, 3 from one group and another 3 from another group, you get 3+3+3 = 9. It is therefore impossible to have different numbers, they all have to be the same. Sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 48061
Re: Are all of the numbers in a certain list of 15 numbers  [#permalink]

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04 Mar 2013, 03:10
4
1
pancakeFR wrote:
Hello !

Here is how I solved it. Please correct me if I'm wrong :

(1) : Since you don't have any contraints regarding the numbers : the fifteen numbers can all equal 4 or you can have fourteen 0 and one 60. Not sufficient.

(2) : There are several ways to reach 12 by adding 3 numbers together :
4 + 4 + 4 = 12
3 + 3 + 6 = 12
8 + 2 +2 = 12
etc...

Let's consider the ways where you have at least 2 different numbers. For examples : 3 + 3 + 6. Let's say your fifteen numbers are divided in 5 groups of numbers composed by 3, 3 and 6 :

Statements 2 tells us we can pick any 3 numbers and get 12 by adding them. If you pick one full group : 3+3+6, you get 12. But if you pick 3, 3 from one group and another 3 from another group, you get 3+3+3 = 9. It is therefore impossible to have different numbers, they all have to be the same. Sufficient.

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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Math Expert
Joined: 02 Sep 2009
Posts: 48061
Re: Are all of the numbers in a certain list of 15 numbers  [#permalink]

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21 Feb 2016, 22:14
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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Joined: 09 Sep 2013
Posts: 7776
Re: Are all of the numbers in a certain list of 15 numbers  [#permalink]

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10 Feb 2018, 05:46
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Re: Are all of the numbers in a certain list of 15 numbers &nbs [#permalink] 10 Feb 2018, 05:46

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