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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] New post 09 Oct 2005, 05:25
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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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The OA is B. I picked E. It is not B in my opinion because according to (2) the numbers could be either all 4s or, as example, in any set of 3, a 10 and two 1s. Any comment?

Thanks
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 [#permalink] New post 09 Oct 2005, 05:32
Think about it for a moment... of ANY three numbers in the set.

Imagine you take your example.. one 10 and two 1s. What about the rest of the 15 numbers. They'd have to be such, that taking two of them plus the 10 equals 12, and taking those same two numbers plus the 1 also equals 12. This is not possible. Thus, all are equal.
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 [#permalink] New post 09 Oct 2005, 05:41
I got (B) for the same reason. The keyword is "any", this inferes that at random you could pick any three and they would = 12. The only way this is possible is if all 15 numbers were 4.

B.
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 [#permalink] New post 09 Oct 2005, 06:17
nero44 wrote:
Think about it for a moment... of ANY three numbers in the set.

Imagine you take your example.. one 10 and two 1s. What about the rest of the 15 numbers. They'd have to be such, that taking two of them plus the 10 equals 12, and taking those same two numbers plus the 1 also equals 12. This is not possible. Thus, all are equal.


DIDNT GET IT AT ALL!!!!!
Could you please explain in a simpler way?? Thanks!
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Cheers, Rahul.

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 [#permalink] New post 09 Oct 2005, 06:25
I'll try my best. ;)
ok lets use some numbers here.

The example given by maxn was: a "10" and two "1"s. So the sum of these three numbers is 12. This set of numbers then will start like this:
10,1,1,A,B,C,D,E,F,G,H,I,J,K,L whereas the letters are any numbers.

now you'd have to chose numbers for the letters, such as 10 + A + B =12
But also that 1 + A + B = 12...
so you can see.. by definition, the ONLY way that these equations can be true, if A=B=C=D=E... and son on...
They must all be the same, because 10 + E + L = 12 and 1 + E + L = 12
It applies to all. Thus, all must be equal.

To put differently: Prove the statement wrong by picking numbers. You will see, you wont be able to find numbers to fulfill statement 2.
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Re: DS - Wrong OA? [#permalink] New post 09 Oct 2005, 06:26
maxn 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

____________________________






The OA is B. I picked E. It is not B in my opinion because according to (2) the numbers could be either all 4s or, as example, in any set of 3, a 10 and two 1s. Any comment?

Thanks


To prove this, let make an investigation into any 2 sets of 3
a1+b1+c1=12
a2+b2+c2=12

Since a1+b1+b2=a1+b1+c1=12--->b2=c1
a1+b1+c1=a1+b1+c2=12--->c1=c2

cotinue this way , we can prove that all 6 numbers are equal.
Repeat this method,we can prove that all 15 numbers are equal.
Re: DS - Wrong OA?   [#permalink] 09 Oct 2005, 06:26
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