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

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

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New post 11 Jan 2018, 15:04
1
Walkabout 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.


We need to determine whether all of the numbers in the certain list of 15 numbers are equal.

Statement One Alone:

The sum of all the numbers in the list is 60.

Using the information in statement one, we see that all the numbers could be equal or could not be equal. In one scenario, all the numbers could equal 4, and in another scenario 13 of 15 the numbers could equal 4 and the last two numbers could be 6 and 2. In either case, the sum would be 60. Thus, statement one alone is not sufficient to answer the question.
Statement Two Alone:

The sum of any 3 numbers in the list is 12.

Let’s create variables for all 15 numbers in our list.

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O

Using the information in statement two, we see that, regardless of which 3 numbers we select, they MUST sum to 12.

For example, A + B + C = 12 or A + B + N = 12 or A + C + N = 12.

We see that the only way this is possible is if all the numbers are the same value. Statement two alone is sufficient to answer the question.

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

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New post 23 Sep 2018, 18:25
Tricky question magic is in the statement "any 3 numbers"
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Re: Are all of the numbers in a certain list of 15 numbers equal  [#permalink]

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New post 23 Sep 2018, 19:46
For the second case, we can sort all numbers:
a<=b<=c<=d
a+b+c <= b+c+d
a <= d
if a = d => min == max all same
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Re: Are all of the numbers in a certain list of 15 numbers equal &nbs [#permalink] 23 Sep 2018, 19:46

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