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

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

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New post 27 Nov 2018, 04:41
Quote:
I still didn't get you....

There are 15 different numbers, but we took only 4 for our example.

what if a + b+ c = 12
and d + e+ f = 12


Say our list is:

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o

I just took the first four numbers and proved a=d. There's nothing special about the first four numbers in the list; I can use the same logic to prove that any two numbers are equal here. For example, if I want to prove that b=d, we have

b + c + a = 12
d + c + a = 12

Subtract the second equation from the first:

b - d = 0
b = d

So now we know that b = d. Since we saw that a=d as well, a, b and d are all equal. We can do this for all the letters in the list, so they all must be 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 27 Nov 2018, 04:42
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Are all of the numbers in a certain list of 15 numbers equal? &nbs [#permalink] 27 Nov 2018, 04:42

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