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# If the average (arithmetic mean) of six numbers j, k, m, n, p, and q

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Joined: 24 Jun 2012
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If the average (arithmetic mean) of six numbers j, k, m, n, p, and q  [#permalink]

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28 Jul 2017, 04:01
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Difficulty:

55% (hard)

Question Stats:

58% (01:48) correct 42% (02:03) wrong based on 72 sessions

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If the average (arithmetic mean) of six numbers j, k, m, n, p, and q is 56, how many of the numbers are equal to 56?

(1) The sum of j and p is 128.
(2) The sum of m, n, and q is 152.

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Re: If the average (arithmetic mean) of six numbers j, k, m, n, p, and q  [#permalink]

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28 Jul 2017, 05:46
When you use both statements here, you find j+p+m+n+q = 280, and since the sum of all six numbers is 336, the remaining number k must be equal to 336 - 280 = 56. So using both statements, at least one value in the set is exactly 56. But it's certainly possible other values are also 56. Looking at Statement 1, we might have j = 56 and p = 72, for example, in which case we'd have at least one other value equal to 56, but there's no need for one of j or p to be 56 -- we could have j = 0 and p = 128, say. Similarly, some of m, n and q might equal 56, but there's no need for that to be true. So the answer is E.

It would perhaps be a more interesting question if it asked whether at least one of the numbers was equal to 56. In that case, the two statements would be sufficient together.
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Re: If the average (arithmetic mean) of six numbers j, k, m, n, p, and q  [#permalink]

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28 Jul 2017, 11:43
I think this is not a high quality question. It is clear that one or more of the numbers could equal 56.
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Re: If the average (arithmetic mean) of six numbers j, k, m, n, p, and q  [#permalink]

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04 Aug 2017, 04:53
sananoor wrote:
If the average (arithmetic mean) of six numbers j, k, m, n, p, and q is 56, how many of the numbers are equal to 56?

(1) The sum of j and p is 128.
(2) The sum of m, n, and q is 152.

I would go for E

Since 1) J and P can be any value ( No idea about M, N and P) Insufficient
2) same as above M, N, Q can be any value ( No idea about J and P) Insufficient

both 1 and 2 ( J, P, M, N, Q) can again be any value to make the sum 290 Insufficient
Re: If the average (arithmetic mean) of six numbers j, k, m, n, p, and q   [#permalink] 04 Aug 2017, 04:53
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