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If the mean (arithmetic average) of eight numbers is 60, how many of

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If the mean (arithmetic average) of eight numbers is 60, how many of  [#permalink]

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New post 26 Mar 2018, 23:07
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If the mean (arithmetic average) of eight numbers is 60, how many of the eight numbers equal 60?

(1) None of the eight numbers is less than 60.
(2) None of the eight numbers is greater than 60.

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If the mean (arithmetic average) of eight numbers is 60, how many of  [#permalink]

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New post 26 Mar 2018, 23:56
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Bunuel wrote:
If the mean (arithmetic average) of eight numbers is 60, how many of the eight numbers equal 60?

(1) None of the eight numbers is less than 60.
(2) None of the eight numbers is greater than 60.


1. If none of the eight numbers is less than 60, none of the eight numbers is greater than
60. So, 8 numbers must be 60. If either of the 8 numbers is greater than 60, the average
is greater than 60. (Sufficient)

2. If none of the eight numbers is greater than 60, none of the eight numbers is less than
60. So, all 8 numbers must be 60. If either of the 8 numbers is greater than 60, the average
is greater than 60. (Sufficient - Option D)
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Re: If the mean (arithmetic average) of eight numbers is 60, how many of  [#permalink]

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New post 28 Mar 2018, 02:42

Solution



Given:
    • Mean of 8 numbers = 60

Working Out:
    •We need to find out how many numbers in the list are equal to 60.

Statement 1: None of the eight numbers is less than 60.

    • This means all the numbers in the list ≥ 60.

However, even if one of the numbers exceed 60, the average will become more than 60, since all the other numbers, at the minimum, are 60 each.

    • Thus, the only possible condition for the average of the 8 numbers to be 60 is when all the numbers are equal to 60.

Thus, Statement 1 alone is sufficient.

Statement 2: None of the eight numbers are greater than 60.”

    • This means that all the numbers in the list ≤ 60.

However, even if one of the numbers is less than 60, the average would fall below 60. This is because all the other numbers can at maximum be equal to 60 and not more than that.

    • Thus, the only possible condition for the average to be 60 is when all the numbers are equal to 60.

Thus, Statement 2 alone is sufficient to answer our question.

Answer: Option D

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Re: If the mean (arithmetic average) of eight numbers is 60, how many of &nbs [#permalink] 28 Mar 2018, 02:42
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