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Math Expert V
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A set of integers, S, contains more than one element. Is the range of  [#permalink]

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A set of integers, S, contains more than one element. Is the range of S greater than its mean?

(1) S does not contain positive integers.
(2) The mean of S is negative.

Kudos for a correct solution.

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Re: A set of integers, S, contains more than one element. Is the range of  [#permalink]

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Bunuel wrote:
A set of integers, S, contains more than one element. Is the range of S greater than its mean?

(1) S does not contain positive integers.
(2) The mean of S is negative.

Kudos for a correct solution.

Statement 1: if it doesn't contain positive numbers, we have 2 scenario's

Scenario 1: If set contains only 0's... S= {0,0,0,0......} We have Mean, Median, Range all are zero.
Scenario 2: If it contains atleast one negative integers, we will some value for mean & range.

So we get 2 answers, Statement-1 is not sufficient.

Statement 2: If mean is negative. The set must contain negative numbers, And the range will always be positive. Hence Range> Mean.

Statement-2 alone sufficient- Answer is B.
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A set of integers, S, contains more than one element. Is the range of  [#permalink]

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Bunuel wrote:
A set of integers, S, contains more than one element. Is the range of S greater than its mean?

(1) S does not contain positive integers.
(2) The mean of S is negative.

Kudos for a correct solution.

Range = Highest Term - Smallest Term of the set
i.e. Range > 0

Question : Is Range > Mean ?

Statement 1: S does not contain positive integers.

For Non-Positive Terms in the set, The mean would also be non-Positive
But when all the terms in the set are equal to zero then Mean = Range
and in other cases Mean < Range
Hence, NOT SUFFICIENT

Statement 2: The mean of S is negative.
Range can only be Non Negative.
and Non-Negative > negative
Hence, Range > Mean
SUFFICIENT

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Math Expert V
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Posts: 58402
Re: A set of integers, S, contains more than one element. Is the range of  [#permalink]

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Bunuel wrote:
A set of integers, S, contains more than one element. Is the range of S greater than its mean?

(1) S does not contain positive integers.
(2) The mean of S is negative.

Kudos for a correct solution.

800score Official Solution:

If S does not contain positive integers, as statement (1) defines, then S contains negative integers and/or zeroes.

If S consists of zeroes only, S = {0, 0, …, 0}, then its range is 0, because all the elements are the same. Besides, its mean is 0 as well, because the sum of the elements is 0. So in this case the mean and the range are equal.

If there is at least one non-zero element in S, then the sum will be negative (because S doesn't contain any positive numbers). The range is always a non-negative number, so it will be greater than the mean (which is negative).

Therefore statement (1) gives us two possible answers to the main question. Statement (1) by itself is NOT sufficient.

From Statement (2) we know that the mean is negative. Any range is a non-negative number. Therefore the range is greater than the mean. Statement (2) by itself is sufficient.

Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).

If this seems too abstract, it helps to pick some numbers, like the set {-5, -4, 2}, to see how the range will be greater than the mean. The mean is negative, and the range is 2 – (-5) = 7.
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A set of integers, S, contains more than one element. Is the range of  [#permalink]

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Bunuel wrote:
A set of integers, S, contains more than one element. Is the range of S greater than its mean?

(1) S does not contain positive integers.
(2) The mean of S is negative.

Kudos for a correct solution.

1. we can have 0; 0 => mean =0, range=0 so mean=range.
or we can have -1; -1 -> range =0; mean=-1.
moreover, statement says no positive INTEGERS, thus, some of the elements can be 3.3; 5.2; etc, which are POSITIVE!
2 outcomes, A and D are out.

2. mean is negative. which means that the set contains negative numbers. since range is always positive, range always will be greater than the mean.

B.
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Re: A set of integers, S, contains more than one element. Is the range of  [#permalink]

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Bunuel wrote:
Bunuel wrote:
Any range is a non-negative number.

If I would have thought about this, I could have answered this Q without putting pen on paper! Thanks! Non-Human User Joined: 09 Sep 2013
Posts: 13243
Re: A set of integers, S, contains more than one element. Is the range of  [#permalink]

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_________________ Re: A set of integers, S, contains more than one element. Is the range of   [#permalink] 07 Mar 2019, 10:06
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