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by prachi18oct » Fri May 29, 2015 1:45 pm
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Please let me know what is wrong in my approach

(1) S can have elements as 0 or negative.

Mean can be 0 or negative
Range can be zero(0,0,0)or positive ( -5,-3,-1)=> range = 4
INSUFFICIENT

(2) -4,-2,0 => range = 4 positive so mean < range
-4,-3,-2 => range => positive

so mean < range SUFFICIENT

How is (1) also sufficient?
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri May 29, 2015 1:53 pm
Set S contains more than one element. Is the range of the set S larger than its mean?

1) Set S does not contain positive elements
2) The median of set S is negative
Target question: Is the range of the set S greater than its mean?

Statement 1: Set S does not contain positive elements
There are several sets of numbers that meet this condition. Here are two:
Case a: Set S = {-1, -2}, in which case the range (1) is greater than the mean (-1.5)
Case b: Set S = {0, 0}, in which case the range (0) is not greater than the mean (0)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The median of set S is negative
If the median is negative, then there are two possible scenarios, both of which lead us to the same conclusion.
Scenario 1: all of the values are negative. In this scenario, the mean must be negative. Since the range is always greater than or equal to zero, we can be certain that the range is greater than the mean.
Scenario 2: some values are negative, and some are positive. In this scenario, the mean will be greater then the smallest value and less than the biggest value. Since the range equals the biggest value (a positive value) minus the smallest value (a negative value), the range will greater than the biggest value in the set. So, we can be certain that the range is greater than the mean.
In both possible scenarios, we come to the same conclusion: the range is greater than the mean.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by Brent@GMATPrepNow » Fri May 29, 2015 1:55 pm
prachi18oct wrote:
How is (1) also sufficient?
Statement 1 is not sufficient

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by Ian Stewart » Fri May 29, 2015 3:15 pm
The source might say Statement 1 is sufficient, because by 'set' they might mean the true mathematical definition of 'set' - in math, a set is a group of distinct things. But if that's what they mean, there's really a problem with the question, because real GMAT questions don't test if you know the mathematical definition of a set. If repeated elements are important to consider in a real GMAT question, that question will tell you that you have a 'list of values', or a 'data set'. In a list or in a data set, it is perfectly fine to have repeated values. If a question only wants you to think of a collection of distinct values, it will say very clearly that the values in the set are distinct.

Here, if we know the values in the set are distinct, and if Statement 1 tells us the set does not contain any positive elements, then that guarantees the median of the set is negative (it can't be 0, because the set contains at least two elements). So if Statement 2 is sufficient, then Statement 1 must be, because Statement 1 is a special case of Statement 2.

And Statement 2 is sufficient. If the median is negative, then so must be the smallest element S. So we know

S < 0

If L is the largest element, then if we add L on both sides of this inequality, then subtract S from both sides, we find

L + S < L
L < L - S

which just says "the range is bigger than the largest element in the set". But the largest element is bigger than the mean in any set of distinct values, so the range must be bigger than the mean.

So the answer is either D or B, depending on what they mean by the word 'set'.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by Amrabdelnaby » Thu Nov 19, 2015 6:08 am
Hi Brent,

Just to understand better, suppose that statement 1 said that set us contains only negative integers; in this case would it be sufficient?
Brent@GMATPrepNow wrote:
Set S contains more than one element. Is the range of the set S larger than its mean?

1) Set S does not contain positive elements
2) The median of set S is negative
Target question: Is the range of the set S greater than its mean?

Statement 1: Set S does not contain positive elements
There are several sets of numbers that meet this condition. Here are two:
Case a: Set S = {-1, -2}, in which case the range (1) is greater than the mean (-1.5)
Case b: Set S = {0, 0}, in which case the range (0) is not greater than the mean (0)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The median of set S is negative
If the median is negative, then there are two possible scenarios, both of which lead us to the same conclusion.
Scenario 1: all of the values are negative. In this scenario, the mean must be negative. Since the range is always greater than or equal to zero, we can be certain that the range is greater than the mean.
Scenario 2: some values are negative, and some are positive. In this scenario, the mean will be greater then the smallest value and less than the biggest value. Since the range equals the biggest value (a positive value) minus the smallest value (a negative value), the range will greater than the biggest value in the set. So, we can be certain that the range is greater than the mean.
In both possible scenarios, we come to the same conclusion: the range is greater than the mean.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Nov 19, 2015 12:11 pm
Amrabdelnaby wrote:Hi Brent,

Just to understand better, suppose that statement 1 said that set us contains only negative integers; in this case would it be sufficient?
Yes.
A set of negative numbers will have a NEGATIVE MEAN, and the range of any set is always GREATER THAN OR EQUAL TO ZERO.
So, in this case the range of the set S must be greater than its mean.

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