Can you help with this DS problem?

[yumi2012]

s={1,2,5,7,x}
If x is a positive integer, is the mean of set S greater than 4?

1) The median of set S is greater than 2
2) The median of set S is equal to the mean of set S

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Can't figure out statement 2.....

[Brent@GMATPrepNow]

s={1,2,5,7,x}
If x is a positive integer, is the mean of set S greater than 4?

1) The median of set S is greater than 2
2) The median of set S is equal to the mean of set S

Target question: Is the mean of set S greater than 4?

In other words, is (1+2+5+7+x)/5 > 4?
Simplify: Is 1+2+5+7+x > 20?
Simplify: Is 15+x > 20?
Simplify: Is x > 5?

Now that we've rephrased the target question as "Is x > 5?", the question is much easier to handle.

Aside: If a set consists of an odd number of elements, the median will be the middle number.

Statement 1: The median of set S is greater than 2
So, the middle number (the median) is not 2. So, it must be either 5 or x (if x between 2 and 5).
What does this tell us about x? Here are two possibilities.
case a: x=3, which gives us {1,2,3,5,7}. In this case, the median is 3 and x is not greater than 5.
case b: x=6, which gives us {1,2,5,6,7}. In this case, the median is 5 and x is greater than 5.
Since we have conflicting answers to the rephrased target questions, statement 1 is NOT SUFFICIENT

Statement 2: The median of set S is equal to the mean of set S
We know that the mean = (x+15)/5,.
We can rewrite this as: the mean = (x/5) + (15/5) or the mean = (x/5) + 3

Important: Since x must be a positive integer, and since the other four numbers are positive integers, we know that the median must be a positive integer. If the median = mean, then the mean is also a positive integer.

For (x/5) + 3 to be a positive integer, x must be divisible by 5.
Let's see what happens when x=5.
When x=5, the median=5 and the mean=4. Nope. x cannot equal 5.

Let's see what happens when x=10.
When x=10, the median=5 and the mean=5.
Great, that works.
Now, should we keep checking other values of x to see what happens? No, we don't need to.
Remember that our rephrased target question: Is x > 5?
We already saw that x can't equal 5, and we've shown that x must be a positive integer that's divisible by 5. Since x could equal 10, we've already shown that x must be greater than 5.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT.

Answer = B

Cheers,
Brent

[GMATGuruNY]

s={1,2,5,7,x}
If x is a positive integer, is the mean of set S greater than 4?

1) The median of set S is greater than 2
2) The median of set S is equal to the mean of set S

If the mean of the 5 integers is 4, then their sum = number*mean = 5*4 = 20.
If the sum = 20, then x = 20 - (1+2+5+7) = 5.
For the mean to be GREATER than 4, the sum must be GREATER than 20, implying that x>5.
Question stem, rephrased: Is x>5?

Statement 1: The median of set S is greater than 2.
Case 1: 1,2,x=3,5,7, in which case the median is 3.
Here, x<5.
Case 2: 1,2,5,7,x=10, in which case the median = 5.
Here, x>5.
INSUFFICIENT.

Statement 2: The median of set S is equal to the mean of set S.
Case 3: If the mean=4, then x=5, yielding the following list of values:
1,2,5,5,7.
Since the mean of 4 is not equal to the median of 5, Case 3 does not satisfy statement 2.
Case 4: If the mean=3, then the sum = 5*3=15, with the result that x = 15 - (1+2+5+7) = 0.
Since x must be positive, Case 4 is not viable.
Since it is not possible that the mean in statement 2 is less than or equal to 4, the mean must be GREATER than 4.
SUFFICIENT.

The correct answer is B.