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Notice that since the set consists of even number of integers then the median will be the average of two middle elements.

(1) Exactly half of all elements of set \(S\) are positive. Either all other elements are negative for example \(S\) can be {-30, -20, -10, 1, 2, 3} or all other elements but 0 are negative, for example \(S\) can be {-3, -2, -1, 0, 1, 2, 3, 4}. Not sufficient.

(2) The largest negative element of set \(S\) is -1. Not sufficient.

(1)+(2) We have that exactly half of all elements are positive and the largest negative element is -1. Two cases for the median:

If zero is in \(S\), the median equals \(\frac{0 + positive}{2}=positive\);

If zero is NOT in \(S\), the median equals \(\frac{-1+\text{positive integer}}{2} \ge 0 = \text{non-negative}\).

So, the answer to the question whether the median is negative is NO. Sufficient.

what if the subset is [-100,-1,2,3]. The mean here is negative, and the larger negative number is still -1.

It's not clear what you are implying.

The question asks: is the median of set S negative? When combined we get a NO answer to the question, the median is NOT negative. For your example the answer remains the same the median = (-1 + 2)/2 = 1/2, so it's not negative. All possible cases give a NO answer, so the statements combined are sufficient.
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Hi Bunuel, If we consider the set(-1,0) the median here is -1/2 which is negative .Kindly justify.

(1) says that exactly half of all elements of set S are positive. How does your set satisfy this statement? 0 is NOT a positive integer.
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That could mean that the smallest negative could be -1.

So we can have a Set such as {-100,-100,1,1}

In this case, the median is negative.

If statement two implied that the "absolute value" of a negative integer is <=1 , then I can understand why C is the answer. However, the word "LARGEST" is ambiguous.

If set SS consists of even number of integers, is the median of set SS negative? (1) Exactly half of all elements of set SS are positive. (2) The largest negative element of set SS is -1.

Statement 2 is implying that the LARGEST element is -1.

That could mean that the smallest negative could be -100.

So we can have a Set such as {-100,-100,1,1}

In this case, the median is negative.

If statement II implied that the "absolute value" of a negative integer in Set SS is <=1 , then I can understand why C is the answer. However, the word "LARGEST" is ambiguous.

Answer should be E. who says that the values have to be integers, can be fractions as well.
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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

Answer should be E. who says that the values have to be integers, can be fractions as well.

The answer is C, not E. How does fractions change the answer? Can you please given one of example which gives TWO different answers when we combine the statement?
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