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1. The median of set (x,1-1,3,-x) is 0 2. The median of set (x,1-1,3,-x) is x/2

Please explain your answer

Stat 1:
There are 5 elements which means the 3rd element has to be 0. -x and -1 have to be the 1st 2 elements. 1 and 3 have to be last 2 elements which leaves x = 0. Suff.

Stat 2:
Same reasoning as 1 but x can = 0 or 1; insuff.

1. The median of set (x,1-1,3,-x) is 0 2. The median of set (x,1-1,3,-x) is x/2

Please explain your answer

I think the only problem with this question is that it is missing a comma.

What is x?

1. The median of set (x, 1, -1, 3, -x) is 0 2. The median of set (x, 1, -1, 3, -x) is x/2

Solution:

Median of a set is the middle value when the numbers are arranged in increasing order. When there are odd number of numbers e.g. 5 here, the median is simply the 3rd number.

Arranging the set in increasing order: (-1, 1, 3) Now there are two numbers x and -x too in this set which we don't know where to place right now.

1. The median of set (x, 1, -1, 3, -x) is 0 We are given that the median here is 0 which means the third number must be 0. Since we don't have any 0 yet in the set, x (and hence -x too) must be 0. The set must be (-1, 0, 0, 1, 3). There is no other way to get a median of 0. Hence x = 0. Sufficient.

2. The median of set (x, 1, -1, 3, -x) is x/2 We saw above that x could be 0 in which case median will be x/2 = 0/2 = 0. So the value x = 0 satisfies this condition. The median could also be the middle number right now i.e. 1. If x = 2, we get the set (-2, -1, 1, 2, 3) and the median here is 1 which is x/2. Hence x = 2 also satisfies this condition. This means we have two values for x (0 and 2) and not a unique value so this statement alone is not sufficient.

Re: What is x? 1. The median of set (x,1-1,3,-x) is 0 2. The [#permalink]

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17 Feb 2014, 23:59

VeritasPrepKarishma wrote:

bmwhype2 wrote:

What is x?

1. The median of set (x,1-1,3,-x) is 0 2. The median of set (x,1-1,3,-x) is x/2

Please explain your answer

I think the only problem with this question is that it is missing a comma.

What is x?

1. The median of set (x, 1, -1, 3, -x) is 0 2. The median of set (x, 1, -1, 3, -x) is x/2

Solution:

Median of a set is the middle value when the numbers are arranged in increasing order. When there are odd number of numbers e.g. 5 here, the median is simply the 3rd number.

Arranging the set in increasing order: (-1, 1, 3) Now there are two numbers x and -x too in this set which we don't know where to place right now.

1. The median of set (x, 1, -1, 3, -x) is 0 We are given that the median here is 0 which means the third number must be 0. Since we don't have any 0 yet in the set, x (and hence -x too) must be 0. The set must be (-1, 0, 0, 1, 3). There is no other way to get a median of 0. Hence x = 0. Sufficient.

2. The median of set (x, 1, -1, 3, -x) is x/2 We saw above that x could be 0 in which case median will be x/2 = 0/2 = 0. So the value x = 0 satisfies this condition. The median could also be the middle number right now i.e. 1. If x = 2, we get the set (-2, -1, 1, 2, 3) and the median here is 1 which is x/2. Hence x = 2 also satisfies this condition. This means we have two values for x (0 and 2) and not a unique value so this statement alone is not sufficient.

Answer (A)

Thanks Karishma
_________________

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Note that the median of a set with odd number of elements is just the middle element, when arranged in ascending/descending order.

(1) The median of set \(\{x, -1, 1, 3, -x\}\) is 0. The median of this set of 5 (odd) elements must be the middle term, hence \(x=0\). Sufficient.

(2) The median of set \(\{x, -1, 1, 3, -x\}\) is \(\frac{x}{2}\). It could be that \(x=0\) (in this case the set is {-1, 0, 0, 1, 3}) as well as it could be that \(x=2\) (in this case the set is {-2, -1, 1, 2, 3}). Not sufficient.

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