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# M14-05

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:51
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Difficulty:

95% (hard)

Question Stats:

37% (01:35) correct 63% (01:04) wrong based on 125 sessions

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If set $$S$$ consists of even number of integers, is the median of set $$S$$ negative?

(1) Exactly half of all elements of set $$S$$ are positive.

(2) The largest negative element of set $$S$$ is -1.

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16 Sep 2014, 00:51
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Official Solution:

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.

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16 Sep 2015, 03:24
{-1,-1,-1,0,0,0} median = -0.5
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16 Sep 2015, 03:41
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prodigypringle wrote:
{-1,-1,-1,0,0,0} median = -0.5

(1) says that exactly half of all elements of set S are positive.

0 is NOT a positive integer.
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28 Nov 2015, 00:18
I think this is a high-quality question and I don't agree with the explanation.
Intern
Joined: 08 Feb 2015
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29 May 2016, 05:32
mainulalam1988 wrote:
I think this is a high-quality question and I don't agree with the explanation.

Why do you disagree?
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11 Aug 2016, 12:03
What if the set is -4,-3,-2,-1,1,2,3,4

half the integers are psoitive
biggest negative element is -1

then the median is (-1+1)/2=0 and zero is neither positive or negative. How is the answer not E?
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12 Aug 2016, 06:53
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joannaecohen wrote:
What if the set is -4,-3,-2,-1,1,2,3,4

half the integers are psoitive
biggest negative element is -1

then the median is (-1+1)/2=0 and zero is neither positive or negative. How is the answer not E?

The answer is still NO. All possible cases give a NO answer, so the statements combined are sufficient.
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22 Oct 2016, 20:05

If the set is {-1,0.1}, median=-0.45, so median is negative. so choose E.
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22 Oct 2016, 20:07
sorry , it is integer, so the answer is right
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30 Jan 2017, 23:26
what if the subset is [-100,-1,2,3]. The mean here is negative, and the larger negative number is still -1.
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30 Jan 2017, 23:41
RoseBCN wrote:
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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Joined: 09 Apr 2016
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10 Apr 2017, 17:48
Hi Bunuel,
If we consider the set(-1,0) the median here is -1/2 which is negative .Kindly justify.
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10 Apr 2017, 22:18
Kumargouravnayak wrote:
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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06 Aug 2017, 09:54
Hi ,

It's implying that the LARGEST element is -1.

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.

Thanks,
Neel
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Joined: 23 Aug 2014
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06 Aug 2017, 09:57
Hi ,

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.

Thanks,
Neel
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Joined: 01 Sep 2016
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16 Sep 2017, 16:41
1
Answer should be E. who says that the values have to be integers, can be fractions as well.
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17 Sep 2017, 02:42
bkpolymers1617 wrote:
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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Re: M14-05   [#permalink] 17 Sep 2017, 02:42
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# M14-05

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