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Math Expert V
Joined: 02 Sep 2009
Posts: 55231
M14-05  [#permalink]

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5 00:00

Difficulty:   95% (hard)

Question Stats: 37% (01:35) correct 63% (01:09) wrong based on 133 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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Math Expert V
Joined: 02 Sep 2009
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Re M14-05  [#permalink]

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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.

Answer: C
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Re: M14-05  [#permalink]

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What about this set when both conditions are satisfied
{-1,-1,-1,0,0,0} median = -0.5
Math Expert V
Joined: 02 Sep 2009
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Re: M14-05  [#permalink]

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prodigypringle wrote:
What about this set when both conditions are satisfied
{-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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Re M14-05  [#permalink]

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I think this is a high-quality question and I don't agree with the explanation.
Intern  Joined: 08 Feb 2015
Posts: 4
Re: M14-05  [#permalink]

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mainulalam1988 wrote:
I think this is a high-quality question and I don't agree with the explanation.

Why do you disagree?
Current Student B
Joined: 26 Jan 2016
Posts: 103
Location: United States
GPA: 3.37
Re: M14-05  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
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Re: M14-05  [#permalink]

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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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Intern  S
Joined: 27 Aug 2016
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Re: M14-05  [#permalink]

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What about this example?

If the set is {-1,0.1}, median=-0.45, so median is negative. so choose E.
Intern  S
Joined: 27 Aug 2016
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Re: M14-05  [#permalink]

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sorry , it is integer, so the answer is right
Intern  B
Joined: 11 Dec 2016
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Re: M14-05  [#permalink]

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what if the subset is [-100,-1,2,3]. The mean here is negative, and the larger negative number is still -1.
Math Expert V
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Re: M14-05  [#permalink]

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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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GMAT 1: 690 Q50 V33 Re: M14-05  [#permalink]

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Hi Bunuel,
If we consider the set(-1,0) the median here is -1/2 which is negative .Kindly justify.
Math Expert V
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Re: M14-05  [#permalink]

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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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Re: M14-05  [#permalink]

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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
Intern  B
Joined: 23 Aug 2014
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GMAT 1: 670 Q49 V32 GPA: 3.6
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Re: M14-05  [#permalink]

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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
Manager  G
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GMAT 1: 690 Q49 V35 Re: M14-05  [#permalink]

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1
Answer should be E. who says that the values have to be integers, can be fractions as well.
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Math Expert V
Joined: 02 Sep 2009
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Re: M14-05  [#permalink]

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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]

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Bunuel wrote:
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.

This Question appeared in my GMATclub test

After combining (1)+(2)

{ -100, -1, 0.5, 5 ) Now the median is (-1+0.5)/2 = -0.25 So now the Median is Negative. Doesnt it mean that the answer is now E
Math Expert V
Joined: 02 Sep 2009
Posts: 55231
Re: M14-05  [#permalink]

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jovn94 wrote:
Bunuel wrote:
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.

This Question appeared in my GMATclub test

After combining (1)+(2)

{ -100, -1, 0.5, 5 ) Now the median is (-1+0.5)/2 = -0.25 So now the Median is Negative. Doesnt it mean that the answer is now E

Check the stem:

If set S consists of even number of integers, is the median of set S negative?
_________________ Re: M14-05   [#permalink] 10 Sep 2018, 21:45
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