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Math Expert V
Joined: 02 Sep 2009
Posts: 59590
Set Q consists of 6 consecutive even integers beginning with -4, and S  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (02:17) correct 22% (02:38) wrong based on 129 sessions

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Set Q consists of 6 consecutive even integers beginning with -4, and Set P consists of 4 consecutive odd integers beginning with 1. If Set M consists of all numbers from both Set P and Set Q, how much greater is the median of Set M than the mean of Set M?

A. 3
B. 2.5
C. 0.8
D. 0.3
E. 0.25

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4125
Re: Set Q consists of 6 consecutive even integers beginning with -4, and S  [#permalink]

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Top Contributor
Bunuel wrote:
Set Q consists of 6 consecutive even integers beginning with -4, and Set P consists of 4 consecutive odd integers beginning with 1. If Set M consists of all numbers from both Set P and Set Q, how much greater is the median of Set M than the mean of Set M?

A. 3
B. 2.5
C. 0.8
D. 0.3
E. 0.25

Set Q: {-4, -2, 0, 2, 4, 6}
Set P: {1, 3, 5, 7}

So, set M = {-4, -2, 0, 1, 2, 3, 4, 5, 6, 7}

Median of set M: Since set M has an EVEN number of values, the median is equal to the mean of the 2 middlemost values.
{-4, -2, 0, 1, 2, 3, 4, 5, 6, 7}
So, the median of set M = (2 + 3)/2 = 5/2 = 2.5

Mean of set M = [(-4) + (-2) + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7]/10 = 22/10 = 2.2

How much greater is the median of Set M than the mean of Set M?
2.5 - 2.2 = 0.3

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Re: Set Q consists of 6 consecutive even integers beginning with -4, and S  [#permalink]

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Bunuel wrote:
Set Q consists of 6 consecutive even integers beginning with -4, and Set P consists of 4 consecutive odd integers beginning with 1. If Set M consists of all numbers from both Set P and Set Q, how much greater is the median of Set M than the mean of Set M?

A. 3
B. 2.5
C. 0.8
D. 0.3
E. 0.25

Set Q is {-4, -2, 0, 2, 4, 6}.

Set P is {1, 3, 5, 7}

Set M is {-4, -2, 0, 1, 2, 3, 4, 5, 6, 7}

We can see that the median of set M is the average of the two middle values: (2 + 3)/2 = 2.5. The sum of the numbers in set M is -6 + 28 = 22. Therefore, the mean of set M is 22/10 = 2.2. So the median is 2.5 - 2.2 = 0.3 greater than the mean.

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Re: Set Q consists of 6 consecutive even integers beginning with -4, and S  [#permalink]

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Set Q: {-4, -2, 0, 2, 4, 6}
Set P: {1, 3, 5, 7}
Combining both the sets
set M = {-4, -2, 0, 1, 2, 3, 4, 5, 6, 7}

Median of set M is (2+3)/2 = 2.5
Mean of set M = 2.2
difference 0.3

Hence D Re: Set Q consists of 6 consecutive even integers beginning with -4, and S   [#permalink] 10 Jun 2019, 07:53
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