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Bunuel
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What is the difference between the mean and the median of the positive 29 Mar 2018, 00:24
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Question Stats:

90% (01:11) correct 10% (01:58) wrong based on 88 sessions

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What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k
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A
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What is the difference between the mean and the median of the positive 29 Mar 2018, 01:27
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Bunuel
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k
Show more

In a set of 6 elements, the median is the average of the middle two terms.

The median of the 6 elements is \(\frac{k+4+k+8}{2} = k+6\)

The mean of the 6 elements is \(\frac{6k + (3+4+8+9+12)}{6} = \frac{6k + 36}{6} = k + 6\)

Therefore, the difference between mean and median is 0(Option A)
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What is the difference between the mean and the median of the positive 29 Mar 2018, 02:55
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As for equally spaced data, median = mean.

Their difference = 0.

Answer = A

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What is the difference between the mean and the median of the positive 29 Mar 2018, 04:11
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Bunuel
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k
Show more

GMAT INSIGHT:

Mean - Sum of the numbers in the sets / Number of terms in the Set

Median - Middle term (If the number of terms in the set is ODD) OR Average of two middle terms (If the number of terms in the set is EVEN) After arranging the term in Increasing/Decreasing order

Mean = Sum of (k, k + 3, k + 4, k + 8, k + 9, k + 12) / 6 = 6k+36 / 6 = k+6

Median = Average of ( k + 4 and k + 8) = 2k+12 / 2 = k+6

Mean - Median = (k+6) - (k+6) = 0

Answer: option A
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What is the difference between the mean and the median of the positive 29 Mar 2018, 14:30
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Mean = Median = k+6

Hence, A.
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What is the difference between the mean and the median of the positive 30 Mar 2018, 10:50
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Bunuel
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k
Show more

The mean is:

(6k + 3 + 4 + 8 + 9 + 12)/6 = (6k + 36)/6 = k + 6

The median is:

(k + 4 + k + 8)/2 = (2k + 12)/2 = k + 6

So the difference is zero.

Answer: A
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What is the difference between the mean and the median of the positive 30 Mar 2018, 17:32
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As an alternative way of solving this, you can plug in k = 1 to solve for the median and mean. Doing so gives you the set {1, 4, 5, 9, 10, 13}

Median = (5 + 9) / 2 = 7
Mean = (1 + 4 + 5 + 9 + 10 + 13) / 6 = 7

7 - 7 = 0

Answer A
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What is the difference between the mean and the median of the positive 08 May 2019, 10:39
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gmatbusters
As for equally spaced data, median = mean.

Their difference = 0.

Answer = A

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Hi gmatbusters

How come here the terms are equally spaced ?
k, k + 3, k + 4, k + 8, k + 9, k + 12
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What is the difference between the mean and the median of the positive 08 May 2019, 19:05
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You are right,
The terms are not equally spaced. It was an error on my part.
pandajee
gmatbusters
As for equally spaced data, median = mean.

Their difference = 0.

Answer = A

Posted from my mobile device

Hi gmatbusters

How come here the terms are equally spaced ?
k, k + 3, k + 4, k + 8, k + 9, k + 12
Show more
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What is the difference between the mean and the median of the positive 22 Dec 2020, 06:33
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Bunuel
What is the difference between the mean and the median of the positive numbers, k, k + 3, k + 4, k + 8, k + 9, k + 12?

(A) 0
(B) 1
(C) 6
(D) 2k
(E) 5k
Show more

I plugged \(1\) for \(k, \)

The mean \(= \frac{1+4+5+9+10+13}{6}=\frac{42}{6}=7\)

The median\(= \frac{5+9}{2}=7\)

The difference \(= 7-7=0\)

The answer is \(A\)
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