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The arithmetic mean of the list of numbers above is 4. If k

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The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k ≠ m, what is the median of the list?

(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

Problem Solving
Question: 161
Category: Arithmetic Statistics
Page: 83
Difficulty: 600


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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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SOLUTION

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k#m, what is the median of the list?


(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

We have the list {2, 3, 3, 8, K, M} --> mean=4 --> sum=(2+3+3+8+K+M)=4*6 --> K+M=8. Now, both K and M can not be more than 3 (as given that K ≠ M and thus K=M=4 is out and for other values more than 3 K+M>8), also both K and M can not be less than 3 as in this case K+M<8. Son one of them must be less than or equal to 3 and another more than 3 and in this case two middle numbers will be 3 and 3, which gives median of (3+3)/2=3

Answer: C.

Possible lists: {2, 3, 3, 3, 5, 8} or {2, 2, 3, 3, 6, 8} or {1, 2, 3, 3, 7, 8} ...
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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k#m, what is the median of the list?

(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E)

Sol: from the given information we can say that k+m=8

Consider various values of k and m satisfying the above condition, we have

1,7
2,6
3,5

Note k and m can be any of the above numbers

Now for each combintion we see that median is average of 3rd and 4th term and in case it is 3

Ans C

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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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SOLUTION

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k#m, what is the median of the list?


(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

We have the list {2, 3, 3, 8, K, M} --> mean=4 --> sum=(2+3+3+8+K+M)=4*6 --> K+M=8. Now, both K and M can not be more than 3 (as given that K ≠ M and thus K=M=4 is out and for other values more than 3 K+M>8), also both K and M can not be less than 3 as in this case K+M<8. Son one of them must be less than or equal to 3 and another more than 3 and in this case two middle numbers will be 3 and 3, which gives median of (3+3)/2=3

Answer: C.

Possible lists: {2, 3, 3, 3, 5, 8} or {2, 2, 3, 3, 6, 8} or {1, 2, 3, 3, 7, 8} ...
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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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New post 23 Nov 2015, 20:43
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I see that people have spent on average 2.50 mins on this problem. Here is an approach that will help you solve it within 30/45 secs. Important thing to know here is we don't need to test all the possible values. This a PS problem and the answer has to be unique. If different sets gave different answers the question would be invalid. Thus, even if we test one set of values, we can answer the question. So I just tested 1 and 7 for m and k which gives 3 as median. --> Ans: C
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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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New post 12 Nov 2016, 09:04
@
Bunuel wrote:
SOLUTION

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k#m, what is the median of the list?


(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

We have the list {2, 3, 3, 8, K, M} --> mean=4 --> sum=(2+3+3+8+K+M)=4*6 --> K+M=8. Now, both K and M can not be more than 3 (as given that K ≠ M and thus K=M=4 is out and for other values more than 3 K+M>8), also both K and M can not be less than 3 as in this case K+M<8. Son one of them must be less than or equal to 3 and another more than 3 and in this case two middle numbers will be 3 and 3, which gives median of (3+3)/2=3

Answer: C.

Possible lists: {2, 3, 3, 3, 5, 8} or {2, 2, 3, 3, 6, 8} or {1, 2, 3, 3, 7, 8} ...




Hello Bunuel

need some help


List = {2,3,3,8,K,M}

Given that mean is more than 4

which implies 2+3+3+ 8+ K+M >4*6 --> K+M> 8

and we know K!=M

there fore

K=1 M=8 median = 3 { 1,2,3,3,8,8}

K=5 M =10 median = 4 {2,3,3,5,8,10}



I am sure I missing some thing can you please highlight my mistake
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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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New post 12 Nov 2016, 09:14
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utkarsh240884 wrote:
@
Bunuel wrote:
SOLUTION

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k#m, what is the median of the list?


(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

We have the list {2, 3, 3, 8, K, M} --> mean=4 --> sum=(2+3+3+8+K+M)=4*6 --> K+M=8. Now, both K and M can not be more than 3 (as given that K ≠ M and thus K=M=4 is out and for other values more than 3 K+M>8), also both K and M can not be less than 3 as in this case K+M<8. Son one of them must be less than or equal to 3 and another more than 3 and in this case two middle numbers will be 3 and 3, which gives median of (3+3)/2=3

Answer: C.

Possible lists: {2, 3, 3, 3, 5, 8} or {2, 2, 3, 3, 6, 8} or {1, 2, 3, 3, 7, 8} ...




Hello Bunuel

need some help


List = {2,3,3,8,K,M}

Given that mean is more than 4

which implies 2+3+3+ 8+ K+M >4*6 --> K+M> 8

and we know K!=M

there fore

K=1 M=8 median = 3 { 1,2,3,3,8,8}

K=5 M =10 median = 4 {2,3,3,5,8,10}



I am sure I missing some thing can you please highlight my mistake


mean=4 not more that 4.

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above (meaning above this line) is 4.
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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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New post 22 Mar 2017, 15:48
as the mean for 6 numbers is 4 then the sum is 6*4=24. 8=m+k
hence if we try random numbers the median is 3
Answer is C
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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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New post 12 Apr 2018, 07:14
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k ≠ m, what is the median of the list?

(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4


The arithmetic mean of the list of numbers above is 4.
So, (3 + k + 2 + 8 + m + 3)/6 = 4
Multiply both sides by 6 to get: 3 + k + 2 + 8 + m + 3 = 24
Simplify: 16 + k + m = 24
Subtract 16 from both sides to get: k + m = 8

If k and m are integers k ≠ m, what is the median of the list?
Let's assign some values to k and m that satisfy the above condition AND such that k + m = 8
How about k = 1 and m = 7

So, our set of values becomes {3, 1, 2, 8, 7, 3}

What is the median of the list?
Arrange numbers in ASCENDING ORDER to get: { 1, 2, 3, 3, 7, 8}
Since we have an EVEN number of values, the median will equal the AVERAGE of the 2 middlemost values
Median = (3 + 3)/2 = 6/2 = 3

Answer: C

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Re: The arithmetic mean of the list of numbers above is 4. If k [#permalink]

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New post 16 Apr 2018, 16:21
Quote:

3, k, 2, 8, m, 3
The arithmetic mean of the list of numbers above is 4. If k and m are integers and k ≠ m, what is the median of the list?

(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4


Using the average formula: average = sum/number, we see that the sum of these numbers is 24. Thus we have:

3 + k + 2 + 8 + m + 3 = 24

16 + k + m = 24

k + m = 8

Since k ≠ m and assuming that k < m, then the ordered pairs of (k, m) could be (3, 5), (2, 6), (1, 7), (0, 8), etc.

Let’s investigate the possible ordered pairs further:

If (k, m) = (3, 5), then the numbers in ascending order are:

2, 3, 3, 3, 5, 8 --- with median = 3

If (k, m) = (2, 6), then the numbers in ascending order are:

2, 2, 3, 3, 6, 8 --- with median = 3

If (k, m) = (1, 7), then the numbers in ascending order are:

1, 2, 3, 3, 7, 8 --- with median = 3

If (k, m) = (0, 8), then the numbers in ascending order are:

0, 2, 3, 3, 8, 8 --- with median = 3

At this point, we can see that no matter how we “stretch” k and m (e.g., let’s say (k, m) = (-92, 100)), we would still have median = 3.

Answer: C
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Re: The arithmetic mean of the list of numbers above is 4. If k   [#permalink] 16 Apr 2018, 16:21
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