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Re: The arithmetic mean of the list of numbers above is 4. If k
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13 Mar 2014, 01:31

1

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
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15 Mar 2014, 10:03

1

1

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
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23 Nov 2015, 19:43

1

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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My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Re: The arithmetic mean of the list of numbers above is 4. If k
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12 Nov 2016, 08:04

@

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} ...

Re: The arithmetic mean of the list of numbers above is 4. If k
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12 Nov 2016, 08:14

1

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} ...

Re: The arithmetic mean of the list of numbers above is 4. If K and M are
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22 Feb 2018, 16:48

Baten80 wrote:

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 can create the following equation:

(3 + 2 + 8 + 3 + K + M)/6 = 4

16 + K + M = 24

K + M = 8

Since K cannot equal M, there is no way for K and M to be 4. Also, since both K and M are integers, one of the numbers must be less than or equal to 3 and the other greater than or equal to 5.

If one of the numbers is 3 and the other is 5, then in ascending order, the list would be:

2, 3, 3, 3, 5, 8

We see that the median is 3.

If one of the numbers is less than 3 and the other is greater than 5 (say K < 3 and M > 5), we see that when we list the numbers in ascending order, K will be before the two 3’s and M will be after the two 3’s. Thus, the two 3’s must be in the 3rd and 4th positions, making the the median to be 3 again.

Answer: C
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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

Re: The arithmetic mean of the list of numbers above is 4. If k
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15 Aug 2018, 14:13

1

Hi, here is 45 sec aprroach for this question

We find that K+m=8, and k ≠ m, So of the k and m one value must be <=3 and other value must be >4 so we have one of the values in the range (2 3 3) which makes total value in the range is 4 and other value in the range (5 8 ) which makes total values in this range 3. Since median of odd number of values is the even term , which is 4TH term so median is 3.

Probus.

gmatclubot

Re: The arithmetic mean of the list of numbers above is 4. If k
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15 Aug 2018, 14:13