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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) 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} ...
_________________
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 [#permalink]
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23 Nov 2015, 20:43
1
This post received KUDOS
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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Please contact me for super inexpensive quality private tutoring
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 [#permalink]
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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} ...
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} ...
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