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

Question

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

Divyadisha · Accepted Answer

Sum of all numbers = 4*6= 24

k+m= 24- 16 (sum of teh given digits)

k+m= 8

k is not equal to m, that means k or m is not 4.

So, one of them is <3, >3 and this leaves 3 and 3 as the numbers in the middle, giving 3 as the median.

C is the answer

Bunuel · Answer

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} ...

BrentGMATPrepNow · Answer

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

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=Y9f_0QJU1ug

WoundedTiger · Answer

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

Posted from my mobile device

NoHalfMeasures · Answer

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

utkarsh240884 · Answer

@

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

Bunuel · Answer

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.

JeffTargetTestPrep · Answer

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

ScottTargetTestPrep · Answer

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

MI83 · Answer

Why K or M cannot be negative?
Thank you.

Posted from my mobile device

vipulshahi · Answer

MI83

Lets consider the negative ones also,
As we know, k+m = 8
then possible pair (9,-1) ; (10,-2) ; (11,-3).....

(1) In (9,-1) case ; the sequence becomes -1,2,3,3,8,9
Median will be = (3+3)/2 = 3

(2)In (10,-2) case; the sequence becomes -2,2,3,3,8,10
Median will be = (3+3)/2=3

(3)In(11,-3) case; the sequence becomes -3,2,3,3,8,11
Median will be = (3+3)/2 = 3

Median will always be "3"

Hope it helps

CEdward · Answer

Neat question.

2,3,3,8,k,m

2 + 3 + 3 + 8 + k + m / 6 = 4
16 + k + m = 24

What's clear is that k < 8 and m < 8. So what could k and m possible be? We know they have to sum to 8.

1. k = 1, m = 7 (or vice versa) <--- Gives us: 1,2,3,3,7,8 so a median of 3
2. k = 2, m = 6 (or vice versa) <--- 2,2,3,3,6,8 so a median of 3
3. k = 5, m = 3 (or vice versa) <--- 2,3,3,3,5,8 ...3

Median is 3.

C IMO.

hkalabdu · Answer

There are 6 numbers. The total sum of the 6 numbers equals 24 ( 6 multiplied by 4)

K+ M = 24 - 16 = 8

8 can be 5 and 3, or 7 and 1 or 6 and 2.

Regardless of what was the option above once we arrange the number is ascending order, we will find the median is 3

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=GrUl5fD53Us Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards