Three positive integers: m. n and q, their average is 10,

Question

Three positive integers: m. n and q, their average is 10, median is m+6. what is the greatest possible value of Q ?

eschn3am · Answer

M+N+Q = 30
Median = M+6, but since we have 3 integers and the median is the middle integer, N=M+6

Now try to solve using the smallest possible numbers for M and N.

M=1
N=(1+6) = 7
Q=30-(1+7)=22

{1,7,22} where Q = 22.

pmenon · Answer

22

m+n+q=30

n=m+6

2m+6+q=30 --> 2m+q=24.

for the largest value of q, make m as small as possible. since it is a positive integer, m's smallest value is 1.

so we have: q=24-2=22

sondenso · Answer

Nice! The same to my reasoning, but I missed the point that all m, n and q is positive interger!

bmwhype2 · Answer

i cant believe i subtracted wrong...

kbulse · Answer

how can we know that n is middle number? are these numbers consecutive?

prasannar · Answer

Three positive integers: m. n and q,  their average is 10,  median is  m+6 .  what is the greatest possible value of Q  ?

kazakhb you don't need to know about n because, you are being asked about Q and the other given values are 10 and the m+6 since you need Q

m+n+q=30
m+m+6+q=30

2m+q=24

q=22

Since you are asked about Q and you are given the median value in terms of m, it would be easy to solve the equation if we take the third unknown n as m+6. Hope this helps

eschn3am · Answer

Like Prass said, it's not absolutely necessary to find n, but while they're all there we might as well see what the numbers are.

We have 3 numbers and we're looking for the largest possible Q so Q will be the biggest of the 3.
Since we have 3 numbers, the middle of the 3 will be the median.
It says the median is M+6, so we know M isn't the median. Leaving us with N as the median and equal to M+6
Then we just plug in the smallest numbers we can use since they're all positive integers (1 and 1+6). Subtract out and get 22!

blog · Answer

i am not getting this thing that how can we know the value of m as 1 ?

after 2m+q=24 
how do we get 22 ?

eschn3am · Answer

because we're looking for the  maximum  possible value of Q. Q will be at it's greatest possible value when M and N are at their lowest. 1 is the lowest positive integer so M=1

manylander · Answer

22  from me as well.... And below is another explanation of essentially the same solution.

1) reorder the numbers as m, (m+6)=n, q.
2) q is at the end because we are trying to find its max value
3) m+n+q= 30 (since their average is 10).
4) 30 = 2m+6+q (from (2) and (3))
5) 24 = 2m+q
6) to maximize q, we need to minimize m
7) lowest positive integer = 1
8) 24 = 2+q
 9) q =22

Three positive integers: m. n and q, their average is 10,

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