Question

5 counting number has averageis12 what is the last number

Answer 1

Acc. to the ques., the 5 counting nos can be supposed to be consecutive .
So , Let the nos be x,x+1,x+2,x+3,x+4
Given ,(5x+10)/5 = 12
x = 10
So , last no : x+4 = 14

Answer 2

numbers are 1*10^24 + 24 and -1*10^24 

add these numbers together and you get 24 because the 1*10^24 cancels the -1*10^24. 

divide by 2 and the average is 12. 

so i'll assume you mean that the numbers can't be negative. 

using that assumption. 

if 1 number, then the max is 12 because 12/1 = 1 

if 2 numbers, then the max is 24 because 24 + 0 = 24/2 = 12 

if 3 numbers, then the max is 36 - 1 = 35 because 35 + 0 + 1 = 36 / 3 = 12 

if 4 numbers, then the max is 48 - 3 = 45 because 45 + 0 + 1 + 2 = 48/4 = 12 

there's a pattern developing. 

let n = number of numbers 

max number = n*12 - sum(x) from x = 0 to x = n-2. 

assuming n = 4, this becomes 4*12 = 48 - (0+1+2) = 48-3 = 45 which we know is good from above. 

the 4 numbers are: 

0
1
2
45 


using this with n = 12, we get: 

12*12 - sum(x) from x = 0 to x = 10. 

this would be an arithmetic progression starting at 0 and ending at 10 



the answer is 55 because it was easier to just add the numbers up. 

if the numbers were higher, it might be easier to use the formula for the sum of an arithmetic progression. 

that formula is: 

sn = n(t1 + tn)/2 

our first number was 0 and out last number was 10 

we had 11 numbers. 

formula becomes 11 * 10 / 2 = 110/2 = 55 (it works !!!!!) 

with nj = 12, our highest number becomes: 

144 - 55 = 89 

89 should be the maximum number assuming none of the numbers can be negative. 

let's see if this holds up; 

we have:
0
1
2
3
4
5
6
7
8
9
10
89 

sum is 144 / 12 = average of 12.