Average of 11 Prime Numbers

The average of 11 prime numbers less than 45 is also a prime no.

Then find :
1. Average.
2. Maximum no.

Questions by cool1agra

Showing Answers 1 - 18 of 18 Answers

praveen_v

  • Jan 13th, 2008
 

The prime no's before 45 are  2,3,5,7,11,13,17,19,23,29,31,37,41,43.

From which  5,7,11,13,17,19,29,31,37,41,43 are selected.

So,    (5+7+11+13+17+19+29+31+37+41+43)/11 = 23


Therefore,

1)  Average = (5+7+11+13+17+19+29+31+37+41+43)/11 = 23   { Which is also a prime no.}

2)  Maximum no. is 43.

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The prime no's before 45 are 2 3 5 7 11 13 17 19 23 29 31 37 41 43.(totally 14 numbers)
add all 14 numb=281.so the sum of 11 numb will def be around 281.
nw d average s a whole numb and also prime.so find a number among the above such that sum s less than 281 and and also is a multiple of 11 and one of d above numbers.sotake 29
29*11=319
23*11=253
19*11=209

taking 253:
281-253=28(so remove 2,3,23)from the list

if you take 209 removal of 3 numbrs will not be possibe....

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dmanborn

  • Dec 15th, 2009
 

Prime Nos below 45 are  2 ,3,5,7,11,13,17,19,23,29,31,37,41,43.

Sum of all the above numbers = 262; divding 262 by 11 { q=23; r= 9}. Hence
subtract 9 from 262, gives you 253. Sum of 14 primes number gives you 262. Therefore
sum of any 11 of the above prime numbers must be 253, so that dividing 253 (sum of 11
prime nos below 45) by 11 gives you 23 (average; with no remainder), but this is impossible. Hence trying the same technique for the number which is a prime no. when multiplied by 11 gives a numb that can be formed by summing any 11 above said prime number, that is 209 (2 +5+11+13+17+19+23+29+31+37+41).  Check 209 by dividing it by 11 will give you 19 which is a prime number.


Answer:    1) 19    2) 41

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The prime no's before 45 are 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43.(If we consider 1 as a prime number)


From which  1 7 11 13 17 23 29 31 37 41 43 are selected.

So (1+7+11+13+17+23+29+31+37+41+43)/11= 23(which is a prime number)

The prime no's before 45 are  2 3 5 7 11 13 17 19 23 29 31 37 41 43.(If we don't consider 1 as a prime number)

From which   5 7 11 13 17 19 29 31 37 41 43 are selected.

So (5+7+11+13+17+19+29+31+37+41+43)/11= 23(which is a prime number)
Therefore 


1) Average =23 { Which is also a prime no.}

2) Maximum no. is 43.

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