Question

If the average of 13 distinct integers is 58. Maximum how much numbers can be greater than 58?

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Answer 1

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If the average of 13 distinct integers is 58. Maximum how much integer can be greater than 58?

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Ramakrishnan Parthasarathy

Answered December 15

If you consider positive integers alone, a maximum of 11 integers can be greater than 58 . If you accommodate negative integers, a maximum of 12 integers can be greater than 58 .

Consider a least excessive set of 12 continuous distinct integers starting from 59 and ending in 70 ; the sum of the set is 58×12+12(12+1)2=774>58×13=754 (the sum of the 13 distinct integers). 12 integers are obviously not possible.

This means that, for the case of all positive integers, even if you take out the minimum of those 12 continuous integers, i.e., 59 , you have the sum of the remaining 11 integers as equal to 774–59=715 , which leaves a number room of 754–715=39 for the remaining two positive integers. This is easily possible, so 11 maximum distinct integers it is.

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Satish Gs

Answered January 2

This question is either incorrectly framed or else the question intends to test your reading skills and definition of average.

Anyways I'll give every possible answer for different cases.

Case 1:-

If in the integers atleast one can be either positive, negative or zero.

If this is the case then there is no definite solution for maximum possible integer as it can tend to infinity.

This is the solution for your question as integer means whole numbers including negatives of natural numbers.

Case 2:-

If all the integers should be either positive or zero (meaning whole numbers only)

This might be the most appropriate solution for your incorrectly framed question.

Answer 2

The  maximum numbers which can be greater than 58 is 12.

Step-by-step explanation:

Given:

The average of 13 distinct integers is 58.

To Find:

The  maximum numbers which can be greater than 58.

Solution:

As given,the average of 13 distinct integers is 58.

The average of 13 distinct integers = 58.

$The\ average\ of\ 13\ distinct\ integers =\frac{Sum\ of\ 13\ distinct\ integers\ }{Number\ of\ distinct\ integers}$

                                                      $58 =\frac{Sum\ of\ 13\ distinct\ integers\ }{13}$

 $Sum\ of\ 13\ distinct\ integers\ =58\times13 =754$

If  we divide 754 from 58 $=\frac{754}{54} =13$.

$\implies$if we have all distinct integers and its average is 58 then we should put 12 numbers grater than 58 to get sum 754.

The  maximum numbers which can be greater than 58 is 12.

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