Question

Average of 7 no is 20. Find the largest value ?

Answer 1

If we take 7 positive integers whose average is 20, the largest among them can have the value of integers from 23 to 39 only. Its maximum value should be 39.

Assume the 7 numbers are 1, 2, 3, 20, 37, 38, 39. Here the largest number has its maximum value.

The largest can't have the values of integers less than 23. Because,

Assume that the largest among them is 22. A sequence is given below:

22, 21, 20, 19, 18, 17, 23

Here 22 is taken as the largest but 23 is here! A contradiction has been occurred!

If the value of some numbers here are to be increased, they'll never have a value without by exceeding 23! If the values are to be decreased, maybe the value of 23 will be increased!

∴ The largest among the 7 numbers have the values of positive integers from 23 to 39, and its possible largest value is 39.

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