S is a finite set of positive integers. Let there be N integers in the set and the arithmetic mean of all the integers be M. The sum of all the integers in the set S is M*N.

When the greatest integer in S is removed from S, the arithmetic mean of the integers remaining is 32. Let the greatest integer be G.

This gives M*N - G = 32*(N-1).

When the least integer in S is also removed, the average value of the integers remaining is 35. Let the least integer in the set be S.

This gives M*N - G - S = 35*(N-2).

If the greatest integer is then returned to the set, the average value of the integers rises to 40.

This gives M*N - S = 40*(N-1).

The greatest integer in the original set S is 72 greater than the least integer in S, or G - S = 72.

M*N - G = 32*(N-1) ...(1)

M*N - G - S = 35*(N-2) ...(2)

M*N - S = 40*(N-1) ...(3)

G - S = 72 ...(4)

(1) - (3)

M*N - G - (M*N - S) = 32*(N-1) -40*(N-1)

S - G = (N - 1)*(32 - 40)

-72 = (N - 1)*(-8)

N - 1 = 9

N = 10

Substituting N = 10 and G = S + 72 in M*N - G - S = 35*(N-2).

10*M - S -72 - S = 35*8

=> 10M - 72 - 2S = 280

=> 10M - 2S = 352

=> S = (10M - 352)/2

M*N - S = 40*(N-1)

=> 10M - S = 360

Substituting S = (10M - 352)/2.

10M - (10M - 352)/2 = 360

=> 20M - 10M + 352 = 720

=> 10M = 368

=> M = 36.8

The average value of all the integers in the set S is 36.8

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now