The sum of three from the four numbers A, B, C, D are 7564 , 7512 , 7458 and…

Key idea: add all four given three-number sums. Each original number appears in exactly three of those sums, so the total equals three times the sum of the four numbers.

Compute the total of the four given sums: 7564 + 7512 + 7458 + 7781 = 30315. Divide by 3 to get the sum of the four numbers: 30315 ÷ 3 = 10105.

• A = total − (b + c + d) = 10105 − 7512 = 2593

• B = total − (a + c + d) = 10105 − 7458 = 2647

• C = total − (a + b + d) = 10105 − 7781 = 2324

• D = total − (a + b + c) = 10105 − 7564 = 2541

Therefore the largest of the four numbers is 2647.