The sum of three from the four numbers A,B,C,D are 3740 , 3850 , 4034 and 4120…

Concept: When you are given the sums of every possible group of three numbers chosen out of four numbers, adding all of those triplet-sums together counts each of the four numbers exactly three times, because each number is left out of exactly one triplet and appears in the other three. So the sum of all four triplet-sums equals 3 times the grand total of all four numbers. Once the grand total is known, each individual number equals the grand total minus the one triplet-sum that excludes it.

Application:

1. Add the four given triplet sums: 3740 + 3850 + 4034 + 4120 = 15744.

2. This total equals 3(A + B + C + D), so A + B + C + D = 15744 / 3 = 5248.

3. Each individual number equals the grand total minus the triplet sum that excludes it: 5248 - 3740 = 1508, 5248 - 3850 = 1398, 5248 - 4034 = 1214, and 5248 - 4120 = 1128.

4. Comparing the four resulting values 1508, 1398, 1214 and 1128, the largest is 1508.

Cross-check: Adding any three of the four derived values reproduces one of the original given sums - for example 1508 + 1398 + 1214 = 4120 and 1398 + 1214 + 1128 = 3740 - confirming the four values were computed correctly.