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This problem trains for: SAT-I, AMC-8, GMAT.

Four farmers herd together 456 geese. Find out the difference between the largest number of geese and the smallest number of geese owned by a farmer knowing that, if the first, third and fourth farmers each gave 3 geese to the second farmer, they would own numbers of geese that are consecutive odd numbers.

The total number of geese has not changed - it is the same before and after the 'donations'. Since the number of geese is invariant, we can set up an equation accordingly.

Let us consider 4 numbers that are consecutive odds and add them up to get 456:

equation

equation

Therefore, the numbers of geese after the hypothetical donation are: 111, 113, 115 and 117.

We find the numbers of geese each of them owns by inverting the hypothetical donation:

equation
equation
equation
equation

The largest number of geese a farmer owns is 120 and the smallest is 104. The difference is 16.