F.4 Four integers of two digit

There are four integers of two digit. 

The sum and difference of two numbers of these four numbers were all investigated. 

The largest number in sum is 187 and the smallest number is 137. 

The largest number in difference is 40 and the smallest number is 10. 

Find the 2nd smallest number among four numbers. 




Answer
78

Solution
Four integers of two digit are set to A, B, C, and D at large order. 

Since the largest sum is 187, combination of A and B are considered as (A, B) = (99, 88), (98, 89) (97, 90), -------. 

Since the smallest difference is 10, A and B are determined as A= 99 and B= 88. 

Since the largest difference is 59, D = 99 - 40 = 59. 

Since the smallest sum is 137, C = 137 - 59 = 78.