There were 42 students who took a test in mathematics.there were 36 students who passed test 1, and there were 38 who passed test 2.find the maximum mumber of students who did not passed both tests

We are giiven with two realms:  36 students who passed test 1 and 38 who passed test 2 in which 42 students overall took the test. to determine U' or those who didn't pass either of the tests, then we use the formula:  
A or B = (A+B)-AandB
A/B = (36+38)-AandB= 74-AandB
42 = A+ B - AandB + U'; 42 = 74-  AandB+ U'

where U' is the number who did not pass

U'= -32 + AandB
U' cannot be negative but can be zero,
AandB = 32 @ minimum number of those who fail.
AandB cannot be greater than 38 but can be greater than 36, hence
U' = -32 + 38 @ maximum number of those who fail.

Answer then is 6. 

6 1 / 5 = 31 / 5;
8 3 / 10 = 83 / 10;
But, 31 / 5 = 62 / 10 ;
62 / 10 - ( - 83 / 10 ) = 62 / 10 + 83 / 10 = 145 / 10 = 29 / 2 .