Question

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

Answer 1

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.