Pat took 'N' whole days to complete the project. If the dash represent

Total number of hours = N*24

So the total number of hours has to be a multiple of 24. To find out if the number of hours is divisible by 24, we need to know all the digits. However the question stem says which of the values could be the number of hours so we need to eliminate answer choices based on the information we have.

We know that the number is divisible by 24, hence the number should be divisible by 4.

To find if the number is divisible by 4, we only need to check if the number formed by the last 2 digits is divisible by 4. We do not need the missing digit to know if the number is divisible by 4. All the options have the last 2 digits so we can check the divisibility by 4.
a) number formed by last 2 digits = 98 . Not divisible by 4
b) number formed by last 2 digits = 36 . Divisible by 4
c) number formed by last 2 digits = 50 . Not divisible by 4
d) number formed by last 2 digits = 90 . Not divisible by 4
e) number formed by last 2 digits = 62 . Not divisible by 4

Hence we can see that whatever the missing digit may be, options a,c,d and e will never be divisible by 4 and hence also not divisible by 24.

Answer is B.