Answer:
When both the conditions hold true, F is prime.
Explanation:
AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.
AB
+ CD
--------
EF
1st condition, B and D are consecutive.
Adding B and D gives us F.
Possible values can be (F being the unit value after adding not considering the carry over):
B + D = F
1+2=3
2+3=5
3+4=7
4+5=9
5+6=1
6+7=3
7+8=5
8+9=7
Here F is not prime (because 9 is not prime).
Now, let us consider the 2nd condition as well.
i.e. C = 8
For the following
AB
+ CD
--------
EF
C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.
So, E = 8 + 1 = 9
Now, B and D are consecutive and can not be 1, 8 or 9.
So, possible values are:
B + D = F
2 + 3 = 5
3 + 4 = 7
Here F is prime.
So, when both the conditions hold true, F is prime.