let me try:
(1) x and y both are divisible by 2 and 5 (they have both the prime factors 2 and 5). this gives us no information if xy is divisible by 8.
(2) either x or y has got two times the prime factors 2. and the same or the other one has got two times the prime factor 5. this gives us no information if xy is divisible by 8.

taken both together, we can take a look at all prime factors together (x and y are multiplied!): 2, 2, 2, 5, 5, 5 .... since a number is divisible by the product of all its primes, the number must be divisble by 8 (2x2x2).

gcd . lcm = a.b

As correctly said by rupam,

To answer the question you need to know the value of product xy.
And to know the value of product xy, you need to konw its gcd and lcm
as xy = gcd * lcm

So we need both the statements

Thanks