Aggregate 15 minute time slots to 30 minutes time slots - asp.net-mvc

Question

I have a list of time slots with a 15 minute interval.
Each slot can have a activity bound to it that makes the slot "reserved".
What is the best way to return the slots in groups of 30 minutes.
So basically, how can I go from this:
10:00
10:15 = this is a reserved slot
10:30
To this:
10:00
10:30
This whole slot is then reserved because it contains the reserved 10:15 slot.
Without changing the slot size itself.
Is this possible to do within the linq query itself or do I have to return the collection of 15 minute slots and apply the 30 minute logic afterwards?
Please point me in the right direction, thanks!
The slots are object with these properties and types:
TimeslotId (int)
SlotStart (DateTime)
ActivityId (int)
UPDATE:
Ok, I tried to group the slots with this query.
var groups = service.TestGrouping().GroupBy(x =>
{
var stamp = x.SlotStart;
stamp = stamp.AddMinutes(-(stamp.Minute % 30));
stamp = stamp.AddMilliseconds(-stamp.Millisecond - 1000 * stamp.Second);
return stamp;
}).Select(g => new Sample() { GroupTime = g.Key, GroupedSlots = g.ToList() }).ToList();
Which takes me a little closer. Now I get the slots aggregated to closest 30 minute, like 8:00-8:30, 8:30-9:00.
However, this does not work for slots that is within quarter to / quarter past. I need some logic to catch all possible half hours:
8:00-8:30, 8:15-8:45, 8:30-9:00, 8:45-9:15.
How would the logic look like?