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An abyssal drake is, conceptually, a really simple creature. A cross between demons, wyverns, and a red dragon. The red dragon provides its fire subtype, while the demons provide resistance to electricity, acid, and cold. The question I have is about how those two elements interact.

When a sorcerer casts an empowered orb of cold spell, hits an abyssal drake (or another vulnerable creature with resistance; the abyssal drake is just a convenient example) with a touch attack, and the damage roll results in 70, how much damage does the abyssal drake take with its vulnerability to cold and resistance 20?

Is the damage 85 points, since the vulnerability increases the damage to 105 and the resistance reduces it by 20? Or is the damage 75 points, since the resistance reduces the damage to 50 and the vulnerability increases the damage it takes by half?

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Usually, resistance is applied before vulnerability, because that's the order most beneficial to the creature.

In your example with 70 points of cold damage, the abyssal drake would take 75.

This problem isn't addressed in any published handbook, the answer comes from the 3.5 FAQ, which even though some regard it as an unreliable source because of some conflictive answers to other questions, it's still an official source and one of its questions explicitly answers yours without conflicting with other published rules.

Official 3.5 FAQ, p.113:

If a monster has resistance and vulnerability to the same kind of damage (such as fire), which effect is applied first? And when does the saving throw come in?

Always roll a saving throw before applying any effects that would increase or reduce the damage dealt. For example, if a frost giant is struck by a fireball that would deal 35 points of damage, it would roll its Reflex save, then apply its vulnerability to fire after determining how much damage the fireball would normally deal. If the save failed, the frost giant would take 52 points of damage: 35 + one-half of 35 (17.5, rounded down to 17). A successful save would mean the frost giant suffered only 25 points of damage: one-half of 35 rounded down (17), plus one-half of 17 rounded down (8).

If the creature has both resistance and vulnerability to the same kind of damage, apply the resistance (which reduces the damage dealt by the effect) before applying the vulnerability (which increases the damage taken by the creature). For example, imagine our frost giant wore a ring of minor fire resistance (granting resistance to fire 10). If the save failed, the frost giant would take 37 points of fire damage: 35 (fireball) – 10 (resistance to fire 10) = 25, plus one-half of 25 (12.5, rounded down to 12). If the save succeeded, the frost giant would take only 10 points of damage: 17 (half damage from the fireball, rounded down) – 10 (resistance to fire 10) = 7, plus one-half of 7 (3.5, rounded down to 3).

As a general guideline, whenever the rules don’t stipulate an order of operations for special effects (such as spells or special abilities), you should apply them in the order that’s most beneficial to the creature. In the case of damage, this typically means applying any damage-reducing effects first, before applying any effects that would increase damage.

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