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It may boil down to whether the magical component counts or not. The text from the faction card does not specify it must be non-magical:
Recover a gem worth at least 400 gp plus 100 gp per level you possess during an adventure.
It seems the game considers pearls to be gems since they are listed as semi-precious Gems having 50gp in value:
http://paizo.com/pathfinderRPG/prd/ultimateEquipment/appendix.html#gems-and -jewelry

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I would say that they do count.
While we can not craft magic items the CRB does state that Crafting Wondrous Items costs half of the final value. Assuming that you are casting the spell from memory/known that means that the cost of materials, ie the pearl/gem, is half the final cost of the item.
Edit: Ninja'd

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Just gonna point this part out on the journal cards:
Some of these goals are really open-ended. Is that on purpose?
Yes. As noted, some are open-ended and others are very precise, and that's by design. It broadens the opportunities that PCs have to pursue these objectives, rather than forcing them to cherry-pick the one or two scenarios that would work—even tougher if you've already played that adventure. What this means is that there is a little GM interpretation involved in whether or not a PC actually fulfilled an objective. The Faction Journal Cards' introductory page advises GMs to err on the side of leniency when making that call.

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This is extremely pedantic, but I would not allow a Pearl of Power to count for the faction goal because a pearl isn't a gem. It's in that same category as ivory, id est yes it's pretty, yes it's used in jewelry, but no it isn't a gemstone.
Like I said, extremely pedantic.

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Count it.
As the introductory page says, leniency.
No need to nit it up.
There is leniency, and the allowing things that by their very definition dont apply.
Semi precious stones and other expensive items are not necessarily synonymous with gems.
Gemstones have a specific definition. Typically they are diamonds, various types of corundum (ruby, sapphire, emerald) and other very rare stones like Opals and Topaz.
So where does leniency take you? Well its a stone and has a value, therefore its a gemstone? I disagree with that concept.

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According to Wikipedia Pearls are Gemstones. and the definition of Gem includes semi precious stones.
gem
jem/Submit
noun
1.
a precious or semiprecious stone, especially when cut and polished or engraved.
synonyms: jewel, gemstone, stone, precious stone, semiprecious stone; More
verbrare
1.
decorate with or as with gems.
So going by the actual definition of Gem and the advice to be lenient in the application of the successes I would say yes.

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The GMG defines gems for pathfinder. Medium value gem stones are roughly 100gp and include most pearls. Pearls of power are defined as average pearls. I'd rank them in this category.
Ioun Stones are defined as crystalline stones. Which would most likely be at best the 50gp variety (typical cost of masterwork mundane items and what crystal stone or quartz sits on the GMG chart).
I will revise my original opinion.
I would give you credit for a 100go gem for a pearl if power or a 50gp gem for an ioun stone.
The magical properties of the stones does not enhance the value of the gem itself.

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The idea is to open up as many possibilities with in the scenarios as possible. Can you list ten scenarios off the top of your head that have a mundane gem worth enough to qualify? We are Pathfinders and are all about the magical items not the gold and jewels. I say yes a pearl of power would count.

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I would use the full value of magical gems, the card doesn't specify inherent or gem only value, it just refers to worth.
I can totally respect that. In my opinion, the value of something is what one can sell it for. But I think your view has merit as well, and certainly is more lenient toward the players—which is a very good thing.

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If we're going to split hairs, then let's not stop halfway. See, pearls of power aren't average pearls; they're "seemingly normal pearl[s] of average size and luster." They're not average, just normal and of average quality. If they were intended to be valued as average pearls from the GMG, then clearly they would have been listed as "average pearls."
That sounds absurd, doesn't it? That's not normal. But on legalism, it is. We're specifically instructed to view these faction missions in the player's favor; I fail to see how we're doing that by arguing that magic gems aren't gems.

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Aren't pearls made from clams or mussels? And gems are some kind of mineral deposit structure / kind of stone? I really just need Steven Huffstutler to come in here and define gems for me--he's got that geologist savvy.
From my basic understanding, however, I think that gems and pearls are pretty different things. Just like I wouldn't allow gold teeth to count as gems, I wouldn't allow pearls of power.

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I guess it depends on if there are any 1500 gp high quality gems or jewels to be found in scenarios.
In the scenarios I've played through, I can't think of any large gems. Now most of those are in the 1-5 tier, but still I don't think they are commonly called out specifically. On the other hand, it may be that I just don't remember them because it was never an issue before.

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@Walter, I just so happen to be a geologist.
Pearls are pretty pure Calcium Carbonate (CaCO3), but then so are the thousand(s)+ ft. limestone cliff exposures of the Rocky Mountains about 75km west of my home here in Calgary. Minearologically, they are the same.
Limestone is an agglomeration of mostly animal skeletal fragments composed of CaCO3, and pearls are an accreted mineral formation made of CaCo3. If one were to bury a pile of pearls, they would become Limestone over time.
[/geology lession]
Anyway, we're near the 50/50 range still with no overwhelming edge in terms of seniority. I think that barring a contraindication from him whose name does not need to be said three times, I'm going to go with Yes, in the spirit of the Leniency stuff outlined above.

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If the GMG is allowed for GM's why is it not listed in the Core Assumption for Gm's then?
Because the GMG includes rules and materials GMs need to reference, and is encompassed by the blanket statement that GMs can use the PRD to prepare scenarios.
For instance, the Chase rules are in the GMG. Some of the scenarios that use Chases include the basics, but the full rules are available only in the GMG.

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My understanding of the point of the faction cards is to add flavor. We know that the sages are interested in gems as a tool for storing memories, as shown in the bonuses on the card. A mundane gem of such value would still be a rare thing, though as Kevin points out, not completely out of the reach of non-adventurers.

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Eric Ives wrote:My understanding of the point of the faction cards is to add flavor. We know that the sages are interested in gems as a tool for storing memories, as shown in the bonuses on the card.Do we know that pearls are unsuitable for such purposes? What are you basing that on?
Oh, I have know way of knowing if a mundane pearl could be used, but I don't think an already enchanted pearl could be.

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Eric Ives wrote:My understanding of the point of the faction cards is to add flavor. We know that the sages are interested in gems as a tool for storing memories, as shown in the bonuses on the card.Do we know that pearls are unsuitable for such purposes? What are you basing that on?
Generally if something already has an enchantment on it you can't enchant it again with/to be something else. If a pearl is a receptacle for a spell making it a receptacle for a mind could be harder.
*plants saddle on the fence*

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Aren't pearls made from clams or mussels? And gems are some kind of mineral deposit structure / kind of stone? I really just need Steven Huffstutler to come in here and define gems for me--he's got that geologist savvy.
From my basic understanding, however, I think that gems and pearls are pretty different things. Just like I wouldn't allow gold teeth to count as gems, I wouldn't allow pearls of power.
Alright I'm here.
No Pearls are not minerals.
To be a mineral a substance must be: Naturally occurring, inorganic, solid, definite chemical composition, and an ordered atomic arrangement.
Pearls are made up of CaCO3 an Conchiolin(which is a complex protein). This disqualifies it from being a mineral.
The question as to whether a pearl is a gem is open to some debate. Strictly speaking gems(gemstones) are 'a piece of mineral crystal'; however, that has not stopped people from calling semiprecious stones and organic materials gems.
Examples:
Organic
Amber, Ammolite, Bone, Coral, Jet, Mother of Pearl, Ivory, Pearls, and Shells
Fossilized Organisms
Petrified Woods and Fossil Corals
Inorganic Mineraloids
Obsidian and Opal
Rocks
Lapis lazuli, Unakite, Agates, Jade
Pearl of Power=Gem=Faction Boon Qualification? In my opinion this is firmly at the discretion of the table GM.
Cost: This is the cost in gold pieces to create the item. Generally this cost is equal to half the price of an item, but additional material components might increase this number. the cost to create includes the costs derived from the base cost plus the costs of the components.
In the description for a pearl of power it does not call out the need for a material component worth enough to qualify for the Faction card boon. It is valuable for the magic it contains not for the gem.
That is why at my tables I say no, same as an Elemental Gem would not count. That is how I rule it. If you do not agree, rule it how you want at your tables.

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*Gems will be counted, but magical value on gems will not be counted. Value from magic on gems will be donated to the church of Asmodeus, whom I agree to worship for eternity. Also I agree that I am lame*
The tiefling lowers his magnifying glass.See, It's all here in the fine print. Wait a moment. He rapidly scrolls through the parchment. This isn't the scarab sages faction journal, it's the mortgage I set up for that Half-Orc idiot from the Silver Crusade. Umm... gotta run