Q25 - If A Wig Has Any Handmade

[ohthatpatrick]

Question Type:
Sufficient Assumption

Stimulus Breakdown:
Conclusion: All made-to-measure wigs should be dry-cleaned.
Evidence: Made-to-measure wigs are medium to expensive. If a wig has a handmade foundation, it uses human hair. If a wig contains human hair it shoulds be dry cleaned.

Answer Anticipation:
To solve for the missing idea in Sufficient Assumption, you usually start by looking at the terms in the conclusion: "made-to-measure wigs" and "should be dry-cleaned". To prove that claim, you generally need two ideas: Made-to-measure wigs are XYZ, and "If you're XYZ, you should be dry-cleaned". As we unpack what we know about "made-to-measure" and what we know about "should be dry cleaned", we see that made-to-measure takes us to 'medium to expensive'. And we see that 'handmade foundation' gets us all the way to 'should be dry cleaned'. So we're just missing an internal link from 'medium to expensive' to 'handmade foundation'.

Correct Answer:
A

Answer Choice Analysis:
(A) Yes! "If medium to expensive, then handmade foundation". Now we can get all the way from "If made-to-measure, then should be dry cleaned".

(B) The ONLY thing we know about made-to-measure is that it's medium to expensive. If an answer choice doesn't extend what we can infer from 'medium to expensive', it's not going to go anywhere for us.

(C) Same as (B). This doesn't tell us anything more about made-to-measure wigs, since it doesn't connect up with 'medium to expensive'.

(D) This is just the backwards version of (A). We don't know if made-to-measure wigs have handmade foundations, so the way this rule is written, it doesn't tell us anything about made-to-measure wigs.

(E) Same as (B) and (C). There is no connection to "medium to expensive", so there's no way to apply this rule to made-to-measure wigs.

Takeaway/Pattern: People are sometimes annoyed/surprised that the first sentence is a useless conditional that does nothing for constructing the argument. Work backwards from the conclusion, so that you're only looking for the ideas that matter. Here, in order to get "Made to measure --> should be dry cleaned", we needed to get a link that would connect "Made to measure --> medium to expensive" with "handmade component --> human hair --> should be dry cleaned".

#officialexplanation

[mmotieju]

I am having trouble figuring out the chain of logic for this question. The additional information given in each sentence is hard to keep track of and I cant seem to make the connection that makes A the correct answer. Hopefully I am not just misunderstanding the argument.
Thanks!

[bbirdwell]

These kinds of questions are often best understood by symbolizing.

1. handmade components --> more expressive

2. made-to-measure --> medium priced to expensive

3. ~human hair --> ~handmade foundation

4. human hair --> dry cleaned

Therefore:
made-to-measure --> dry cleaned

When checking out the choices, look for one that would connect the evidence to the conclusion and "make it work."

(A) medium to expensive --> handmade. This one would match up with #3 if we contrapose it to read: "handmade --> human hair." Now, if we add this choice to it, we get "medium to expensive --> handmade --> human hair --> dry cleaned." That's what we need, so this is the correct answer.

Does that make sense?

[wallace.rachael]

Is the first premise not used in the question? It seems like it doesn't connect at all.

I picked C because I thought it connected the first premise and the conclusion. I understand why A is correct, but I'm having trouble explaining why C is wrong. Can someone go over why C is incorrect?

Thank you!

[ajc428]

I'll give this a go.

C is a trap answer for one major reason. If you build out the logic chain, you see it doesn't actually connect made to measure wigs with the bigger chain. Why? Because we don't know from the passage that made-to-measure wigs have handmade components -- but we might have mistakenly assumed that they do from the first two sentences:

"If a wig has any handmade components, it is more expensive than one with none. Similarly, a made-to-measure wig ranges from medium-priced to expensive."

If we're reading quickly (which I totally was) we might think "similarly" refers to made-to-measure wigs also having handmade components, but that's NOT what it's referring to. "Similarly" is referring to the price range, and it doesn't tell us a whole lot anyway -- just relative prices. The first sentence doesn't matter to this argument -- I think it's there just to throw us off our game/trick us into a false assumption. The second sentence tells us the only thing we actually know about made to measure wigs.

If we make the false assumption that made to measure wigs have handmade components at this stage, it could be easy to assume that "a wig that has any handmade components should be dry-cleaned" since that would be a nice over-arching principle-type answer to tie this all together. But that's a trap! If you set up the logic chain, you'll see that doesn't help us connect "made to measure wigs" to the rest of the chain. EVEN IF it's true that a wig that has any handmade components should be dry-cleaned, we DON'T ACTUALLY KNOW that made to measure wigs have any handmade components. Tricky.

All we know about made to measure wigs is:

made to measure wigs --> medium-expensive price range

the the rest of the chain becomes:

not human hair --> no handmade components

handmade components --> human hair

human hair --> dry cleaned

Conclusion:

MMW --> should be dry-cleaned

So then we have to connect the only thing we really know about made to measure wigs (that they're in the mid-expensive price range) to the rest of the chain. That's why answer A is correct.

MMW --> medium-priced to expensive price range -->

handmade components --> human hair --> Dry Cleaned

So, if it's true that ALL medium priced to expensive price range wigs (which includes made to measure wigs) have handmade components, then we can logically conclude that MMWs should be dry cleaned.

[kevin]

This is all stated in bbirdwell post, but i wanted to add this post to emphasize a common error with this question that prevents it from being answered correctly!

For anyone having problem with this question, remember to be EXTREMELY careful when reading these statements and formulating the symbolic statements. I easily messed up on this premise which prevented me from linking the variables to get the correct answer!


Handmade foundations are never found on wigs that do not use human hair.

this is the CORRECT way to symbolize this statement:


~HH --> ~HF
Contrapositive: [HF - HH]


We now need to find the assumption that proves all wigs with handmade components (WHC) should be dry Cleaned (DC)

To see how answer choice A (Med To Exp --> HF) completes this chain:


WHC --> Med to Exp --> HF -->HH --> DC

[DeylanK182]

A good way to approach these questions is to first assign each "characteristic" with a letter as you go through the stimulus.

For instance:

If a wig has any handmade components (A), it is more expensive than one with none (B). Similarly, a made-to-measure wig (C) ranges from medium-priced to expensive (D). Handmade foundations (A) are never found on wigs that do not use human hair (E). Furthermore, any wig that contains human hair (E) should be dry-cleaned (F). So all made-to-measure wigs (C) should be dry-cleaned (F).

We hence have these six "characteristics":

- Handmade components (A)
- More expensive than wigs without handmade components (B)
- Made-to-measure (C)
- Medium-priced to expensive (D)
- Use human hair (E)
- Should be dry-cleaned (F)

We can now turn our arguments into a diagrammed set of conditional statements:

A --> B
C --> D
Not E --> not A
(Contrapositive: A --> E)
E --> F

Our conclusion holds that C --> F

We now simply need to connect our arguments to our conclusion

C -->D and A --> E --> F

In order for these to be connected, we simply require that D --> A

That is, medium-priced to expensive wigs have hand-made components.

Answer choice A delivers this by providing that "Any wig whose price falls in the medium-priced to expensive range has a handmade foundation."

A is therefore correct.