#17 - If a motor is sound-insulated, then it is quiet enough

[Administrator]

Complete Question Explanation

Must Be True—SN. The correct answer choice is (B)

This stimulus presents a fact set containing three conditional relationships. The first relationship tells us that when a motor is sound-insulated, it is quiet enough to be used in home appliances. We diagram this relationship as:


SI = sound-insulated
HA = quiet enough to be used in home appliances

Sufficient Necessary

SI HA


Next, we are told that a motor quiet enough to use in home appliances (HA) is quiet enough to use in institutional settings:


IS = quiet enough to use in institutional settings

.....HA IS


However, if a motor is manufactured by EM Industries, then it is not quiet enough to use in home appliances:


EM = manufactured by EM Industries

.....EM HA


and its contrapositive, to make use of the common term HA:


.....HA EM


We can combine these terms together to get additive inferences, starting with the first and second relationships:


SI HA IS, which we can shorten to SI IS


to gain the inference that if a motor is sound-insulated (SI), then it is quiet enough to use in institutional settings (IS).

We can also combine the first and third relationships together:


SI HA EM, which we can shorten to SI EM


to gain the inference that if a motor is sound-insulated (SI), then it is not manufactured by EM Industries (EM).

The question stem indicates that this is a Must Be True question. Our prephrase is that the correct answer choice may test us on any of the conditional relationships or inferences described above.

Answer choice (A): Diagrammed as IS SI, this is a Mistaken Reversal of our first inference (SI IS).

Answer choice (B): This is the correct answer choice. Diagrammed as EM SI, this is the contrapositive of our second inference (SI EM).

Answer choice (C): While the stimulus tells us that a motor quiet enough to be used in home appliances can be used in institutional settings, the evidence does not tell us whether motors that are too noisy for use in home appliances can be used in institutional settings.

Answer choice (D): Diagrammed as HA SI, this is a Mistaken Reversal of our first relationship (SI HA).

Answer choice (E): As with answer choice (C), the stimulus does not tell us whether motors that are too loud for use in home appliances can be used in institutional settings.

[catatom]

Answer choice (E): As with answer choice (C), the stimulus does not tell us whether motors that are too loud for use in home appliances can be used in institutional settings.

I don't understand how answer E is wrong because although the stimulus does not tell us whether motors that are too loud for use in home appliances can be used in institutional settings, the stimulus does tell us that if a motor is quite enough to use in home then it is quite enough to use in institutional then the stimulus says that none of the motors manufactured by EM are quite enough to use in home so therefore if EM are not quite enough to use in home then they are not quite enough to use in institutional. Right? How is this wrong?

[Jeremy Press]

Hi catatom,

It's true that the second sentence tells us that IF a motor is quiet enough to use in home appliances, THEN it can be used in institutional settings. In conditional terms, the diagram of that relationship would be: QE IS. The necessary condition in that relationship (indicated by the term "THEN") is "can be used in institutional settings." What you have to remember is that any necessary condition is something that could potentially be present with OR without its sufficient condition. So, a motor might be able to be used in an institutional setting but NOT be quiet enough to use in home appliances. Since that possibility exists, we can't infer solely from the fact that EM's motor are not quiet enough to use in home appliances that they cannot be used in institutional settings. To make that inference would be to make a mistake PowerScore calls a "Mistaken Negation" (taking the absence of a sufficient condition as proof that a necessary condition didn't happen).

Here's a simpler (real-world true) example: IF you attend a law school, THEN you must have applied to that law school. In conditional terms, the diagram of that relationship would be: Attend Apply. The necessary condition in that relationship is "applied (to the law school)." It can occur (someone can apply) with or without that person ever attending that law school. So, just because someone does NOT attend a particular law school doesn't mean that person did NOT apply to that school. Indeed, a person might apply and then decide not to attend (for whatever reason), or they might apply and then not be admitted, etc.

I hope this helps!