If a motor is sound-insulated, then it is quiet enough to use in home appliances. If a motor is quiet enough to use i...

Mehran on November 27, 2017

Hi @franco, thanks for your post. This is a Must Be True question, which means that the correct answer choice must follow from the information found in the stimulus.

The stimulus presents us with a set of facts.
Premise 1: If a motor is sound-insulated, then it is quiet enough to use in home appliances.
SI ==> UHA
cp: not UHA ==> not SI

Premise 2: If a motor is quiet enough to use in home appliances, then it can be used in institutional settings.
UHA ==> UIS
cp: not UIS ==> not UHA

Premise 3: None of the motors manufactured by EM Industries are quiet enough to use in home appliances.
EM ==> not UHA

All right. Let's examine the correct answer choice (B), and your incorrect answer choice (E).

Answer choice (B) says: None of the motors manufactured by EM Industries are sound-insulated.

This must be true. Connect the positive of Premise 3 (EM ==> not UHA) with the contrapositive of Premise 1 (not UHA ==> not SI):
EM ==> not UHA ==> not SI

Therefore: None of the motors manufactured by EM Industries are sound-insulated. This must be true according to the premises presented in the stimulus.

Answer choice (E) says: None of the motors manufactured by EM Industries can be used in institutional settings. This would be diagrammed as EM ==> not UIS.

There is no way to reach this transitive conclusion using the positive or contrapositive formulations of the premises provided. For this reason, answer choice (E) does not satisfy the "must be true" requirement, and can be eliminated.

Hope this helps! Please let us know if you have any additional questions.