If the majority of the residents of the apartment complex complain that their apartments are infested with ants, then...

Victoria July 6, 2019

Hi @Mia-Partridge. Sure thing!

This is a flawed parallel reasoning question, so we are looking for the answer choice that commits the same error in reasoning as the original passage.

Let's start by going through the passage.

"If the majority of the residents of the apartment complex complain that their apartments are infested with ants, then the management of the complex will have the engage the services of an exterminator."

Although this sentence does include a quantifier - 'the majority of' or 'most' - the focus of the sentence is on the actions of the complex management resulting from a majority complaint as opposed to the majority itself. Therefore, we can diagram this as a S&N statement:

Most residents complain ant infestation - > Management engage exterminator
Management does not engage exterminator - > Most residents did not complain ant infestation

The passage concludes that "the management of the complex will not have to engage the services of an exterminator." Why? Because "the majority of the residents of the complex indicate that their apartments are virtually free of ants."

The passage has effectively based its conclusion on the logic that: if the majority does not complain about an ant infestation, the management does not have to engage an exterminator.

We can see that this does not match the contrapositive statement we have diagrammed above. It is simply a negation of the original statement as opposed to the required negation and reversal, or a "mistaken negation."

Therefore, we are looking for the answer choice that makes this same error - simply negating, as opposed to negating and reversing - a S&N statement.

Answer choice A states: "a theater will be constructed in the fall if funds collected are at least sufficient to cover its cost."

Funds collected sufficient - > Theater constructed in fall
Theater not constructed in fall - > Funds collected not sufficient

A concludes: "to date, the funds collected exceed the theater's cost, so the theater will be constructed in the fall." This is a logical conclusion and is, therefore, incorrect.


Answer choice B states: "the number of flights operated by the airlines cannot be reduced unless the airlines can collect higher airfares."

Remember with 'unless' statements, you need to negate the sufficient condition.

Flights reduced - > Collect higher airfares
Did not collect higher airfares - > Flights not reduced

B concludes: "people will not pay higher airfares, so it is not the case that the number of flights will be reduced." This uses the contrapositive statement to draw a logical conclusion and, therefore, is incorrect.


Answer choice C states: "in order for the company to start the proposed building project, both the town council and the mayor must approve."

Company start building - > Town council approve AND mayor approve
Town council not approve OR mayor not approve - > Company not start building

C concludes that, "since the mayor has already approved, the building project will be started soon."

This is an incomplete case of mistaken reversal as C takes one of the necessary conditions to conclude the sufficient condition. Therefore, C is incorrect.


Answer choice E states: "either the school's principal or two thirds of the parent council must approve a change in the school dress code in order for the code to be changed."

Dress code changed - > School principal approve OR two thirds of parent council approve
School principle not approve AND two thirds of parent council not approve - > Dress code not changed

E concludes that, "since the principal will not approve a change in the dress code, the code will not be changed."

This is incomplete as we know that two thirds of the parent council must also not approve if the dress code will not be changed. However, this is not a mistaken negation and is, therefore, incorrect.


Finally, answer choice D states: "most employees will attend the company picnic if the entertainment committee is successful in getting a certain band to play at the picnic."

Committee gets band - > Most employees attend
Most employees do not attend - > Committee did not get band

D concludes that, because "that band will be out of the country on the day of the picnic... it is not true that most employees will attend."

We can see that this simply negates the original statement:

Committee gets band - > Most employees attend
Committee did not get band - > Most employees do not attend

This is the same error committed by the stimulus and is, therefore, the correct answer.

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