Q11 - John works five days each

[noah]

The conclusion of this argument is that John worked M-Th at the insurance company. Why?

Because there were no holidays and he didn't take a vacation, and we know that if there's no holiday or vacation he works 4 days per week at the insurance company. Oh, also, on Fridays he works as a blacksmith. (What a diverse career!)

So, what's the gap(s)? It seems like a strong argument - hard to say! But, probably we've all added in the assumption that the 4 days have to be only during the weekdays - couldn't John work Saturday or Sunday? That's the issue that (D) addresses. Since the question is asking for a necessary assumption, let's use our negation test. If we negate (D), and have John working on Saturday and/or Sunday, since Friday is locked in at the blacksmith shop (smithy?) we'll need to have John take a day off between Monday and Thursday.

Let's look at the wrong answers:

(A) is out of scope - we know that John's not on vacation. Who cares how long he vacations for at other times?

(B) is tempting, but try negating it: at some point last week, John worked a half day. Perhaps that seems like it would disqualify a day, but the argument doesn't talk about full days or half days - for all we know, a half day is fine.

(C) is simlar to (A) - it's about vacations, and we know he didn't vacation that week.

(E) is super tempting! Its negated form seems to suggest that perhaps John worked Friday both as a blacksmith and an insurance agent. But, it actually doesn't specifically suggest that. If we negate (E) we learn that there were some days on which John worked both jobs. Which day? If it was Friday, that'd be a problem for our argument. But, if it were Tuesday, who cares? Then it'd be that John did insurance M-Th, and worked as a blacksmith Tuesday and Friday.

We need the negated form of a necessary assumption to do more than simply open up an opportunity to destroy the argument, we need it to definitively destroy the argument. In this case, it's OK if John does a double shift; it would not be OK if he did a double shift on Friday - but (E) doesn't tell us about Friday.

[pewals13]

1) What is our task?

To determine what absolutely HAS to be true for the premises given in this argument to have any shot at guaranteeing the conclusion.

2) What is the conclusion?

"John must have worked in the insurance company on Monday, Tuesday, Wednesday, and Thursday last week."

3) What is the support?

i. John works five days each week except when on vacation or during weeks in which national holidays occur.
ii. Four days a week he works in an insurance company; on Fridays he works as a blacksmith
iii. Last week there were no holidays and John was not on vacation.

4) What is the gap?

We know via the contrapositive that John worked five days last week. [If NOT Vacation and If NOT National Holiday----> John works a five day week] (This is because we can translate "except" to "if not" and negate all that follows it to create a logical statement)

Because he worked five days last week, we know he spent Friday working as a blacksmith and four days working at the insurance company. Note that we do not know which four, out of the possible days in the week he worked at the insurance company.

Thus, concluding that he worked at the insurance company on Monday, Tuesday, Wednesday, and Thursday, represents an unwarranted assumption.

5.) Which answer choices are clearly wrong?

A) "John never takes a vacation of more than one week in length"
This is a premise booster--we already know that John was not on vacation last week from the stimulus, therefore, it is not the necessary assumption we are looking for.

B) "Every day last week that John worked, he worked an entire workday"
This does not appear to be relevant--I kept this one in my back pocket just in case I was missing an angle.

C) "John does not take vacations in weeks in which national holidays occur"
This is irrelevant--we already know that John was not on vacation or on holiday last week-- and thus must have been working based on the logic of the stimulus.

(D) "Last week John worked neither on Saturday nor Sunday"
This could be the correct answer, because if John did work on one of those days, he could have fulfilled his four day workweek at the insurance company without going in on Monday through Thursday.

(E) "There were no days last week on which John both worked in the insurance company and also worked as a blacksmith"
I kept this answer choice. Maybe if on Friday John both worked as a blacksmith and at the insurance company, he would not have had to keep up the Monday through Thursday workweek outlined in the conclusion.

6.) Select the correct answer

This is the phase of the answer choice selection process where I apply the negation test. Ask yourself: "Can the logic of the argument still hold if I insert the negated form of the prospective answer choice into the stimulus as a premise?"

B) NEGATION: Every day last week that John worked, he did not necessarily work for an entire workday
Could the conclusion still be guaranteed based on the evidence? Yes. If John worked a partial day on Monday, it still could be true that he "worked" at the insurance company on Monday, Tuesday, Wednesday, and Thursday.

CORRECT: D) NEGATION: John worked on both Saturday and on Sunday
If John worked on Saturday and Sunday, could the conclusion still be potentially guaranteed based on the evidence? No, if John worked on Saturday or Sunday, he would no longer need to work Monday, Tuesday, Wednesday, and Thursday to fulfill his four day workweek at the insurance company. Therefore, you must assume he did not work on Saturday or Sunday to reach the conclusion in the stimulus.

E) NEGATION: There were days last week on which John both worked in the insurance company and also worked as a blacksmith.
If this is true, do the premises have a shot at guaranteeing the conclusion? Yes. John could have worked at the blacksmith on other days in addition to Friday, while also working at the insurance company on Monday, Tuesday, Wednesday, and Thursday.

[a8l367]

Imagine that John worked the week:
M-B
T-I
W-I
T-I
F-IB

- works five days each week
- four days a week he works in an insurance company
- on Fridays he works as a blacksmith

- Therefore, he must have worked in the insurance company on Monday, Tuesday,Wednesday, and Thursday last week

So two assumptions:
1. No work on weekedns
2. Either - "only on Fridays he works as a blacksmith "
or - "four whole days a week he works in an insurance company"

Do the Stem means that
- "only on Fridays he works as a blacksmith "
- "four whole days a week he works in an insurance company"

Please clarify

[AlexisE386]

Although I picked (D) because I thought (D) is the better answer, I still do not understand why (E) is wrong.

If there were days on which John both worked in an insurance company and also worked as a blacksmith, maybe he could have worked as a blacksmith on Friday and worked in the insurance company on Mon, Tue, Wed, Fri (this means he did two jobs on Fri). This obviously goes against the conclusion of the stimulus, which says he must have worked in the insurance company on Mon, Tue, Wed and Thur.

Could anyone help explain it?

[Laura Damone]

Hi Alexis!

Like Noah said in the #officialexplanation, E isn't strictly necessary because opening up the possibility that John worked at the insurance agency on Friday is not the same as guaranteeing that he did. The argument does assume that John did not work at the insurance agency on Friday. By extension, the argument assumes that he didn't work both in the insurance agency and as a blacksmith on Friday. But the argument doesn't assume that he didn't work in both capacities on Monday, Tuesday, Wednesday, or Thursday. That's why E is incorrect. He could double up on any other weekday without destroying the argument. Make sense?