Neighborhood blog post on Saturday morning: During the past 5 days, traffic was bad on Wednesday, worse on Monday, and...

Phase 1: Owning the Dataset

Argument Analysis Table

Argument Structure

We have two separate chains of traffic comparisons:

• Chain 1: \(\mathrm{Monday} > \mathrm{Wednesday} > \mathrm{Tuesday}\) (worst to best)
• Chain 2: \(\mathrm{Thursday} > \mathrm{Friday}\) (worse to better)

The key insight: These chains aren't connected! We don't know how Thursday/Friday relate to Monday/Wednesday/Tuesday.

Phase 2: Question Analysis & Prethinking

Understanding What Each Part Asks

Part 1 - Could determine worst: We need a statement that would establish which single day had the worst traffic among all five days.

Part 2 - Could determine best: We need a statement that would establish which single day had the best traffic among all five days.

Prethinking for Each Part

For determining worst:

• Currently, Monday is worst in Chain 1 and Thursday is worst in Chain 2
• We need to know: Is Monday or Thursday worse?
• A statement comparing Monday to Thursday (or any connection between chains that reveals this) would work

For determining best:

• Currently, Tuesday is best in Chain 1 and Friday is best in Chain 2
• We need to know: Is Tuesday or Friday better?
• A statement comparing Tuesday to Friday (or any connection revealing this) would work

Phase 3: Answer Choice Evaluation

Evaluating Each Choice

1. "Traffic was better on Thursday than on Monday"
   • Means: \(\mathrm{Monday} > \mathrm{Thursday}\) (Monday had worse traffic)
   • Impact: Makes Monday worse than all days (\(\mathrm{Monday} > \mathrm{Thursday} > \mathrm{Friday}\))
   • For worst: ✓ This establishes Monday as definitively worst
   • For best: ✗ Still can't determine if Tuesday or Friday is best
2. "Traffic was better on Wednesday than on Thursday"
   • Means: \(\mathrm{Thursday} > \mathrm{Wednesday}\)
   • Impact: We'd have \(\mathrm{Thursday} > \mathrm{Wednesday}\) and \(\mathrm{Monday} > \mathrm{Wednesday}\)
   • For worst: ✗ Can't determine if Monday or Thursday is worse
   • For best: ✗ Doesn't help with Tuesday vs. Friday
3. "Traffic was better on Friday than on Wednesday"
   • Means: \(\mathrm{Wednesday} > \mathrm{Friday}\)
   • Impact: Connects chains but doesn't establish extremes
   • For worst: ✗ Still unsure about Monday vs. Thursday
   • For best: ✗ Still unsure about Tuesday vs. Friday
4. "Traffic was worse on Thursday than on Tuesday"
   • Means: \(\mathrm{Thursday} > \mathrm{Tuesday}\)
   • Impact: We'd know \(\mathrm{Thursday} > \mathrm{Tuesday}\) and \(\mathrm{Wednesday} > \mathrm{Tuesday}\)
   • For worst: ✗ Still need Monday vs. Thursday comparison
   • For best: ✗ Doesn't definitively establish best day
5. "Traffic was worse on Friday than on Tuesday"
   • Means: \(\mathrm{Friday} > \mathrm{Tuesday}\) (Tuesday has better traffic)
   • Impact: Since \(\mathrm{Thursday} > \mathrm{Friday} > \mathrm{Tuesday}\) and \(\mathrm{Wednesday} > \mathrm{Tuesday}\) and \(\mathrm{Monday} > \mathrm{Wednesday}\)
   • For worst: ✗ Doesn't help determine if Monday or Thursday is worst
   • For best: ✓ This makes Tuesday better than all other days!

The Correct Answers

For "Could determine worst": Choice A

• Adding "Traffic was better on Thursday than on Monday" establishes Monday as having worse traffic than all other days

For "Could determine best": Choice E

• Adding "Traffic was worse on Friday than on Tuesday" establishes Tuesday as having better traffic than all other days

Common Traps to Highlight

Choice B might seem attractive because it connects the two chains through Wednesday. However, it creates ambiguity rather than clarity—we'd have both Monday and Thursday worse than Wednesday, but wouldn't know which is worst overall.

Choice D also connects chains but creates a similar problem. It tells us Thursday is worse than Tuesday, but since we already know Monday and Wednesday are also worse than Tuesday, we still can't determine the single worst day.

The key to this problem is recognizing that we need statements that definitively establish one day as the extreme (worst or best) across all five days, not just create more connections.