Participants in a certain road race competed not only against the entire field, but also against several smaller subfields based...

OWNING THE DATASET

Let's start by understanding this race time rankings table with a focus on efficiency. This dataset shows how participants performed in different subfields (G, H, J, K) of a race.

Key observations that will help us solve quickly:

• Lower numbers represent better rankings (1st place is better than 8th)
• Not all participants competed in all subfields (marked as 'n/a')
• We need to compare participants 13, 17, and 41 against participant 30

Looking at participant 30's row as our reference point:
Participant 30: G(4), H(6), J(5), K(n/a)

Key insight: To determine if someone had a faster overall race time, we don't need to calculate anything - we just need to check if they consistently ranked better than participant 30 in the subfields they both competed in.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: Participant 13 had a faster overall race time than participant 30.
What we're looking for:

• Participant 13's rankings in subfields where both 13 and 30 competed
• Whether 13 consistently ranked better (lower numbers) than 30 in these shared subfields

In other words: Did participant 13 generally outperform participant 30 in the subfields they both participated in?

Let's compare their rankings efficiently:

Subfield G: 13(3) vs 30(4) → 13 ranked better ✓
Subfield H: 13(5) vs 30(6) → 13 ranked better ✓

We've found a clear pattern! Participant 13 ranked better than participant 30 in both subfields G and H. This consistent pattern provides strong evidence that participant 13 had a faster overall race time.

Teaching callout: Notice how we didn't need to check subfields J and K. When we see a consistent pattern across multiple subfields, we can make a confident determination without examining every single data point. This is the 2-Point Pattern rule in action.

Statement 1 verdict: Yes, participant 13 had a faster overall race time than participant 30.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: Participant 17 had a faster overall race time than participant 30.
What we're looking for:

• Participant 17's rankings in subfields where both 17 and 30 competed
• Whether 17 consistently ranked better than 30 in these shared subfields

In other words: Did participant 17 generally outperform participant 30 in their shared subfields?

Let's compare efficiently:

Subfield G: 17(6) vs 30(4) → 30 ranked better ✗
Subfield J: 17(7) vs 30(5) → 30 ranked better ✗

Here's where our efficient approach pays off! We've found two subfields where participant 30 consistently ranked better than participant 17. This pattern clearly indicates that participant 17 did NOT have a faster overall race time than participant 30.

Teaching callout: Having two consistent data points showing participant 30 outperforming participant 17 gives us sufficient confidence in our answer. We don't need to waste time checking subfield K.

Statement 2 verdict: No, participant 17 did not have a faster overall race time than participant 30.

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: Participant 41 had a faster overall race time than participant 30.
What we're looking for:

• Participant 41's rankings in subfields where both 41 and 30 competed
• Whether 41 consistently ranked better than 30 in these shared subfields

In other words: Did participant 41 generally outperform participant 30 in the subfields they both competed in?

Let's compare efficiently:

Subfield G: 41(8) vs 30(4) → 30 ranked better ✗
Subfield H: 41(8) vs 30(6) → 30 ranked better ✗

The evidence is even stronger here! Not only did participant 30 outrank participant 41 in both subfields, but the differences are substantial (4 vs 8 and 6 vs 8). This provides compelling evidence that participant 41 did NOT have a faster overall race time than participant 30.

Teaching callout: The magnitude of the differences matters! When we see large gaps in rankings (like 4 vs 8), it provides even stronger evidence than smaller gaps. This allows us to be more confident in our conclusion with fewer comparisons.

Statement 3 verdict: No, participant 41 did not have a faster overall race time than participant 30.

FINAL ANSWER COMPILATION

Based on our efficient analysis:

• Statement 1 (Participant 13 vs 30): Yes
• Statement 2 (Participant 17 vs 30): No
• Statement 3 (Participant 41 vs 30): No

Therefore, our answer is: Yes, No, No