The table shows information about the 6 types of specialty screws manufactured by ACME Hardware. These screws can be purchased...

OWNING THE DATASET

Let's start by understanding this hardware table with the intention of "owning the dataset" completely. We're looking at a small but information-rich table with only 6 screws (E through J) with several key characteristics.

Looking at this small dataset, we immediately notice:

• There are three different head types: pan, flat, and button
• There are two drive types: Phillips and flat
• The "Factory Outlet" column shows "Yes" or "No" (this likely indicates special order requirements)
• Price per box varies from around $11 to $17
• Each box contains 50 screws

Key insight: With only 6 screws to analyze, visual scanning will be faster than formal sorting. Let's keep this entire dataset in our working memory as we approach the statements.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "The button head screw with the flat drive can be purchased at the factory outlet."
What we're looking for:

• Find all button head screws
• Check which ones have flat drive
• Verify if that screw can be purchased at factory outlet (is "Yes")

In other words: Is the button head + flat drive screw available at the factory outlet?

Let's use our small dataset size to our advantage. Instead of checking every screw for both criteria:

1. First, let's identify all button head screws: Looking through our 6 screws, we see only screw G has a button head.
2. Now check if G has a flat drive: Yes, it does have a flat drive.
3. Finally, check if G is available at the factory outlet: Yes, it shows "Yes" in the factory outlet column.

Therefore, statement 1 is REQUIRES SPECIAL ORDER - the button head screw with flat drive (G) can be purchased at the factory outlet.

Teaching callout: Notice how we filtered by the most restrictive criterion first (button head) since there was only one such screw. With tiny datasets like this one, identifying the most restrictive property first can dramatically reduce our work.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "The pan head screw with the Phillips drive requires special order."
What we're looking for:

• Find all pan head screws
• Check which ones have Phillips drive
• Verify if that screw requires special order (factory outlet = "No")

In other words: Does the pan head + Phillips drive screw require special order?

Using our strategic filtering approach:

1. First, identify all pan head screws: Screws E, H, and J all have pan heads.
2. Among these three, check which have Phillips drive: Only screw H has Phillips drive.
3. Check if H requires special order: Looking at the factory outlet column, it shows "No".

Since "No" in the factory outlet column means special order is required, statement 2 is REQUIRES SPECIAL ORDER - the pan head screw with Phillips drive (H) does require special order.

Teaching callout: We used the same efficient filtering approach, working from a broader category (pan head) to a narrower one (Phillips drive). This approach is especially efficient when the first criterion gives us a manageable subset to work with.

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "It is possible to purchase 250 Phillips head screws for less than $65 without special order."
What we're looking for:

• Find all Phillips drive screws
• Calculate cost of 250 screws (5 boxes) for each
• Check if any cost less than $65
• Verify if those can be purchased without special order (factory outlet = "Yes")

In other words: Can we buy 250 Phillips drive screws for under $65 from the factory outlet?

Let's break this down efficiently:

1. Identify all Phillips drive screws: Screws F, H, and I have Phillips drive.
2. Calculate approximate cost for 5 boxes (250 screws):
   • Screw F: \(\sim\mathrm{\$14} \times \mathrm{5} = \sim\mathrm{\$70}\) (over our $65 limit)
   • Screw H: \(\sim\mathrm{\$12} \times \mathrm{5} = \sim\mathrm{\$60}\) (under our limit)
   • Screw I: \(\sim\mathrm{\$17} \times \mathrm{5} = \sim\mathrm{\$85}\) (over our limit)
3. Only screw H falls under our $65 budget, but we already determined in Statement 2 that H requires special order.

Therefore, statement 3 is DOES NOT REQUIRE SPECIAL ORDER - it's not possible to purchase 250 Phillips drive screws for less than $65 without special order.

Teaching callout: We used quick estimation rather than exact calculations, which saved time. We also leveraged knowledge from Statement 2 about screw H requiring special order, which eliminated the need to recheck that information.

FINAL ANSWER COMPILATION

Let's compile our findings:

• Statement 1: REQUIRES SPECIAL ORDER - The button head screw with flat drive can be purchased at factory outlet
• Statement 2: REQUIRES SPECIAL ORDER - The pan head screw with Phillips drive requires special order
• Statement 3: DOES NOT REQUIRE SPECIAL ORDER - It's not possible to purchase 250 Phillips screws for less than $65 without special order

The answer is B (Statements 1 and 2 are true, Statement 3 is false).

LEARNING SUMMARY

Skills We Used

• Visual Processing: With only 6 screws, we processed the entire dataset visually rather than using formal sorting
• Strategic Filtering: We identified the most restrictive property first to quickly narrow down our search
• Quick Estimation: For Statement 3, approximating prices was sufficient to determine which options were viable
• Knowledge Transfer: Information from Statement 2 helped us solve Statement 3 more efficiently

Strategic Insights

• Dataset Size Determines Strategy: For tiny datasets \((\leq\mathrm{7} \text{ items})\), visual processing beats formal sorting
• Property Restriction: Always filter by the most restrictive property first to minimize the number of items to check
• Cross-Statement Learning: Information learned in one statement can be applied to others for efficiency

Common Mistakes We Avoided

• We didn't waste time sorting the tiny dataset when visual scanning was faster
• We didn't perform exact calculations when approximations were sufficient
• We avoided redundant checks by using information we had already established
• We didn't check all screws for multiple criteria simultaneously when sequential filtering was more efficient

Remember, in table analysis questions, adapting your approach to the dataset size is crucial:

• Tiny datasets \((\leq\mathrm{7} \text{ items})\): Use visual processing
• Small datasets \((\mathrm{8-15} \text{ items})\): Mental grouping then visual scanning
• Medium datasets \((\mathrm{16-30} \text{ items})\): Quick sort then look for patterns
• Large datasets \((>\mathrm{30} \text{ items})\): Sort + systematic processing

This flexible approach will help you tackle any table analysis question with maximum efficiency!