For each of 18 recent purchases that included each of Products A–D, the table shows the product subtotals (the unit...

OWNING THE DATASET

Let's start by understanding what we're working with in this table. The data shows purchase amounts in euros (€) for three different products: A, B, and C. Each product has 18 purchase amounts recorded.

A quick scan reveals some critical patterns we can leverage:

• Product A: All values are whole numbers with the smallest being €6
• Product B: Many values end in ".5" (like €7.5, €27.5, €42.5)
• Product C: Only one decimal value (€16.5) with the smallest amount being €3

These observations will be crucial for our efficient solving approach. Remember, in GMAT table analysis, spotting patterns can save us significant time compared to calculating everything.

ANALYZING STATEMENT A

Statement A Translation:
Original: "The unit price of Product A exceeds €3."
What we're looking for:

• The unit price of Product A
• Whether this unit price is greater than €3

In other words: Is each unit of Product A sold for more than €3?

Let's apply a constraint-based approach rather than calculating the exact unit price:

First, we know that all products must be sold in whole units (integers). This is a powerful constraint we can use.

Looking at our dataset, we identify the smallest purchase amount for Product A is €6. This immediately tells us something important:

• If the unit price were greater than €3, then €6 would represent fewer than 2 whole units ( €6 ÷ €3 = 2 )
• If the unit price were greater than €3 (let's say €3.01), then €6 would buy 1.99 units, which violates our integer constraint

Since purchases must be in whole units, and €6 is the smallest purchase amount, the unit price cannot exceed €6 ÷ 2 = €3.

Therefore, Statement A is SUFFICIENT. The unit price of Product A cannot exceed €3.

Teaching Callout: Notice how we didn't need to calculate the GCD of all 18 values! By focusing on the minimum purchase amount and applying the integer constraint, we found our answer with minimal calculation.

ANALYZING STATEMENT B

Statement B Translation:
Original: "The unit price of Product B exceeds €3."
What we're looking for:

• The unit price of Product B
• Whether this unit price is greater than €3

In other words: Is each unit of Product B sold for more than €3?

For Product B, we notice a revealing pattern - many values end in ".5" (like €7.5, €27.5, €42.5). This decimal pattern immediately suggests the unit price likely ends in .5 as well.

Let's apply our efficient approach:

1. The smallest purchase amount is €5
2. If the unit price were greater than €3, then €5 would buy fewer than 2 whole units
3. What unit price both ends in .5 AND works with our constraints?
   • €2.5 is the only logical candidate ( €5 / €2.5 - 2 whole units)

Let's quickly verify: €7.5 / €2.5 = 3 units ✓

So the unit price for Product B is €2.5, which is less than €3.

Therefore, Statement B is SUFFICIENT. The unit price of Product B does not exceed €3.

Teaching Callout: By recognizing the decimal pattern (.5), we immediately narrowed down possible unit prices without converting to integers or calculating GCDs. This pattern recognition is a powerful tool in GMAT table analysis.

ANALYZING STATEMENT C

Statement C Translation:
Original: "The unit price of Product C exceeds €3."
What we're looking for:

• The unit price of Product C
• Whether this unit price is greater than €3

In other words: Is each unit of Product C sold for more than €3?

For Product C, we have a different pattern - only one value has a decimal (€16.5), and the smallest amount is €3.

Let's apply our logical approach:

1. Since the smallest purchase is €3, the unit price cannot exceed €3 (otherwise, €3 would represent less than 1 whole unit, which is impossible)
2. The unit price must divide evenly into €16.5 (our only decimal value)
3. What value is both ≤ €3 AND divides evenly into €16.5?
   • €1.5 is the only logical candidate ( €16.5 / €1.5 = 11 whole units)

Let's verify: €3 / €1.5 = 2 units ✓

So the unit price for Product C is €1.5, which is less than €3.

Therefore, Statement C is SUFFICIENT. The unit price of Product C does not exceed €3.

Teaching Callout: By focusing on both the minimum value constraint AND the single decimal value, we quickly found the unit price without needing extensive calculations. This combination of constraints is extremely powerful.

ANSWER COMPILATION

Statement A: SUFFICIENT - The unit price of Product A cannot exceed €3
Statement B: SUFFICIENT - The unit price of Product B is €2.5, which does not exceed €3
Statement C: SUFFICIENT - The unit price of Product C is €1.5, which does not exceed €3

Therefore, all three statements are sufficient to decide whether each unit price exceeds €3.

LEARNING SUMMARY

Skills We Used

1. Constraint-Based Reasoning: We used the "integer units" constraint as a powerful filter to eliminate impossible unit prices
2. Strategic Value Selection: We focused on smallest values and decimal patterns first, which revealed the answers much faster
3. Elimination Before Calculation: We used logical bounds to narrow down possible unit prices before computing exact values

Strategic Insights

1. Smallest Purchase Insight: The smallest purchase amount immediately tells us the maximum possible unit price (since units must be whole numbers)
2. Decimal Pattern Recognition: When values consistently end with the same decimal, the unit price likely has that decimal pattern
3. Single Decimal Value Focus: When only one value has a decimal, it provides crucial information about the unit price

Common Mistakes We Avoided

1. Exhaustive GCD Calculations: We didn't need to calculate the GCD of all 18 values for each product
2. Converting Decimals Unnecessarily: For Product B, we didn't convert all values to integers before finding patterns
3. Testing Multiple Unit Prices: We used constraints to identify the only possible unit price rather than testing multiple candidates

Remember: In GMAT Table Analysis, constraints and patterns almost always provide faster paths than exhaustive calculations. Always look for the minimum values, unusual decimals, and patterns before diving into calculations!