Last year company A and company B produced the same product. Last year company A's revenue from the product was...

Understanding the Question

We need to find the exact dollar difference between Company A's revenue and Company B's revenue from the same product.

What We Need to Determine

The question asks for a specific value: \(\mathrm{Revenue_A - Revenue_B}\) (in dollars).

Since revenue = price per unit × quantity sold, we're looking for:
\(\mathrm{(Price_A \times Quantity_A) - (Price_B \times Quantity_B)}\)

Key Insight

For a definitive answer, we need either:

1. Actual values for prices and quantities, OR
2. Relationships that allow us to calculate a unique dollar difference regardless of the specific values

Analyzing Statement 1

Statement 1 tells us: Company A's price per unit was $2.25 higher than Company B's price per unit.

This gives us the price relationship, but we still don't know:

• The actual prices charged by either company
• How many units each company sold

Testing Different Scenarios

Let's check if different quantities lead to the same revenue difference:

Scenario 1: Both companies sell 100 units
- Company A's extra revenue = \(\mathrm{\$2.25 \times 100 = \$225}\)

Scenario 2: Both companies sell 1,000 units
- Company A's extra revenue = \(\mathrm{\$2.25 \times 1,000 = \$2,250}\)

Since different quantities produce different revenue differences, we cannot determine a unique value.

Statement 1 alone is NOT sufficient.

[STOP - Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: Company A sold 150 more units than Company B.

This gives us the quantity relationship, but we still don't know:

• The actual quantities sold by either company
• The prices charged by either company

Testing Different Scenarios

Let's check if different prices lead to the same revenue difference:

Scenario 1: Both companies charge $10 per unit
- Company A's extra revenue = \(\mathrm{150 \text{ units} \times \$10 = \$1,500}\)

Scenario 2: Both companies charge $20 per unit
- Company A's extra revenue = \(\mathrm{150 \text{ units} \times \$20 = \$3,000}\)

Since different prices produce different revenue differences, we cannot determine a unique value.

Statement 2 alone is NOT sufficient.

[STOP - Sufficient!] This eliminates choices B and D (already eliminated).

Combining Statements

Now we know both:

• Company A charged $2.25 more per unit than Company B
• Company A sold 150 more units than Company B

Why Together They Aren't Sufficient

The revenue difference comes from three sources:

1. Extra revenue from A's higher price on the units both companies sold
2. Revenue from A's additional 150 units at A's price
3. The missing comparison revenue from B not selling those 150 units

Let's test if different base values for Company B yield the same revenue difference:

Test Case 1: Company B sold 100 units at $10

• Company A sold 250 units (100 + 150) at $12.25 ($10 + $2.25)
• Company A's revenue: \(\mathrm{250 \times \$12.25 = \$3,062.50}\)
• Company B's revenue: \(\mathrm{100 \times \$10 = \$1,000}\)
• Revenue difference = $2,062.50

Test Case 2: Company B sold 200 units at $10

• Company A sold 350 units (200 + 150) at $12.25 ($10 + $2.25)
• Company A's revenue: \(\mathrm{350 \times \$12.25 = \$4,287.50}\)
• Company B's revenue: \(\mathrm{200 \times \$10 = \$2,000}\)
• Revenue difference = $2,287.50

Since we get different revenue differences ($2,062.50 vs $2,287.50) depending on Company B's actual values, the statements together are still not sufficient.

The statements together are NOT sufficient.

[STOP - Sufficient!] This eliminates choices C (and A, B, D already eliminated).

The Answer: E

Even with both the price difference ($2.25) and quantity difference (150 units), the actual revenue difference depends on Company B's base price and quantity, which remain unknown.

Answer Choice E: "The statements together are not sufficient."