Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last...

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## Understanding the Question

We need to determine: **Did the company sell more than 21,000 units of product X last year?**

This is a yes/no question - we need to definitively answer YES or NO to have sufficiency.

### Given Information
- The company manufactured and sold every unit of product X it produced
- Total expenses = $100,000 + 5% of total revenue
- The company made a profit on product X

### What We Need to Determine
To answer whether units sold > 21,000, we need either:
- The number of units sold directly, OR
- Enough information to calculate units sold (Revenue ÷ Price per unit)

### Key Insight
Since the company made a profit:
- Revenue > Expenses
- Revenue > $100,000 + 0.05 × Revenue
- This means Revenue must be substantially above $100,000

## Analyzing Statement 1

**Statement 1**: The company's total revenue from the sale of product X last year was greater than $110,000.

### What This Tells Us
We know revenue exceeds $110,000, but we still don't know the price per unit.

### Testing Different Scenarios
Without the price per unit, we can't determine how many units were sold:
- If price = $1 per unit and Revenue > $110,000 → Units > 110,000 (YES, more than 21,000)
- If price = $10 per unit and Revenue > $110,000 → Units > 11,000 (NO, less than 21,000)

Since different prices lead to different answers to our yes/no question, Statement 1 is **NOT sufficient**.

**[STOP - Not Sufficient!]** This eliminates choices A and D.

## Analyzing Statement 2

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

**Statement 2**: For each unit of product X sold last year, the company's revenue was $5.

### What This Reveals
Now we know the price per unit is $5. Let's check what happens at the threshold of exactly 21,000 units:

**At 21,000 units:**
- Revenue = $5 × 21,000 = $105,000
- Expenses = $100,000 + 5% × $105,000 = $100,000 + $5,250 = $105,250
- Profit = $105,000 - $105,250 = **-$250 (a LOSS!)**

### The Critical Insight
Since selling exactly 21,000 units would result in a loss, and we know the company made a profit, they MUST have sold MORE than 21,000 units.

Statement 2 is **sufficient** - we can definitively answer YES.

**[STOP - Sufficient!]** This eliminates choices C and E.

## The Answer: B

Since only Statement 2 provides sufficient information to answer the question, the answer is B.

**Answer Choice B**: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."

Understanding the Question

We need to determine: Did the company sell more than 21,000 units of product X last year?

This is a yes/no question - we need to definitively answer YES or NO to have sufficiency.

Given Information

• The company manufactured and sold every unit of product X it produced
• Total expenses = $100,000 + 5% of total revenue
• The company made a profit on product X

What We Need to Determine

To answer whether units sold > 21,000, we need either:

• The number of units sold directly, OR
• Enough information to calculate units sold (Revenue ÷ Price per unit)

Key Insight

Since the company made a profit:

• \(\mathrm{Revenue} > \mathrm{Expenses}\)
• \(\mathrm{Revenue} > \$100,000 + 0.05 \times \mathrm{Revenue}\)
• This means Revenue must be substantially above $100,000

Analyzing Statement 1

Statement 1: The company's total revenue from the sale of product X last year was greater than $110,000.

What This Tells Us

We know revenue exceeds $110,000, but we still don't know the price per unit.

Testing Different Scenarios

Without the price per unit, we can't determine how many units were sold:

• If price = $1 per unit and Revenue > $110,000 → Units > 110,000 (YES, more than 21,000)
• If price = $10 per unit and Revenue > $110,000 → Units > 11,000 (NO, less than 21,000)

Since different prices lead to different answers to our yes/no question, Statement 1 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

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

Statement 2: For each unit of product X sold last year, the company's revenue was $5.

What This Reveals

Now we know the price per unit is $5. Let's check what happens at the threshold of exactly 21,000 units:

At 21,000 units:

• \(\mathrm{Revenue} = \$5 \times 21,000 = \$105,000\)
• \(\mathrm{Expenses} = \$100,000 + 5\% \times \$105,000 = \$100,000 + \$5,250 = \$105,250\)
• \(\mathrm{Profit} = \$105,000 - \$105,250 = -\$250\) (a LOSS!)

The Critical Insight

Since selling exactly 21,000 units would result in a loss, and we know the company made a profit, they MUST have sold MORE than 21,000 units.

Statement 2 is sufficient - we can definitively answer YES.

[STOP - Sufficient!] This eliminates choices C and E.

The Answer: B

Since only Statement 2 provides sufficient information to answer the question, the answer is B.

Answer Choice B: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."