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

GMAT Data Sufficiency : (DS) Questions

Source: Official Guide

Data Sufficiency

DS - Money

HARD

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Notes

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Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $\$100,000$ plus $5\%$ of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than $21,000$ units of product X last year?

The company's total revenue from the sale of product X last year was greater than $\$110,000$.
For each unit of product X sold last year, the company's revenue was $\$5$.

Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

Solution

markdown
## 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."

Answer Choices Explained

Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.

Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

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markdown ## 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."