At a history museum, the price of each regular admission ticket sold last Sunday was 30% less than the price...

Understanding the Question

Let's break down what we're looking for: the museum's revenue from Saturday ticket sales alone.

Given Information

• Sunday's ticket price was 30% less than Saturday's (meaning \(\mathrm{Sunday} = 70\% \text{ of } \mathrm{Saturday}\))
• Total revenue from both days combined = \(\$6,150\)
• We need Saturday's revenue specifically

What We Need to Determine

To find Saturday's revenue, we need to know either:

• The exact price and quantity of Saturday tickets, OR
• How the \(\$6,150\) total splits between the two days

Think of this as a puzzle where \(\mathrm{Saturday's\ revenue} + \mathrm{Sunday's\ revenue} = \$6,150\). We need enough information to isolate Saturday's portion.

Key Insight

Since Sunday's price is locked at 70% of Saturday's price, the key question becomes: what's the relationship between the quantities sold each day? Without knowing how ticket quantities relate, we can't determine how the revenue splits.

Analyzing Statement 1

Statement 1: Sunday sold 50% more tickets than Saturday.

What Statement 1 Tells Us

This gives us the critical quantity relationship we were missing. If Saturday sold "1 unit" of tickets, then Sunday sold "1.5 units."

Logical Analysis

Here's where it gets interesting. We now know:

• Sunday sold \(1.5 \times\) as many tickets as Saturday
• BUT Sunday's tickets cost only \(0.7 \times\) as much

So Sunday's revenue = \(1.5 \times 0.7 = 1.05\) times Saturday's revenue.

This means our \(\$6,150\) total breaks down as:

• \(\mathrm{Saturday\ revenue} + 1.05 \times \mathrm{Saturday\ revenue} = \$6,150\)
• \(2.05 \times \mathrm{Saturday\ revenue} = \$6,150\)

We can now determine Saturday's revenue uniquely (it would be \(\$6,150 \div 2.05 = \$3,000\)).

Conclusion

[STOP - Sufficient!] Statement 1 is sufficient because it gives us the missing piece - the quantity relationship - which combined with the known price relationship allows us to determine exactly how the total revenue splits.

This eliminates choices B, C, and E.

Analyzing Statement 2

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

Statement 2: Saturday's ticket price was $10.

What Statement 2 Provides

We now know:

• Saturday price = \(\$10\)
• Sunday price = \(\$7\) (since it's 70% of Saturday's)
• Total revenue = \(\$6,150\)

What We Still Don't Know

The crucial missing piece is: how many tickets were sold each day? We have one equation with two unknowns:

• \(\$10 \times (\mathrm{Saturday\ tickets}) + \$7 \times (\mathrm{Sunday\ tickets}) = \$6,150\)

Testing Different Scenarios

Let's see if different quantity combinations could work:

Scenario 1: If Saturday sold 300 tickets and Sunday sold 450 tickets:

• Saturday revenue = \(\$10 \times 300 = \$3,000\)
• Sunday revenue = \(\$7 \times 450 = \$3,150\)
• Total = \(\$6,150\) ✓

Scenario 2: If Saturday sold 400 tickets and Sunday sold 307 tickets:

• Saturday revenue = \(\$10 \times 400 = \$4,000\)
• Sunday revenue = \(\$7 \times 307 = \$2,149\)
• Total = \(\$6,149 \approx \$6,150\) ✓

Since different quantity combinations give us different Saturday revenues (\(\$3,000\) vs \(\$4,000\)), we cannot determine a unique answer.

Conclusion

Statement 2 is NOT sufficient because without knowing the relationship between quantities sold, we can't determine Saturday's specific revenue.

This eliminates choice D.

The Answer: A

Since Statement 1 alone is sufficient (it provides the quantity relationship needed to determine the revenue split) but Statement 2 alone is not sufficient (it leaves the quantity relationship unknown), the answer is A.

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