A monthly magazine receives revenue from exactly 3 sources: advertising, newsstand sales, and subscriptions. By what percent must subscription revenue...

Understanding the Question

We need to find a specific percentage: by what percent must subscription revenues rise to offset the decreases in advertising and newsstand revenues?

What We Need to Determine

The question asks for a precise percentage value. To answer this, we need:

1. The total dollar amount that decreased (from advertising and newsstand combined)
2. The current subscription revenue (this will be our percentage base)

The required percentage = \((\mathrm{Total\,decrease\,amount} ÷ \mathrm{Current\,subscription\,revenue}) \times 100\%)\)

Key Insight

Here's the critical insight: We're looking for a percentage, which requires both a numerator (the decrease amount) and a denominator (subscription revenue). Without either piece, we cannot determine the percentage. Pay special attention to whether we ever learn anything about subscription revenue.

Analyzing Statement 1

Statement 1 tells us: Advertising revenue decreased by \(25\%\) and newsstand sales decreased by \(40\%\).

This gives us the percentage decreases, but notice what's missing:

• We don't know the original dollar amounts for advertising or newsstand revenues
• We have no information about subscription revenue whatsoever

Let's test different scenarios to confirm we can't determine a unique answer:

Scenario 1: Suppose advertising was originally \(\$20,000\) and newsstand was \(\$10,000\)

• Advertising decrease: \(25\% \times \$20,000 = \$5,000\)
• Newsstand decrease: \(40\% \times \$10,000 = \$4,000\)
• Total decrease to offset: \(\$9,000\)
• But we still don't know subscription revenue!

Scenario 2: Suppose advertising was originally \(\$25,000\) and newsstand was \(\$5,000\)

• Advertising decrease: \(25\% \times \$25,000 = \$6,250\)
• Newsstand decrease: \(40\% \times \$5,000 = \$2,000\)
• Total decrease to offset: \(\$8,250\)
• Again, no subscription revenue information!

Even if we could somehow determine the exact decrease amount, without knowing subscription revenue, we cannot calculate what percentage of it equals that decrease.

Statement 1 is NOT sufficient.

[STOP - Insufficient!] 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: Before the recent decreases, the total revenue from advertising and newsstand sales was \(\$35,500\) per month.

This gives us the combined pre-decrease amount, but we're still missing:

• How the \(\$35,500\) splits between advertising and newsstand
• What percentage or dollar amounts the revenues decreased by
• Most crucially: the subscription revenue

Without knowing how much the revenues decreased or what the subscription revenue is, we cannot determine the required percentage increase.

Statement 2 is NOT sufficient.

[STOP - Insufficient!] This eliminates choice B.

Combining Both Statements

Now let's see what we learn from both statements together:

• From Statement 2: Advertising + Newsstand = \(\$35,500\) (before decreases)
• From Statement 1: Advertising decreased by \(25\%\), newsstand decreased by \(40\%\)

Here's where students often get trapped. Even though we don't know the exact split of the \(\$35,500\), we might think we're getting closer. Let's test this carefully:

Test Case 1: If advertising was \(\$20,000\) and newsstand was \(\$15,500\):

• Advertising decrease: \(25\% \times \$20,000 = \$5,000\)
• Newsstand decrease: \(40\% \times \$15,500 = \$6,200\)
• Total decrease: \(\$11,200\)

Test Case 2: If advertising was \(\$25,000\) and newsstand was \(\$10,500\):

• Advertising decrease: \(25\% \times \$25,000 = \$6,250\)
• Newsstand decrease: \(40\% \times \$10,500 = \$4,200\)
• Total decrease: \(\$10,450\)

So different splits give us different total decreases (\(\$11,200\) vs \(\$10,450\)). But here's the crucial point that makes this problem unsolvable: We still have absolutely no information about subscription revenue!

Whether the total decrease is \(\$11,200\), \(\$10,450\), or any other amount, without knowing the subscription revenue base, we cannot calculate what percentage of it this represents.

Think of it this way: If subscription revenue is \(\$5,000\), then a \(\$10,450\) decrease requires a \(209\%\) increase. But if subscription revenue is \(\$50,000\), then the same \(\$10,450\) decrease requires only a \(20.9\%\) increase. Since we have no information about subscription revenue, we cannot determine the percentage.

The statements together are NOT sufficient.

[STOP - Insufficient!] This eliminates choice C.

The Answer: E

The statements together are not sufficient because we never receive any information about subscription revenue, which is the essential denominator for calculating the required percentage increase.

Answer Choice E: The statements together are not sufficient.