Generally, not every person who has reserved a seat on a commercial airline flight arrives to board the flight. If...

Understanding the Question

Let's break down what we're being asked. We have:

• 100 people reserved seats
• Only 95 seats available on the plane
• Not everyone who reserves actually shows up

What We Need to Determine: Was there a seat for each person who arrived?

This is a yes/no question. To answer "yes," we need to prove that at most 95 people arrived (everyone who showed up got a seat). To answer "no," we need to prove that more than 95 people arrived (some people who showed up didn't get seats).

The key insight: We need to determine whether \(\mathrm{arrivals} \leq 95\) or \(\mathrm{arrivals} > 95\).

Analyzing Statement 1

Statement 1 says: At most 96% of the 100 people who reserved arrived.

This means: Number of arrivals \(\leq 96\% \times 100 = 96\) people

Testing Different Scenarios

Let's check if this gives us a definitive answer:

• If exactly 96 people arrived: Since we only have 95 seats, one person wouldn't get a seat. Answer: NO
• If exactly 95 people arrived: Everyone gets a seat. Answer: YES
• If fewer than 95 people arrived: Everyone gets a seat. Answer: YES

Since we can get both YES and NO answers depending on the actual number within our constraint, Statement 1 is NOT sufficient.

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

Analyzing Statement 2

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

Statement 2 says: At least 4% of the 100 people who reserved did not arrive.

This means at least 4 people didn't show up, so at most 96 people arrived.

Wait—this gives us the exact same constraint as Statement 1: \(\mathrm{arrivals} \leq 96\).

Testing Different Scenarios

Since we have the same constraint, we get the same possibilities:

• If exactly 96 people arrived: Not enough seats. Answer: NO
• If 95 or fewer arrived: Enough seats. Answer: YES

Since we can still get both YES and NO answers, Statement 2 is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Statements

Using both statements together:

• Statement 1: At most 96 people arrived
• Statement 2: At most 96 people arrived

Both statements provide identical information! They both tell us that \(\mathrm{arrivals} \leq 96\).

Even with both pieces of information combined, we still face the same uncertainty:

• Could be 96 arrivals → Answer: NO (not enough seats)
• Could be 95 or fewer arrivals → Answer: YES (enough seats)

Since we can still get different answers to our yes/no question, the statements together are NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice C.

The Answer: E

The statements together are not sufficient because they both provide the same constraint (at most 96 arrivals), which still allows for both YES and NO answers to our question.

To be sufficient, we would need to know either:

• The exact number of arrivals, OR
• That arrivals were definitely \(\leq 95\) (guaranteeing YES), OR
• That arrivals were definitely \(> 95\) (guaranteeing NO)

Since neither statement alone nor both together provide this certainty, the answer is E.