The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute...

Understanding the Question

Let's break down what we're really asking here. We have a phone call with a specific cost structure:

• First 3 minutes: \(\$0.75\) flat fee
• Each additional minute: \(\$0.20\)

The question asks: Did the call last longer than 15 minutes?

This is a yes/no question. We need sufficient information to answer either "Yes, it definitely lasted longer than 15 minutes" or "No, it definitely did not last longer than 15 minutes."

Key Insight

Since the cost increases linearly with time after 3 minutes, there's a direct relationship: higher cost means longer call. Here's the crucial calculation:

A 15-minute call would cost exactly:

• First 3 minutes: \(\$0.75\)
• Additional 12 minutes: \(\$0.20 \times 12 = \$2.40\)
• Total: \(\$0.75 + \$2.40 = \$3.15\)

Therefore, our question transforms into something much simpler: Did the call cost more than $3.15?

• If cost > $3.15 → Call lasted > 15 minutes → Answer is YES
• If cost ≤ $3.15 → Call lasted ≤ 15 minutes → Answer is NO

Analyzing Statement 1

Statement 1 tells us: The cost of the phone call was less than $4.16.

Since we need to know if the cost exceeded $3.15, knowing only that it was less than $4.16 doesn't help us determine the answer. The cost could be:

• $3.00 (which is < $3.15) → Call lasted < 15 minutes → Answer: NO
• $3.50 (which is > $3.15 but still < $4.16) → Call lasted > 15 minutes → Answer: YES

Both scenarios fit within Statement 1's constraint, but they lead to opposite answers to our question.

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 tells us: The cost of the phone call was greater than $3.35.

This gives us exactly what we need! Since $3.35 > $3.15 (our threshold for 15 minutes), we know the call definitely lasted longer than 15 minutes.

Think about it this way: If the minimum cost was $3.35, and a 15-minute call only costs $3.15, then the call must have gone beyond 15 minutes to reach that higher cost.

We can definitively answer YES to the question.

Statement 2 is sufficient.

[STOP - Sufficient!] Since Statement 1 alone was not sufficient but Statement 2 alone is sufficient, the answer is B.

The Answer: B

Statement 2 alone gives us enough information to answer the question definitively, while Statement 1 alone does not.

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