A computer user wants to save 6 files, each of a different size, on a CD. The CD will hold...

Understanding the Question

The question asks: "Will the CD hold all 6 files?" This is a yes/no question.

What We Need to Determine

We need to know if the total size of all 6 files is \(\leq 700\) megabytes. To answer with certainty, we need either:

• The exact total size of all 6 files, OR
• Enough information to determine definitively whether the total exceeds 700 MB

Given Information

• 6 files, each of a different size
• CD capacity: 700 megabytes
• Files must have distinct sizes (no two files can be the same size)

Analyzing Statement 1

Statement 1: The average size of the 3 largest files is 150 megabytes.

What Statement 1 Tells Us

From this statement, we know:

• Sum of the 3 largest files = \(3 \times 150 = 450\) MB
• We know nothing about the sizes of the 3 smallest files

Testing Different Scenarios

Let's test whether different scenarios give us different answers to determine sufficiency:

Scenario 1: The 3 smallest files are very small

• Say the smallest three are 1 MB, 2 MB, and 3 MB
• Total = \(450 + 6 = 456\) MB \(< 700\) MB
• Answer: YES, the CD will hold all files

Scenario 2: The 3 smallest files are large (but still smaller than the largest three)

• Say the smallest three are 100 MB, 101 MB, and 102 MB
• Total = \(450 + 303 = 753\) MB \(> 700\) MB
• Answer: NO, the CD won't hold all files

Conclusion for Statement 1

Since we can get both YES and NO answers depending on the sizes of the remaining files, Statement 1 is 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: The smallest file is 125 megabytes.

What Statement 2 Provides

This tells us the minimum size constraint for all files. Since all 6 files have different sizes and the smallest is 125 MB, we can determine the minimum possible total.

The Key Insight

Here's the crucial reasoning: If the smallest file is 125 MB and all files must have different sizes, then:

• The 6 files must be at least: 125, 126, 127, 128, 129, and 130 MB
• Why? Because each file needs a different size, and we need the smallest possible values
• Minimum total = \(125 + 126 + 127 + 128 + 129 + 130 = 765\) MB

Since even the minimum possible total (765 MB) exceeds the CD capacity (700 MB), we know with absolute certainty that the answer is NO—the CD cannot hold all 6 files.

[STOP - Sufficient!] Statement 2 alone gives us a definitive answer.

Conclusion for Statement 2

Statement 2 is sufficient because it allows us to definitively answer NO.

This eliminates choices C and E.

The Answer: B

Statement 2 alone provides enough information to determine that the CD cannot hold all 6 files, while Statement 1 alone leaves too much uncertainty about the total size.

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