Tim can buy a certain computer for $800 at a local store, or he can buy the same computer for...

Understanding the Question

We need to find the exact dollar difference in sales tax between buying an \(\$800\) computer at a store versus from a catalog.

Given Information

• Computer price at both locations: \(\$800\)
• Store sales tax rate: \(\mathrm{s\%}\)
• Catalog sales tax rate: \(\mathrm{c\%}\)
• Constraint: \(\mathrm{s} > \mathrm{c}\) (store tax is higher)

What We Need to Determine

Since we're comparing tax amounts on the same \(\$800\) purchase, the key insight is this: we need to determine if we can find a unique value for the tax difference in dollars.

For this value question to be sufficient, we must arrive at exactly one numerical answer.

Analyzing Statement 1

Statement 1 tells us: \(\mathrm{s} = 2\mathrm{c}\)

This means the store tax rate is exactly double the catalog tax rate. But here's the critical question: what ARE these actual rates?

Let's test with concrete examples:

• If catalog charges 5%, then store charges 10%
  • Tax difference = \(\$800 \times (10\% - 5\%) = \$800 \times 5\% = \$40\)
• If catalog charges 10%, then store charges 20%
  • Tax difference = \(\$800 \times (20\% - 10\%) = \$800 \times 10\% = \$80\)

Since different values of c lead to different tax differences, we cannot determine a unique answer.

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 tells us: \(\mathrm{s} = \mathrm{c} + 3\)

This means the store tax rate is exactly 3 percentage points higher than the catalog tax rate.

Here's the elegant insight: When the base amount is fixed at \(\$800\), a fixed percentage point difference always yields the same dollar difference, regardless of the actual tax rates.

The tax difference = \(\$800 \times (\mathrm{s\%} - \mathrm{c\%}) = \$800 \times 3\% = \$24\)

To verify this works for any value of c:

• If c = 5% (making s = 8%): difference = \(\$800 \times 3\% = \$24\)
• If c = 10% (making s = 13%): difference = \(\$800 \times 3\% = \$24\)

The difference is always \(\$24\), no matter what c is.

Statement 2 is sufficient. [STOP - Sufficient!]

This eliminates choices C and E.

The Answer: B

Since Statement 2 alone gives us a unique value for the tax difference (\(\$24\)) while Statement 1 alone does not, the answer is B.

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