Maria can either buy a basket that contains p pounds of apples for $16.50 or buy p pounds of apples...

markdown
Understanding the Question

Let's break down what we're being asked. Maria has two options for buying apples:

Buy a basket containing p pounds for a fixed price of \(\$16.50\)
Buy p pounds individually at \(\$0.95\) per pound


We need to determine: Does the basket cost MORE than buying individually?

This is a yes/no question. For a statement to be sufficient, it must allow us to definitively answer either "Yes, the basket costs more" or "No, the basket doesn't cost more."

What We Need to Determine

The basket costs \(\$16.50\) regardless of weight. Buying individually costs \(\$0.95 \times \mathrm{p}\). So we're asking: Is \(\$16.50 > \$0.95\mathrm{p}\)?

This is essentially a "break-even" problem. The basket becomes a worse deal (costs more) when the weight is small enough that buying individually would be cheaper.

Analyzing Statement 1

Statement 1 tells us: The basket contains less than 20 pounds of apples \((\mathrm{p} < 20)\).

This gives us a range of possible values for p, but let's think about what this means for our comparison.

Testing Different Scenarios

If p is small (say 10 pounds):

Individual purchase: \(10 \times \$0.95 = \$9.50\)
Basket price: \(\$16.50\)
Since \(\$9.50 < \$16.50\), the basket costs MORE ✓


If p is close to 20 (say 19 pounds):

Individual purchase: \(19 \times \$0.95 = \$18.05\)
Basket price: \(\$16.50\)
Since \(\$18.05 > \$16.50\), the basket costs LESS ✗


Since we can get different answers (YES the basket costs more when p is small, and NO it doesn't when p is large), 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: It would cost Maria \(\$18.05\) to buy p + 4 pounds of apples at \(\$0.95\) per pound.

This is actually quite helpful! If (p + 4) pounds costs \(\$18.05\), we can figure out exactly what p pounds would cost.

Logical Analysis

Since 4 additional pounds would cost \(4 \times \$0.95 = \$3.80\), we know that:

(p + 4) pounds costs \(\$18.05\)
p pounds costs \(\$18.05 - \$3.80 = \$14.25\)


Now we can directly compare:

Basket price: \(\$16.50\)
Individual purchase price: \(\$14.25\)


Since \(\$16.50 > \$14.25\), the answer is YES - the basket costs more than buying individually.

[STOP - Sufficient!] Statement 2 gives us enough information to definitively answer the question.

This eliminates choices C and E.

The Answer: B

Statement 2 alone is sufficient because it allows us to calculate the exact cost of buying p pounds individually (\(\$14.25\)) and compare it to the basket price (\(\$16.50\)). We get a definitive "yes" answer.

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