A merchant's markup for an item is the merchant's selling price for the item minus the merchant's total cost for...

Understanding the Question

We need to determine whether the markup for Item X is greater than 45% of the merchant's total cost.

Let's translate this into simple terms:

• Markup = \(\mathrm{Selling\ Price - Total\ Cost}\)
• Question: Is \(\mathrm{Markup} > 45\% \mathrm{\ of\ Total\ Cost}\)?

In other words, if the merchant pays $100 for an item, we're asking: Is the markup more than $45?

What "sufficient" means here: We need to be able to answer definitively YES or NO to whether the markup exceeds 45% of the cost. If we can determine this with certainty, the statement(s) are sufficient.

Given Information

• Markup definition: Selling Price - Total Cost
• We need a yes/no answer about whether markup > 45% of cost

Key Insight

When markup is expressed as a percentage of selling price (rather than cost), it creates a fixed, deterministic relationship with the cost percentage. This will be crucial for Statement 1.

Analyzing Statement 1

Statement 1 tells us: The markup for Item X is 35% of the selling price.

This gives us a specific relationship. Let's think about what this means:

• If the selling price is $100, then the markup is $35
• Since Cost = Selling Price - Markup, the cost must be $65

Here's the key insight: If markup is 35% of selling price, then cost must be 65% of selling price. This creates a fixed ratio between markup and cost.

For every $65 of cost, there's $35 of markup.

The crucial question: Is $35 more than 45% of $65?

Let's check: \(45\% \times \$65 = 0.45 \times \$65 = \$29.25\)

Since \(\$35 > \$29.25\), the answer is YES - the markup is greater than 45% of the cost.

[STOP - Statement 1 is Sufficient!]

Statement 1 gives us a definitive answer. This eliminates choices B, C, and E.

Analyzing Statement 2

Important: We must forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: The markup for Item X is greater than 7/16 of the total cost.

Let's understand what 7/16 means:

• \(\frac{7}{16} = 0.4375\) (or 43.75%)
• This is just slightly less than 45%

So Statement 2 tells us that markup > 43.75% of cost, but we need to know if markup > 45% of cost.

The critical issue: The gap between 43.75% and 45% allows for both YES and NO answers.

Testing Different Scenarios

Scenario 1: What if the markup is exactly 44.5% of cost?

• This satisfies Statement 2 (44.5% > 43.75%) ✓
• But 44.5% < 45%, so the answer to our question is NO

Scenario 2: What if the markup is 46% of cost?

• This satisfies Statement 2 (46% > 43.75%) ✓
• And 46% > 45%, so the answer to our question is YES

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

This eliminates choices B and D.

The Answer: A

Statement 1 alone tells us the exact relationship between markup and cost (35% of selling price = approximately 54% of cost), allowing us to definitively answer YES.

Statement 2 only gives us a lower bound (>43.75%) that's too close to our 45% threshold to be conclusive - it allows both YES and NO answers.

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