All the T-shirts a clothing store stocks are plain—and they are all in one of exactly four colors: blue, green,...

Understanding the Question

We need to determine: Did the store sell more blue T-shirts than red T-shirts last week?

This is a yes/no question. For sufficiency, we need to definitively answer either "yes" (more blue than red) or "no" (not more blue than red).

Given Information

• The store stocks T-shirts in exactly 4 colors: blue, green, red, and yellow
• On any day, the store sells about twice as many blue T-shirts as green T-shirts
• We're asking about last week's sales specifically

Key Insight

Notice that the "about twice as many" relationship between blue and green shirts is given for daily sales, but we're asked about weekly totals. We cannot assume this exact ratio holds for the entire week—some days might have promotions or different customer patterns.

Let's define:

• \(\mathrm{B}\) = blue T-shirts sold last week
• \(\mathrm{G}\) = green T-shirts sold last week
• \(\mathrm{R}\) = red T-shirts sold last week
• \(\mathrm{Y}\) = yellow T-shirts sold last week

Our target: Determine whether \(\mathrm{B > R}\)

Analyzing Statement 1

Statement 1 tells us: Last week, the store sold fewer blue T-shirts than red T-shirts and green T-shirts combined.

This gives us: \(\mathrm{B < R + G}\)

Testing Different Scenarios

Let's see if this constraint alone can answer our question:

Scenario 1: \(\mathrm{B = 10, R = 6, G = 5}\)

• Check constraint: \(\mathrm{B < R + G}\)? → \(\mathrm{10 < 11}\) ✓
• Is \(\mathrm{B > R}\)? → \(\mathrm{10 > 6}\), so YES

Scenario 2: \(\mathrm{B = 10, R = 11, G = 1}\)

• Check constraint: \(\mathrm{B < R + G}\)? → \(\mathrm{10 < 12}\) ✓
• Is \(\mathrm{B > R}\)? → \(\mathrm{10 < 11}\), so NO

Since we get both "yes" and "no" answers while satisfying Statement 1, this statement is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choices A and D.

Analyzing Statement 2

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

Statement 2 tells us: Last week, the store sold more blue T-shirts than half the total number of red T-shirts and yellow T-shirts combined.

This gives us: \(\mathrm{B > (R + Y)/2}\)

Testing Different Scenarios

Can this alone determine whether \(\mathrm{B > R}\)?

Scenario 1: \(\mathrm{B = 10, R = 8, Y = 10}\)

• Check constraint: \(\mathrm{B > (R + Y)/2}\)? → \(\mathrm{10 > 9}\) ✓
• Is \(\mathrm{B > R}\)? → \(\mathrm{10 > 8}\), so YES

Scenario 2: \(\mathrm{B = 10, R = 15, Y = 4}\)

• Check constraint: \(\mathrm{B > (R + Y)/2}\)? → \(\mathrm{10 > 9.5}\) ✓
• Is \(\mathrm{B > R}\)? → \(\mathrm{10 < 15}\), so NO

Again, we get both "yes" and "no" answers while satisfying Statement 2, so this statement is NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice B.

Combining Statements

Now let's examine what happens when we use both statements together:

• From Statement 1: \(\mathrm{B < R + G}\)
• From Statement 2: \(\mathrm{B > (R + Y)/2}\)

Testing Combined Constraints

Scenario 1: \(\mathrm{B = 10, R = 8, G = 3, Y = 10}\)

• Statement 1: \(\mathrm{B < R + G}\)? → \(\mathrm{10 < 11}\) ✓
• Statement 2: \(\mathrm{B > (R + Y)/2}\)? → \(\mathrm{10 > 9}\) ✓
• Is \(\mathrm{B > R}\)? → \(\mathrm{10 > 8}\), so YES

Scenario 2: \(\mathrm{B = 10, R = 11, G = 1, Y = 6}\)

• Statement 1: \(\mathrm{B < R + G}\)? → \(\mathrm{10 < 12}\) ✓
• Statement 2: \(\mathrm{B > (R + Y)/2}\)? → \(\mathrm{10 > 8.5}\) ✓
• Is \(\mathrm{B > R}\)? → \(\mathrm{10 < 11}\), so NO

Even with both statements combined, we can still generate both "yes" and "no" answers. The statements together are NOT sufficient.

[STOP - Not Sufficient!] This eliminates choice C.

The Answer: E

The statements together are not sufficient to determine whether the store sold more blue T-shirts than red T-shirts last week. We've shown that both outcomes (\(\mathrm{B > R}\) and \(\mathrm{B ≤ R}\)) are possible even when both constraints are satisfied simultaneously.

Answer Choice E: "The statements together are not sufficient."