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All the T-shirts a clothing store stocks are plain—and they are all in one of exactly four colors: blue, green, red, and yellow. On any day, the store sells about twice as many blue T-shirts as it does green T-shirts. Last week, did the store sell more blue T-shirts than red T-shirts?
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).
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:
Our target: Determine whether \(\mathrm{B > R}\)
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: \(\mathrm{B < R + G}\)
Let's see if this constraint alone can answer our question:
Scenario 1: \(\mathrm{B = 10, R = 6, G = 5}\)
Scenario 2: \(\mathrm{B = 10, R = 11, G = 1}\)
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.
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: \(\mathrm{B > (R + Y)/2}\)
Can this alone determine whether \(\mathrm{B > R}\)?
Scenario 1: \(\mathrm{B = 10, R = 8, Y = 10}\)
Scenario 2: \(\mathrm{B = 10, R = 15, Y = 4}\)
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.
Now let's examine what happens when we use both statements together:
Scenario 1: \(\mathrm{B = 10, R = 8, G = 3, Y = 10}\)
Scenario 2: \(\mathrm{B = 10, R = 11, G = 1, Y = 6}\)
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 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."