Yesterday Wanda prepared several shipments of lightbulbs and several shipments of electrical cords. How many minutes did Wanda spend preparing...

Understanding the Question

Let's break down what we're being asked: How many minutes did Wanda spend preparing the shipments of lightbulbs yesterday?

This is a value question - we need a specific number of minutes, not a yes/no answer or a comparison.

What We Need to Determine

To answer this question, we need to find the exact time spent on lightbulb shipments. This could come from:

• Direct information about lightbulb preparation time, OR
• Enough information to calculate it uniquely (like knowing the total time AND how it's split between the two types)

Key Insight

The challenge here is that Wanda prepared two types of shipments - lightbulbs and electrical cords. Without knowing either the exact split of time OR the number of each type of shipment, we can't determine the specific minutes spent on lightbulbs.

Analyzing Statement 1

Statement 1: The average time per lightbulb shipment was 20% greater than the average time per cord shipment.

What Statement 1 Tells Us

This gives us the relationship between the two average times - if a cord shipment takes 10 minutes on average, a lightbulb shipment takes 12 minutes (20% more).

Testing Different Scenarios

But here's the crucial question: How many of each type did she prepare?

Scenario 1: What if Wanda prepared 10 lightbulb shipments and just 1 cord shipment?

• Lightbulb time: 10 shipments × (some time per shipment)
• Cord time: 1 shipment × (some smaller time per shipment)
• Most of her time would be spent on lightbulbs

Scenario 2: What if she prepared 1 lightbulb shipment and 10 cord shipments?

• Lightbulb time: 1 shipment × (some time per shipment)
• Cord time: 10 shipments × (some smaller time per shipment)
• Most of her time would be spent on cords, despite each lightbulb taking longer

Without knowing the actual counts or the total time, we can't determine how many minutes went to lightbulbs.

Conclusion

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: Wanda spent a total of 90 minutes preparing all shipments.

What Statement 2 Provides

We now know the total time for both types combined: 90 minutes.

Why This Isn't Enough

But how is this 90 minutes divided? Let's test some possibilities:

• Could it be 45 minutes on lightbulbs and 45 on cords? Yes!
• Could it be 80 minutes on lightbulbs and 10 on cords? Also possible!
• Could it be 10 minutes on lightbulbs and 80 on cords? That works too!

There are infinite ways to split 90 minutes between two activities. Without additional information about the split, we can't determine the answer.

Conclusion

Statement 2 is NOT sufficient.

This eliminates choice B.

Combining Statements

Now let's see what happens when we use both statements together.

Combined Information

From both statements, we know:

• Lightbulb shipments take 20% more time per shipment than cord shipments (Statement 1)
• The total time for all shipments is 90 minutes (Statement 2)

Why Together They Still Aren't Sufficient

Even with both pieces of information, we still don't know the COUNT of each type of shipment. This is the missing piece. Let's prove this with concrete examples:

Test Case 1: Many lightbulbs, few cords

• Suppose: 9 lightbulb shipments and 1 cord shipment
• If cord takes 5 minutes, lightbulb takes 6 minutes (20% more)
• Total: \(\mathrm{9 \times 6 + 1 \times 5 = 54 + 5 = 59}\) minutes
• To scale to 90 minutes: multiply all times by \(\frac{90}{59}\)
• Time on lightbulbs would be about 82 minutes

Test Case 2: Few lightbulbs, many cords

• Suppose: 1 lightbulb shipment and 9 cord shipments
• If cord takes 5 minutes, lightbulb takes 6 minutes (20% more)
• Total: \(\mathrm{1 \times 6 + 9 \times 5 = 6 + 45 = 51}\) minutes
• To scale to 90 minutes: multiply all times by \(\frac{90}{51}\)
• Time on lightbulbs would be about 11 minutes

The key insight: Different shipment counts lead to dramatically different answers (82 minutes vs 11 minutes) for how many minutes were spent on lightbulbs. Without knowing these counts, we cannot determine a unique answer.

Conclusion

The statements together are NOT sufficient.

This eliminates choice C.

The Answer: E

We cannot determine the exact number of minutes spent on lightbulb shipments because we don't know how many shipments of each type Wanda prepared. The missing piece of information - the shipment counts - prevents us from finding a unique answer.

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