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Yesterday Wanda prepared several shipments of lightbulbs and several shipments of electrical cords. How many minutes did Wanda spend preparing the shipments of lightbulbs yesterday?
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.
To answer this question, we need to find the exact time spent on lightbulb shipments. This could come from:
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.
Statement 1: The average time per lightbulb shipment was 20% greater than the average time per cord shipment.
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).
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?
Scenario 2: What if she prepared 1 lightbulb shipment and 10 cord shipments?
Without knowing the actual counts or the total time, we can't determine how many minutes went to lightbulbs.
Statement 1 is NOT sufficient.
This eliminates choices A and D.
Now let's forget Statement 1 completely and analyze Statement 2 independently.
Statement 2: Wanda spent a total of 90 minutes preparing all shipments.
We now know the total time for both types combined: 90 minutes.
But how is this 90 minutes divided? Let's test some possibilities:
There are infinite ways to split 90 minutes between two activities. Without additional information about the split, we can't determine the answer.
Statement 2 is NOT sufficient.
This eliminates choice B.
Now let's see what happens when we use both statements together.
From both statements, we know:
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
Test Case 2: Few lightbulbs, many cords
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.
The statements together are NOT sufficient.
This eliminates choice C.
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."