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GraceSCKao
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03 Jun 2022, 02:20
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IanStewart
Thank you IanStewart !
Your explanations are clear and systematic!
I reviewed the weighted average concept over the past few days.
Could I have some follow-up questions?
1. Can the number of Model P television sold be 0 or 40?
I can understand why you say in your post that there are "41 conceivable situations," since the number of Model P can, theoretically, range from 0 to 40. But I am curious whether there is a constraint in this question that does not allow the number to be o or 40?
Quote:
If we focus on the question itself, which says "Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television. Each Model P television sold for $p and each Model Q sold for $q," do we allow the possibility that all the 40 televisions sold are Model P or Model Q? In other words, the number of Model P can be 0 or 40, cannot it? (In this case, the only one type's price will be $141 itself.)
2. The features of "weighted-average" questions?
I did not find out that this question tests the weighted average concept but only thought that I could approach it algebraically. Reviewing this question and the stamp question, I think the two equations are similar:
4q-3X=564 (q is the price, X is the number of Model P sold)
15x+29y=440 (X is the number of one type of stamp sold and Y is the number of another type)
Hence, I am curious how we see that some questions test the weighted average and some do not. Is the key that if the question tests the concept of weighted average, it should mention at least once the weighted average? (such as the average price, the average capacity or the average concentration)
Sometimes we are given the weighted average and try to figure out the ratio of the weightings of two sides, or sometimes we need to determine the absolute number of one side, or sometimes the direction is flipped.
IanStewart
Thank you for your inspiring suggestions!
26 Sep 2025, 03:28
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This is a classic weighted average data sufficiency problem that many students find tricky. Let's work through it together and see how to approach it systematically.
Understanding What We're Looking For
You need to find the exact number of Model P televisions out of 40 total. We know:
- Total TVs = 40
- Each Model P costs \($p\), each Model Q costs \($q\)
- Average price = \($141\)
Here's what you need to see: This is a weighted average problem. The \($141\) average must fall between prices \(p\) and \(q\). The key insight is that if the average is closer to one price, more of that model was sold.
Analyzing Statement 1: \(p = q - 30\)
Let's think about this... we know the price difference is \($30\), but we don't know the actual prices.
Test different scenarios:
- If \(q = $150\), then \(p = $120\)
The average \($141\) is closer to \($150\), so more Model Q were sold
- If \(q = $180\), then \(p = $150\)
The average \($141\) is closer to \($150\), so more Model P were sold
Notice how different price levels give us different quantity mixes? Without knowing the actual prices, we can't determine a unique answer.
Statement 1 is NOT sufficient.
Analyzing Statement 2: Either \(p = 120\) or \(q = 120\)
We have one price, but not the other.
If \(p = $120\):
- We don't know \(q\), but it must be greater than \($141\) (since average is \($141\))
- Different values of \(q\) would give different quantity mixes
If \(q = $120\):
- Then \(p\) must be greater than \($141\) for the average to work out
- Again, different values of \(p\) would give different mixes
Statement 2 is NOT sufficient.
Combining Both Statements
Here's where it gets interesting! Let's combine what we know:
- From Statement 1: \(p = q - 30\)
- From Statement 2: Either \(p = 120\) or \(q = 120\)
Case 1: If \(p = $120\)
Then \(q = p + 30 = $150\)
This gives us concrete prices! With \(p = $120\), \(q = $150\), and average = \($141\), we can determine the exact mix.
Case 2: If \(q = $120\)
Then \(p = q - 30 = $90\)
But wait... both \($90\) and \($120\) are below the average \($141\). This is impossible!
So only Case 1 is valid, giving us unique values that allow us to solve for the exact number of Model P televisions.
Answer: C - Both statements together are sufficient, but neither statement alone is sufficient.
---
You can check out the step-by-step solution on Neuron by e-GMAT to master the weighted average framework systematically. You'll discover how to quickly identify impossible scenarios and learn alternative approaches that save time on test day. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice here.
Understanding What We're Looking For
You need to find the exact number of Model P televisions out of 40 total. We know:
- Total TVs = 40
- Each Model P costs \($p\), each Model Q costs \($q\)
- Average price = \($141\)
Here's what you need to see: This is a weighted average problem. The \($141\) average must fall between prices \(p\) and \(q\). The key insight is that if the average is closer to one price, more of that model was sold.
Analyzing Statement 1: \(p = q - 30\)
Let's think about this... we know the price difference is \($30\), but we don't know the actual prices.
Test different scenarios:
- If \(q = $150\), then \(p = $120\)
The average \($141\) is closer to \($150\), so more Model Q were sold
- If \(q = $180\), then \(p = $150\)
The average \($141\) is closer to \($150\), so more Model P were sold
Notice how different price levels give us different quantity mixes? Without knowing the actual prices, we can't determine a unique answer.
Statement 1 is NOT sufficient.
Analyzing Statement 2: Either \(p = 120\) or \(q = 120\)
We have one price, but not the other.
If \(p = $120\):
- We don't know \(q\), but it must be greater than \($141\) (since average is \($141\))
- Different values of \(q\) would give different quantity mixes
If \(q = $120\):
- Then \(p\) must be greater than \($141\) for the average to work out
- Again, different values of \(p\) would give different mixes
Statement 2 is NOT sufficient.
Combining Both Statements
Here's where it gets interesting! Let's combine what we know:
- From Statement 1: \(p = q - 30\)
- From Statement 2: Either \(p = 120\) or \(q = 120\)
Case 1: If \(p = $120\)
Then \(q = p + 30 = $150\)
This gives us concrete prices! With \(p = $120\), \(q = $150\), and average = \($141\), we can determine the exact mix.
Case 2: If \(q = $120\)
Then \(p = q - 30 = $90\)
But wait... both \($90\) and \($120\) are below the average \($141\). This is impossible!
So only Case 1 is valid, giving us unique values that allow us to solve for the exact number of Model P televisions.
Answer: C - Both statements together are sufficient, but neither statement alone is sufficient.
---
You can check out the step-by-step solution on Neuron by e-GMAT to master the weighted average framework systematically. You'll discover how to quickly identify impossible scenarios and learn alternative approaches that save time on test day. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice here.
