The 15 homes in a new development are each to be sold for...

[KarlS319]

The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 6 homes?

This is a relatively easy question and should be a good opportunity to stockpile some time but I ended up bouncing back and forth between different methodologies and using up the full 2 minutes!

First, I set it up as an equation to solve for x before realizing that this would be time consuming to solve i.e. 200K = [(4)(170K) + (5)(200K) + 6(200K)] / 15

Then, I thought of the "teeter tooter" method but struggled to set it up properly....

Finally, I recognized that the 4 houses bring the average down (4)(200K - 170K) = (4)(30) = 120 and that this must be made up for with the remaining 6 houses hence 120K / 6 = 20K per house i.e. each house must be sold for 200K + 20K = 220K

Question: is there a way to appropriately tackle this using the "teeter tooter" method? Obviously this can be a very efficient tool so I'm looking for help to understand how it could be applied in this scenario? Also, some general advice on how best to recognize when certain methods can/can't be used for average and weighted average problems would be appreciated as well!

[Sage Pearce-Higgins]

Which source is this question from? Please state this when you're posting a new question. If it's from a paid-for GMAT Prep resource, we'll have to remove it (we don't have copyright to reprint their materials).

You're right that oscillating between methods can be time consuming. Well done for seeing that this is a weighted average question, and I'd recommend a conceptual / graphical method rather than algebra (algebra would be possible, but I can't see the "x" in your equation).

The method that you used can be described as the 'over-under' method. I.e. what's above the average and what's below the average cancel out. Generally that works well if we know the number of items involved. The 'teeter-totter' method is best applied to situations such as mixing liquids of different strengths. However, they share in common the idea of working conceptually rather than algebraically. You could try drawing this out on a teeter-totter, with 200 as the balance point.

However, perhaps the takeaway for you here is that you need to not rush into a strategy, but hold back and consider your options. Also, stay away from Algebra on problems like this.

[KarlS319]

This is from unpaid GMAT prep. I read the rules/guidelines post and recognize that you can't post paid questions on the forums but assumed that we didn't have to restate it was from GMAT prep each time since it was already under the GMAT Prep forum. I'll specify source in future posts.

[Sage Pearce-Higgins]

Thanks.