The percentage of households with an annual income of more than

Hello, everyone. It looks like I get to do the honors and post the first Expert response. Thanks to others for posting their solutions ahead of the reveal.


An inference question does not give us license to read between the lines. We need to be just as careful to stick to the information the passage provides to avoid jumping to wayward conclusions. Here, there are two counties, and we can sum up the information in the following manner.

Merton— highest percentage of household income > $40K
Sommer—highest percentage of household income ≥ $60K

That is it. We can appreciate right away that no upper limit has been set, just a lower limit in two separate cases.


This is too extreme. If you like numbers, keep things simple. Picture three households in each county with the following annual incomes:

Merton—$45K, $50K, $60K
Sommer—$30K, $60K, $65K

Of course, you have to make sure you keep the given information in mind. Merton has 3/3 households, or 100 percent, that earn more than $40,000 but only one, or 33 percent, that earns at least $60,000; Sommer has 2/3 households, or 67 percent, that earn more than $40,000, and those same two earn at least $60,000. We have stuck to the given information, and we have disproved answer choice (A) in the process.


We can make such an inference, not on the basis of what I came up with above, but because notice, again, that, in terms of income, the passage states more than $40,000 and $60,000 or more. Blink, and you might miss the distinction, but these two inequalities are not the same type. Since we know that Sommer county has the greatest percentage of households at or above an annual income of $60K, but that Merton county has the greatest percentage of households above an annual income of $40K, it must be true that some households in the latter earn between $40K and $60K. I know that test-takers can be wary of some, and with good cause: the word pops up in many answers that end up being wrong. At the same time, you never want to stop applying logic to a given answer choice simply because you see a certain word or expression. You still have to think.


Do not conflate a percentage with a number. Take our sample from before, but add a few more households to Sommer county:

Merton—$45K, $50K, $60K
Sommer—$30K, $60K, $65K, $66K, $67K, $68K

Now, it should be evident that it can still be true that Merton county has the highest percentage of households above $40K (100 percent) without having the most households at or above that threshold—3, in my expanded example, versus 5 in Sommer county.


We cannot figure out an average based on nothing more than a vague comparison between percentages. Consider a different set of numbers that conform to the information from the passage:

Merton—$50K, $50K, $50K (average = $50K)
Sommer—$20K, $30K, $70K (average = $40K)

You do not have to go this far, though. To find an average, you need two pieces of information: 1) a sum (which we cannot possibly calculate); and 2) a total number of items to divide (which we do not know). Without either piece of information, we cannot possibly calculate the average annual household income for either county.


I hope you can appreciate by now that we know nothing about this new limit. Anything about the $80K mark is pure speculation.

Perhaps the question makes more sense now. As always, good luck with your studies.

- Andrew

So the catch here was "more than" vs "more than equal". For some reason I thought that both figures were given with "more than equal to".

Is this an OG question? I missed the "more than" part. I have never seen a GMAT OG question tricking us on words.

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