The percentage of households with an annual income of more than

Question

The percentage of households with an annual income of more than $40,000 is higher in Merton county than in any other county. However, the percentage of households with an annual income of $60,000 or more is highest in Sommer county.

If the statements above are true, which of the following can properly be concluded on the basis of them?

If the statements above are true, which of the following can properly be concluded on the basis of them?

(A) No household in Merton county has an annual income of $60,000 or more.

(B) Some households in Merton county have an annual income between $40,000 and $60,000.

(C) The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.

(D) Average annual household income is higher in Sommer than in Merton county.

(E) The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.

Note : Other questions that have nearly the same passage but a different question stem and at least one different answer choice can be found  here  and  here .

winterschool · Answer

The percentage of households with an annual income of more than $40,000 is higher in Merton county than in any other county. However, the percentage of households with an annual income of $60,000 or more is highest in Sommer county.

If the statements above are true, which of the following can properly be concluded on the basis of them?

If the statements above are true, which of the following can properly be concluded on the basis of them?

(A) No household in Merton county has an annual income of $60,000 or more.  Incorrect

cant say this, some households can earn more than 60000 or even greater amount

(B)  Some households in Merton county have an annual income between $40,000 and $60,000.   Correct

clearly. it can be derived from argument

(C) The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.  Incorrect

only know about percentage, dont know about total households in each county. so cant say the number of households

(D) Average annual household income is higher in Sommer than in Merton county.  Incorrect

cant be derive from argument

(E) The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.  Incorrect

irrlevant

harish555 · Answer

The percentage of households with an annual income of more than $40,000 is higher in Merton county than in any other county. However, the percentage of households with an annual income of $60,000 or more is highest in Sommer county.

If the statements above are true, which of the following can properly be concluded on the basis of them?

If the statements above are true, which of the following can properly be concluded on the basis of them?

(A) No household in Merton county has an annual income of $60,000 or more. 
No where in the Passage it is mentioned That no household in that county has an annual income of $60,000 or more

(B) Some households in Merton county have an annual income between $40,000 and $60,000.

It is definitely given in the passage that some households in that county have any annual income between 40,000 and 60000. Because it is given that the percentage of households with an annual income of more than $40,000 is higher in Merton county than in any other county

(C) The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.
This is a tricky option here . they mentioned about percentage only. so percentage is definitely different from number . Though the percentage must be higher but the number can be lesser than the number of people who have $40000 or more in other county

(D) Average annual household income is higher in Sommer than in Merton county.
There Is no guarantee that if the percentage of households with an annual income of $60,000 or more is higher , then the Average annual household income is higher.

(E) The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.
No where in the passage it is mentioned that the percentage of households with this income of 80,000 is higher in Soumen County
So, answer should be B

like my post if you find it useful .

Posted from my mobile device

AndrewN · Answer

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

Paagrio · Answer

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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