The percentage of households with an annual income of more than $40,00

With questions like this, there isn't a whole lot of analysis to be done up front. As always, we have to make sure that we are paying attention to the details and that we understand the given facts. However, we don't have a conclusion or a line of reasoning that we can break down. So let's just make sure we are clear about the given information:

• "The percentage of households with an annual income of more than $40,000 is higher in Merton County (MC) than in any other county." Note that we don't know about the NUMBER of households. Also notice that it says "more than $40,000", so this group does not contain households with an annual income equal to $40,000.
• "The percentage of households with an annual income of $60,000 or more is higher in Sommer County (SC)." Again, we are dealing with percentages and not absolute numbers. However, in this case, the group includes the boundary figure ("$60,000 or more").

If the statements above are true, which of the following must also be true?


MC might have, for example, 2% earning $80k+ while SC only has 1% (or less!) earning $80k+. As long as SC has a higher percentage with an annual income between $60k and $80k, SC could still have a higher percentage earning $60k+. Choice (A) does not have to be true, so eliminate this one.


There could be a third county that has a higher percentage earning $60k than MC. As we'll see in the explanation for choice (C), this would not necessarily mean that the third county has a higher percentage earning above $40k than MC. Choice (B) might be true, but it does not have to be true. Eliminate (B).


Let's think about this logically. MC has the highest percentage above $40k. SC has the highest percentage of $60k or more. So how could that be true? Let's start by ignoring the group earning between $40-60k. We know that the percentage earning $60k or more in MC is lower than the percentage earning $60k or more in SC. So if we omit the group earning between $40-60k, it would look like SC has a greater percentage earning above $40k. But we know that the opposite is true: the percentage earning above $40k is higher in MC than in SC.

So how can we make the $40k+ percentage higher in MC without changing the fact that the $60k+ percentage is higher in SC? The only option is to make the $40-60k percentage higher in MC. In other words, if the $40k percentage is higher in MC even though the $60k percentage is LOWER in MC, then the percentage BETWEEN $40k and $60k must be higher in MC. In that case, the statement in choice (C) would have to be true, so hang on to this one.


The given facts pertain to percentages, not absolute numbers. SC might have a much greater population than MC, in which case choice (D) might not be true. Eliminate (D).


This might be true, but it depends on information that we are not given. SC might have a small percentage earning above $60k while MC has NO households earning above $60k. But MC might have a much larger percentage earning $40-60k. Furthermore, SC could have a much larger percentage earning less than, say, $20k, and that would drag down the overall average. We do not have enough information to determine whether (E) is true, so eliminate this one.

(C) is the best 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 higher in Sommer County.

If the statements above are true, which of the following must also be true?

(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.
(C) Some households in Merton County have an annual income between $40,000 and $60,000.
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.
(E) Average annual household income is higher in Sommer County than in Merton County.

Hello GMATNinja

Passage says -The percentage of households with an annual income of $60,000 or more is HIGHER in SC. But as per your explanation, you are saying passage is saying- SC has HIGHEST Percentage of households with an annual income of $60,000 or more. Could you please explain. Is HIGHER mean HIGHEST in above passage.

Hello GMATNinja

Passage says -The percentage of households with an annual income of $60,000 or more is HIGHER in SC. But as per your explanation, you are saying passage is saying- SC has HIGHEST Percentage of households with an annual income of $60,000 or more. Could you please explain. Is HIGHER mean HIGHEST in above passage.

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 higher in Sommer County.

If the statements above are true, which of the following must also be true?


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

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

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

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

(E) Average annual household income is higher in Sommer County than in Merton County.

AndrewN

Please share your evaluation for my reasoning below:-

PA:-%age of households with annual income more than $40K is higher in Merton County than in any other county. %age of households with annual income of equal to or more than $60K is higher in Somer County than in any other county.

Option A:- This is the incorrect answer choice because households with income equal to or more than $60K are higher in SC. But we don't know the upper limit of this income. The upper limit could be till $70K or $80K. We don't know. Hence, this is incorrect.

Option B:- This is the incorrect answer choice because from the passage above we know that the %age of households with income =>$60K is highest in MC, but we don't know the second highest. It could be SC or any other county. Hence, this is the incorrect answer choice.

Option C:- This is the correct answer choice because the %age of households with income >$40K is highest in SC and the %age of households with income >=$60K is highest in MC. So in between 40K and 60K, there would be some households. Hence, this is the correct answer choice.

Option D:- The passage above talks about percentage. This answer choice is talking about number of households. Hence, we cannot conclude this statement with surety.

Option E:- No mention of per-month income in SC or MC. Average annual household income could be higher in SC or MC. Hence, not necessarily a must be true answer.

Thanks

With questions like this, there isn't a whole lot of analysis to be done up front. As always, we have to make sure that we are paying attention to the details and that we understand the given facts. However, we don't have a conclusion or a line of reasoning that we can break down. So let's just make sure we are clear about the given information:

• "The percentage of households with an annual income of more than $40,000 is higher in Merton County (MC) than in any other county." Note that we don't know about the NUMBER of households. Also notice that it says "more than $40,000", so this group does not contain households with an annual income equal to $40,000.
• "The percentage of households with an annual income of $60,000 or more is higher in Sommer County (SC)." Again, we are dealing with percentages and not absolute numbers. However, in this case, the group includes the boundary figure ("$60,000 or more").

If the statements above are true, which of the following must also be true?


MC might have, for example, 2% earning $80k+ while SC only has 1% (or less!) earning $80k+. As long as SC has a higher percentage with an annual income between $60k and $80k, SC could still have a higher percentage earning $60k+. Choice (A) does not have to be true, so eliminate this one.


There could be a third county that has a higher percentage earning $60k than MC. As we'll see in the explanation for choice (C), this would not necessarily mean that the third county has a higher percentage earning above $40k than MC. Choice (B) might be true, but it does not have to be true. Eliminate (B).


Let's think about this logically. MC has the highest percentage above $40k. SC has the highest percentage of $60k or more. So how could that be true? Let's start by ignoring the group earning between $40-60k. We know that the percentage earning $60k or more in MC is lower than the percentage earning $60k or more in SC. So if we omit the group earning between $40-60k, it would look like SC has a greater percentage earning above $40k. But we know that the opposite is true: the percentage earning above $40k is higher in MC than in SC.

So how can we make the $40k+ percentage higher in MC without changing the fact that the $60k+ percentage is higher in SC? The only option is to make the $40-60k percentage higher in MC. In other words, if the $40k percentage is higher in MC even though the $60k percentage is LOWER in MC, then the percentage BETWEEN $40k and $60k must be higher in MC. In that case, the statement in choice (C) would have to be true, so hang on to this one.


The given facts pertain to percentages, not absolute numbers. SC might have a much greater population than MC, in which case choice (D) might not be true. Eliminate (D).


This might be true, but it depends on information that we are not given. SC might have a small percentage earning above $60k while MC has NO households earning above $60k. But MC might have a much larger percentage earning $40-60k. Furthermore, SC could have a much larger percentage earning less than, say, $20k, and that would drag down the overall average. We do not have enough information to determine whether (E) is true, so eliminate this one.

(C) is the best answer.

Ok Gentlemen, here we go again ... I have some issue with this question ... it says - which of the following MUST BE TRUE?

My logic with (C) was -

If MC has the highest percent of > $40k annual income resident it could also meant that all of them are in two sets: Under $40k (30%), Above $60k (70%), so none b/w 40-60 is possible. Whereas SC could have 90% > $60k and 10% below $60k. This will still keep the above statement true but there will not be any MC resident with income between 40k and 60k, what am I missing? I picked (C) twice by POE but I cannot justify my answer 100% of the time .... yes there's possibility that some of MC resident will make between 40-60k but it's not bullet proof, can you please help

Ok Gentlemen, here we go again ... I have some issue with this question ... it says - which of the following MUST BE TRUE?

My logic with (C) was -

If MC has the highest percent of > $40k annual income resident it could also meant that all of them are in two sets: Under $40k (30%), Above $60k (70%), so none b/w 40-60 is possible. Whereas SC could have 90% > $60k and 10% below $60k. This will still keep the above statement true but there will not be any MC resident with income between 40k and 60k, what am I missing? I picked (C) twice by POE but I cannot justify my answer 100% of the time .... yes there's possibility that some of MC resident will make between 40-60k but it's not bullet proof, can you please help GMATNinja or AndrewN?

Hey IN2MBB2PE,

I can help with this query 😊.

1. I looked at the example numbers you have provided. Here is what you are missing!

2. I can see that you are not 100% sure that option C is Must-Be-True. This video will provide you with clarity about why this choice works beautifully.

There is an important learning here. For me, this question demonstrates the importance of visualizing the given data carefully, keeping every single piece of information in mind. Once small slip can prove disastrous.


Hope this helps!
Harsha