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QOTD: The percentage of households with an annual income of more

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QOTD: The percentage of households with an annual income of more [#permalink]

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Verbal Question of The Day: Day 195: Critical Reasoning


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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.


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[Reveal] Spoiler: OA

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QOTD: The percentage of households with an annual income of more [#permalink]

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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?

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

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.

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

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).

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

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.

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

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).

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

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.
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Re: QOTD: The percentage of households with an annual income of more [#permalink]

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New post 08 Jan 2018, 06:42
souvik101990 wrote:

Verbal Question of The Day: Day 195: Critical Reasoning


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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.


Every question of the day will be followed by an expert reply by GMATNinja in 12-15 hours. Stay tuned! Post your answers and explanations to earn kudos.



Here we need to pay a close attention to question :) it says: If the statements above are true, which of the following must also be true?

This implies that we need to be sure of the data...

(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County. says the same
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more. It can be or cannot be true - keep in mind "MUST" be true
(C) Some households in Merton County have an annual income between $40,000 and $60,000. Who knows perhaps :)
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County. So what ?:-)
(E) Average annual household income is higher in Sommer County than in Merton County. out of scope :)

Now my question:

What if question said: If the statements above are true, which of the following CAN also be true - then I would be opt for both B and C :)
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Re: QOTD: The percentage of households with an annual income of more [#permalink]

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New post 08 Jan 2018, 07:42
souvik101990 wrote:

Verbal Question of The Day: Day 195: Critical Reasoning


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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.


Every question of the day will be followed by an expert reply by GMATNinja in 12-15 hours. Stay tuned! Post your answers and explanations to earn kudos.


(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County. - We can't be sure about it. Maybe, Merton County has more people with annual income greater than $80,000, considering that >$40000 includes all such incomes.
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more. - We don't have enough information to conclude that. What about the data of other counties?
(C) Some households in Merton County have an annual income between $40,000 and $60,000. - This could be true. Maybe, Merton County has many individuals with annual incomes between $40000 and $60000 and therefore, it cannot exceed the annual income of Sommer County.
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County. - From the evidence cited above, this could not be concluded with surety. Maybe, greater percentage of households in Sommer County have annual income less than $40,000
(E) Average annual household income is higher in Sommer County than in Merton County. - We can't conclude this. If 70% households in Merton County have incomes greater than $40,000, while only 15% households have income greater than $60,000, we could have an exception. Additionally, we don't have any info on sample size of both counties. Thus, inconclusive.

Thus, C is the answer.
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Re: QOTD: The percentage of households with an annual income of more [#permalink]

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New post 08 Jan 2018, 12:04
Not sure between between A and C. I???m really confused. IMO both could be true
Re: QOTD: The percentage of households with an annual income of more   [#permalink] 08 Jan 2018, 12:04
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