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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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11 Aug 2009, 05:33
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68% (01:36) correct 32% (01:48) wrong based on 607 sessions

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

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11 Aug 2009, 06:05
2
Economist wrote:
This might have come many times.

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?
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

Can anyone give an example on why D is wrong ? If the percent of households within each county is considered then always average annual household income will be greater in Sommer.
Eg. 50% of all households in Sommer have 60,000 and 49% of all households in Merton have 59,000 income. As per my understanding Sommer's average will always be greater than Merton if we consider "percentage of households separately within each group". Where is the flaw?

Lets say I add the premises - The percentage of households with an annual income below \$10,000 is also highest in Sommer.
I hope you are getting, what I am setting.

You are neglecting the remaining households. In this kind of scenarios, information is incomplete to make such strong inferences as in D.
Also in case of averages, remember that just having the highest values does not suggest the average value will be high.

e.g.
Set 1 (Merton, M)- 41,41,41,41
Set 2 (Sommer, S) - 61,5,5,5

Lets check if satisying the premises of the question
M has >40 (100%), S has 25%
S has >60 (25%). S has 0%
==> average Annual income of M is higher

Set 1 (Merton, M)- 41,41,41,41
Set 2 (Sommer, S) - 500,5,5,5
==> Average annual income of S is higher

Also, in your example, I do not understand your sample figures. Can you explain why you pick that figures 49% and 50%?
M can have x% 40000+ as it has highest % over 40,000
S can have y% 60000+ as it has highest % over 60,000
But, y < x
as 60000+ is a subset of 40000+

if y > x the first premise will be broken.
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Re: QOTD: The percentage of households with an annual income of more  [#permalink]

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15 Apr 2017, 07:30
1
Economist wrote:
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.

Source : OG2017, Diagnostic Test, V72, P35

Merton County

Step 1: Identify the Question

The question asks which of the answers must also be true, so this is an Inference question.

Step 2: Deconstruct the Argument

>40K: M highest %
>60K: S % > M %

Step 3: Pause and State the Goal

On Inference questions, the answer is something that must be true based on the information in the argument. If any part of an answer is not supported by the given information, then that answer is not correct.

Step 4: Work from Wrong to Right

(A) The argument confirms that the percentage of households in Sommer County with incomes above \$60,000 is higher than the percentage in Merton County, but no information is provided about incomes over \$80,000. This answer might not be true if many households in Sommer County have incomes between \$60,000 and \$80,000.
(B) No other counties are mentioned in the argument. Merton County could be the county with the second highest percentage of incomes over \$60,000 (after Sommer County), but there could be other counties above Merton.
(C) CORRECT. For Merton County to have the highest percentage of households with income over \$40,000 but not the highest percentage with income over \$60,000, some households must be in the first group (over \$40,000) but not the second group (over \$60,000). These households are those with income between \$40,000 and \$60,000.
(D) The argument provides information only about percentages of households in each county with certain income levels. The number of households with these income levels depends on the size of the county. If Merton County has many fewer households than Sommer County, this answer might not be true.
(E) The argument provides information only about the percentage of households exceeding particular income thresholds; this information is not sufficient to calculate averages. Consider what might happen to average income if one household with an annual income of \$10B moved from one county to the other.
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Re: QOTD: The percentage of households with an annual income of more  [#permalink]

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08 Jan 2018, 07:10
1
1
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.

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

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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.

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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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08 Jan 2018, 08:42
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.

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Re: QOTD: The percentage of households with an annual income of more &nbs [#permalink] 08 Jan 2018, 08:42
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