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Median - word problem

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by SaraLotfy » Thu Sep 19, 2013 3:12 am
The median annual household income in a certain community of 21 houses is $ 50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median of the community be in 2 years?

A) 50,000
B) 60,000
C) 60,500
D) 65,000
E) Can not get
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by theCodeToGMAT » Thu Sep 19, 2013 3:35 am
The Answer must be [spoiler][E][/spoiler]

Since, We know the median but we have no information about the values of other houses. So we cannot comment what impact of increase in Mean will have.

For Example:

Assume: All 21 houses have same household income
So, MEAN = 50000
So increments after 2 years = 60,500$
here we have no information of which household had increment.
So, it can be
20 households had 50,000 and 21st had higher
Or, ALL Household has slight increment.

[spoiler]HENCE [E][/spoiler]
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by Brent@GMATPrepNow » Thu Sep 19, 2013 6:24 am
SaraLotfy wrote:The median annual household income in a certain community of 21 houses is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median of the community be in 2 years?

A) 50,000
B) 60,000
C) 60,500
D) 65,000
E) Can not get
Are you sure you wrote the question correctly? When you write "a", do you mean only one household experienced an increase? I believe the answer is still E (as theCodeToGMAT noted), I just want to get some clarification.

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by SaraLotfy » Thu Sep 19, 2013 8:48 am
Yes indeed, it was written as "a" household. I thought the wording is bad.
I answered as E
Brent@GMATPrepNow wrote:
SaraLotfy wrote:The median annual household income in a certain community of 21 houses is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median of the community be in 2 years?

A) 50,000
B) 60,000
C) 60,500
D) 65,000
E) Can not get
Are you sure you wrote the question correctly? When you write "a", do you mean only one household experienced an increase? I believe the answer is still E (as theCodeToGMAT noted), I just want to get some clarification.

Cheers,
Brent
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by SaraLotfy » Thu Sep 19, 2013 8:50 am
Food for thought here:
Would the answer have differed if the mean income of ALL the households increased by 10%?
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by [email protected] » Thu Sep 19, 2013 12:43 pm
Hi SaraLotfy,

YES, if the question had stated that "each" or "all" households saw their incomes increased by 10% per year, then the range would "move" and so would the "median"

It would become....

Start = $50,000
Year 1 = +10% = $55,000
Year 2 = +10% = $60,500

In this case, the answer would be C

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by masoom j negi » Fri Dec 21, 2018 9:08 pm
Increase in mean value of a set has no direct relation with the increase in median value of the set. Here, we are given the increase in the mean value but we don't know if the increase is because of change in just 1 value of because of the change in all values. Hence, we can't determine the change in median. Hence, E is the answer.
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by Scott@TargetTestPrep » Sat Mar 02, 2019 8:03 am
SaraLotfy wrote:The median annual household income in a certain community of 21 houses is $ 50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median of the community be in 2 years?

A) 50,000
B) 60,000
C) 60,500
D) 65,000
E) Can not get
It's impossible to determine the median household income from the information given. For example, if the reason the mean household income increases by 10% per year over the next 2 years is because the annual income of every household increases by 10% per year over the next 2 years, then the median household income would also increases by 10% per year over the next 2 years, to 50,000 x 1.1 x 1.1 = $60,500. However, it's possible that only the household with the highest annual income increases by a tremendous amount each year for the next 2 years, such that the mean household income for the community increases by 10% per year over the next 2 years. In that case, the median household income would stay the same at the end of the 2 years, i.e., at $50,000.

Answer: E

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