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A certain builder is selling five homes for the following

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A certain builder is selling five homes for the following [#permalink]

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A certain builder is selling five homes for the following prices: $157,000, $168,000, $195,000, $235,000, and $256,000. If the price of the most expensive home is increased $10,000, which of the following statements best describes the change in the mean and the median of the home prices?

(A) The mean and the median will remain unchanged.
(B) The mean will remain unchanged but the median will increase.
(C) The mean will increase but the median will remain unchanged.
(D) The mean and the median will increase by the same amount.
(E) The mean and the median will increase by different amounts.
[Reveal] Spoiler: OA

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Re: A certain builder is selling five homes for the following [#permalink]

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skamal7 wrote:
A certain builder is selling five homes for the following prices: $157,000, $168,000, $195,000, $235,000, and $256,000. If the price of the most expensive home is increased $10,000, which of the following statements best describes the change in the mean and the median of the home prices?

(A) The mean and the median will remain unchanged.
(B) The mean will remain unchanged but the median will increase.
(C) The mean will increase but the median will remain unchanged.
(D) The mean and the median will increase by the same amount.
(E) The mean and the median will increase by different amounts.


Old set = {157, 168, 195, 235, 256}.

New set = {157, 168, 195, 235, 266} --> the median (middle term) will remain the same and the mean will increase.

Answer: C.
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A certain builder is selling five homes for the following [#permalink]

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New post 15 Nov 2017, 05:49
skamal7 wrote:
A certain builder is selling five homes for the following prices: $157,000, $168,000, $195,000, $235,000, and $256,000. If the price of the most expensive home is increased $10,000, which of the following statements best describes the change in the mean and the median of the home prices?

(A) The mean and the median will remain unchanged.
(B) The mean will remain unchanged but the median will increase.
(C) The mean will increase but the median will remain unchanged.
(D) The mean and the median will increase by the same amount.
(E) The mean and the median will increase by different amounts.

If not sure: Use small numbers that follow the prompt's pattern, namely, five increasing values.

Pick numbers that sum to a multiple of 5, so that the mean is easy to find. Pick four numbers, add them, and have the fifth number (greater than all others) make the total sum = multiple of 5.

The houses sell for:

$1, $2, $3, $4, $10
Median: $3
Mean: \(\frac{$20}{5} = $4\)

The most expensive home increases by $5:
$1, $2, $3, $4, $15
Median: $3
Mean: \(\frac{$25}{5} = $5\)

Mean is increased, median is unchanged.

Answer C
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Re: A certain builder is selling five homes for the following [#permalink]

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New post 15 Nov 2017, 08:31
skamal7 wrote:
A certain builder is selling five homes for the following prices: $157,000, $168,000, $195,000, $235,000, and $256,000. If the price of the most expensive home is increased $10,000, which of the following statements best describes the change in the mean and the median of the home prices?

(A) The mean and the median will remain unchanged.
(B) The mean will remain unchanged but the median will increase.
(C) The mean will increase but the median will remain unchanged.
(D) The mean and the median will increase by the same amount.
(E) The mean and the median will increase by different amounts.


No calculations required for this one as Median of 5 values will remain the same $195,000 , though the mean will increase, among the given options only (C) is correct!!
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Re: A certain builder is selling five homes for the following   [#permalink] 15 Nov 2017, 08:31
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A certain builder is selling five homes for the following

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