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Last year, in a certain housing development, the average (arithmetic m

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Last year, in a certain housing development, the average (arithmetic m  [#permalink]

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New post 20 Jun 2018, 00:15
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Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was $160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was $219,000.
(2) Last year the median of the prices of the 20 houses was $150,000.


NEW question from GMAT® Official Guide 2019


(DS05269)

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Re: Last year, in a certain housing development, the average (arithmetic m  [#permalink]

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New post 20 Jun 2018, 00:43
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Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was $160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was $219,000.
(2) Last year the median of the prices of the 20 houses was $150,000.


NEW question from GMAT® Official Guide 2019


(DS05269)


Questions dealing with average, mean, and std can often be solved with logic, without explicit calculations.
We'll look for such an answer, a Logical approach.

(1) Knowing only one of the 20 values isn't enough, we can, for example, use one house to balance out the $219,000 and divide the rest however we like. They could all be exactly $160,00 (answering the question with NO) or could have more than 9 be a bit less than $160,000 and the rest a bit more than $160,000) (giving YES)
Insufficient.

(2) If the median was $150,000 then either 10 or 11 houses cost less than or equal to $150,000 (depending on if the two middle values were equal or not) meaning the answer to our question must be YES - at least 9 houses had less than $160,000.

(B) is our answer.
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Re: Last year, in a certain housing development, the average (arithmetic m  [#permalink]

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New post 20 Jun 2018, 02:43

Solution



Given:

    • We are given that the average price of 20 houses is $160,000.
To find:

    • We need to find if the price of 9 of the 20 houses is less than the average price i.e $160,000 or not.

Approach and Working:

Statement 1: Last year the greatest price of one of the 20 houses was $219,000.
This does not give us any information about the pricing of remaining 19 houses. Thus, we cannot say whether 9 of the 20 houses are priced less than $160,000 or not.

Statement 2: Last year the median of the prices of the 20 houses was $150,000.
In a set of 20 numbers, the median is the 10th and 11th term or median = 10th term + 11th term/2

Thus, we can get median= $150,000 in two cases:
    • When the values of both, 10th and 11th term is $150,000.
    • Or, when 10th term is as less from $150,000 as 11th term is greater than $150,000.

However, in both the cases at least 10 terms will be less than $150,000.

Hence, statement 2 is sufficient to get the answer.

Answer: B
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Re: Last year, in a certain housing development, the average (arithmetic m  [#permalink]

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New post 02 Jul 2018, 10:10
1
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was $160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was $219,000.
(2) Last year the median of the prices of the 20 houses was $150,000.


The total price of all 20 house was 160,000 x 20 = $3,200,000. We want to determine whether there are more than 9 houses with prices less than the average price of $160,000.

Statement One Alone:

Last year the greatest price of one of the 20 houses was $219,000.

That means the total price of the remaining 19 houses is $3,200,000 - 219,000 = $2,981,000. It’s possible that more than 9 houses were priced less than $160,000. For example, say 14 houses were priced $150,000 each for a total of $2,100,000. Then the last 5 houses could have been priced (2,981,000 - 2,100,000)/5 = 881,000/5 = $176,200 each. However, it’s also possible that no more than 9 houses were priced less than $160,000. For example, say 9 houses were priced $150,000 each for a total of $1,350,000. Then the last 10 houses could have been priced (2,981,000 - 1,350,000)/10 = 1,631,000/10 = $163,100 each.

Statement one alone is not sufficient.

Statement Two Alone:

Last year the median of the prices of the 20 houses was $150,000.

That means the average price of the 10th and 11th houses (assuming the prices of the houses are listed in ascending order) was $150,000. It is possible that the prices of these two houses were $150,000. If that is the case, then there will be at least 11 houses with prices less than the average price of $160,000. It is also possible that the price of the 10th house is less than $150,000 and the price of the 11th house is more than $150,000. If that is the case, we still have at least 10 houses with prices less than the average price of $160,000. Therefore, in either case, we have more than 9 houses with prices less than the average price.

Statement two alone is sufficient.

Answer: B
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Re: Last year, in a certain housing development, the average (arithmetic m &nbs [#permalink] 02 Jul 2018, 10:10
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