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GMAT Prep: Mean & Median

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GMAT Prep: Mean & Median

by Skywalker » Sat Oct 02, 2010 2:48 am
Last month 15 homes were sold in town X. The average sale price of the homes were $150,000 & the median sale price was $130,000 . Which of the following statements MUST be true ?

1) At least one of the homes was sold for more than $165,000
2) At least one of the homes was sold for more than $130,000 & less than $150,000.
3) At least one of the homes was sold for less than $130,000.

[spoiler]OA = 1[/spoiler]
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I really got a little confused here & opted for the wrong answer......whats the best way to deal with this ?
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by narik11 » Sat Oct 02, 2010 3:56 am
Skywalker wrote:Last month 15 homes were sold in town X. The average sale price of the homes were $150,000 & the median sale price was $130,000 . Which of the following statements MUST be true ?

1) At least one of the homes was sold for more than $165,000
2) At least one of the homes was sold for more than $130,000 & less than $150,000.
3) At least one of the homes was sold for less than $130,000.

[spoiler]OA = 1[/spoiler]
-----------------------------------------------------------------

I really got a little confused here & opted for the wrong answer......whats the best way to deal with this ?
The median of 15 values i.e the 8th value is 130,000
The total sum=150,000*15=225*10^4
If the values from 1 to 7 is 130,000 then Sum of values from 1st till 8th= 8*130,000=104*10^4

Therefore avg value for remaining 7 homes = 121*10^4 = 121/7 > 16.5*10^4
So its option (A)

For option 2 and 3 u cant say it definitely. Even in option A if the assumed values from 1 to 7 are lesser than 130,000 u will have at least one home greater than 165,000

Hope it helps
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by goyalsau » Sat Oct 02, 2010 4:47 am
Skywalker wrote:Last month 15 homes were sold in town X. The average sale price of the homes were $150,000 & the median sale price was $130,000 . Which of the following statements MUST be true ?

1) At least one of the homes was sold for more than $165,000
2) At least one of the homes was sold for more than $130,000 & less than $150,000.
3) At least one of the homes was sold for less than $130,000.

[spoiler]OA = 1[/spoiler]
-----------------------------------------------------------------

I really got a little confused here & opted for the wrong answer......whats the best way to deal with this ?
Question says in all 15 homes were sold for the average price of 150,000 .
which means in all 15 * 150,000= 2,250,000

As i know Median means the middle value in any series it does not mean all the values till 8th,
AS per the definition from KAPLAN

The median price is 130,000.
Which means 8th home was sold at 130,000.
Now we have 14 homes that were sold at the total price of 2,120,000
2,250,000 - 130,000 = 2,120,000

We can sell 12 homes at the cost of 151,000 = 1,812,000
2 homes at the cost of 154,000 = 308,000
1 home at the cost of 130,000 = 130,000

IN total 15 homes at the total cost of 2,250,000.

I not able to understand why option 1 is correct,
Please Let me understand :P

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by rima.mehta » Sat Oct 02, 2010 7:17 am
Still not clear on the solution of this question.
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by goyalsau » Sat Oct 02, 2010 8:44 am
rima.mehta wrote:Still not clear on the solution of this question.
It will be really good if any expert comment on this.
I am sure somebody will look to the issue and guide us that should be the answer.
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by narik11 » Sat Oct 02, 2010 9:28 am
goyalsau wrote:
Skywalker wrote:Last month 15 homes were sold in town X. The average sale price of the homes were $150,000 & the median sale price was $130,000 . Which of the following statements MUST be true ?

1) At least one of the homes was sold for more than $165,000
2) At least one of the homes was sold for more than $130,000 & less than $150,000.
3) At least one of the homes was sold for less than $130,000.

[spoiler]OA = 1[/spoiler]
-----------------------------------------------------------------

I really got a little confused here & opted for the wrong answer......whats the best way to deal with this ?
Question says in all 15 homes were sold for the average price of 150,000 .
which means in all 15 * 150,000= 2,250,000

As i know Median means the middle value in any series it does not mean all the values till 8th,
AS per the definition from KAPLAN

The median price is 130,000.
Which means 8th home was sold at 130,000.
Now we have 14 homes that were sold at the total price of 2,120,000
2,250,000 - 130,000 = 2,120,000

We can sell 12 homes at the cost of 151,000 = 1,812,000
2 homes at the cost of 154,000 = 308,000
1 home at the cost of 130,000 = 130,000

IN total 15 homes at the total cost of 2,250,000.

I not able to understand why option 1 is correct,
Please Let me understand :P

Check your Source.........
Median is the middle value obtained after arranging in ascending or descending.
If the 8 th home is sold at 130,000, then the values of 1st home to 7th home has to be<= 130,000 if the order taken is ascending.
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by mj78ind » Sat Oct 02, 2010 6:14 pm
Skywalker wrote:Last month 15 homes were sold in town X. The average sale price of the homes were $150,000 & the median sale price was $130,000 . Which of the following statements MUST be true ?

1) At least one of the homes was sold for more than $165,000
2) At least one of the homes was sold for more than $130,000 & less than $150,000.
3) At least one of the homes was sold for less than $130,000.

[spoiler]OA = 1[/spoiler]
-----------------------------------------------------------------

I really got a little confused here & opted for the wrong answer......whats the best way to deal with this ?

We know the middle term is $130K and the average is $150K. So now we need to balance the 130K with a higher weight so that the average goes to 150K for these two, that can only happen if the other weight is greater than 150+20 = 170K why?

Because it has to be 150 itself and has to cover for the gap of 20 for the 130 weight.

Hence one of them has to be greater than 165........

2 - not necessary we can get a combination where in all values are less than 130K and are balanced by all values greater than 150K to get the mean and median

3 - not necessary we can sell upto 14 homes for 130K and still have a mean of 150K and a median of 130K.

Hope this makes sense.
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by goyalsau » Sat Oct 02, 2010 8:33 pm
I was not arranging them from lower to higher value

That's why i was doing it wrong.
Thanks for your help.
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