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Average - two greatest

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Average - two greatest

by Xbond » Mon Jun 08, 2009 9:03 pm
Hi there,

Could you help me to understand the concept

A certain list consists of five different integers. Is the average (arithmetic mean) of the two greatest integers in the list greater than 70 ?

(1) The median of the integers in the list is 70

(2) The average of the integers in the list is 70

The answer is D but I select A. I didn't succeed to see why (2) is right.
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by tohellandback » Mon Jun 08, 2009 9:58 pm
I think D is the riht answer
option 1 is clear. It is the median so the two greatest numbers will both be greater than 70

2) if we take an average: the ideal case is all numbers are 70. if any number is less than 70, there must be another number greater than 70 to compensate that.
there are five DIFFERENT integers. there must be atleast two numbers less than 70 and two greater than 70

ex: ideal case: 70,70,70,70,70 if the numbers are different
you could write it as
68,69,70,71,72
or66,68,70,72,74
you see, you must increase two numbers to compensate the loss

Hope it helps
The powers of two are bloody impolite!!
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Re: Average - two greatest

by Stuart@KaplanGMAT » Tue Jun 09, 2009 11:36 am
Xbond wrote:Hi there,

Could you help me to understand the concept

A certain list consists of five different integers. Is the average (arithmetic mean) of the two greatest integers in the list greater than 70 ?

(1) The median of the integers in the list is 70

(2) The average of the integers in the list is 70

The answer is D but I select A. I didn't succeed to see why (2) is right.
Here's another way to think about statement (2):

Every set of numbers has an average. If you chop off the lowest number in the set, what happens to the average? Well, unless every number in the set is identical, the average will always go up.

Keeping that in mind, let's rephrase the question, building in statement (2):

A set of 5 different numbers has an average of 70. If you chop off the lowest 3 numbers of the set, do the 2 remaining numbers have an average greater than 70?

Answer: definitely yes!
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by Stuart@KaplanGMAT » Tue Jun 09, 2009 11:39 am
tohellandback wrote:2) if we take an average: the ideal case is all numbers are 70. if any number is less than 70, there must be another number greater than 70 to compensate that.
there are five DIFFERENT integers. there must be atleast two numbers less than 70 and two greater than 70
Your final answer is correct, but your reasoning is off.

The median of a set of numbers has an equal number of terms above it and below it.

However, that's not always true for the average (arithmetic mean) of a set.

For example:

The set {67, 68, 69, 70, 76} has an average of 70, but has 3 terms below 70, 1 term at 70 and 1 term above 70.

The set {66, 67, 68, 69, 80} has an average of 70, but has 4 terms below 70 and 1 term above 70.
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by Xbond » Tue Jun 09, 2009 11:56 am
many thks coach
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by tohellandback » Tue Jun 09, 2009 5:31 pm
Hi Stuart I still think my reasoning was correct.
I think I didn't put it correctly. Let me say the sum of the two greatest integers has to be more than 140.
I hope I am clear now.

Thanks for pointing it out.
Stuart Kovinsky wrote:
tohellandback wrote:2) if we take an average: the ideal case is all numbers are 70. if any number is less than 70, there must be another number greater than 70 to compensate that.
there are five DIFFERENT integers. there must be atleast two numbers less than 70 and two greater than 70
Your final answer is correct, but your reasoning is off.

The median of a set of numbers has an equal number of terms above it and below it.

However, that's not always true for the average (arithmetic mean) of a set.

For example:

The set {67, 68, 69, 70, 76} has an average of 70, but has 3 terms below 70, 1 term at 70 and 1 term above 70.

The set {66, 67, 68, 69, 80} has an average of 70, but has 4 terms below 70 and 1 term above 70.
The powers of two are bloody impolite!!
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