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What is the average (arithmetic mean) height of the n people in a cert [#permalink]

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20 Dec 2005, 09:03

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A

B

C

D

E

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25% (medium)

Question Stats:

65% (01:48) correct
35% (00:56) wrong based on 532 sessions

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What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet 2 1/2 inches, and the average height of the rest of the people in the group is 5 feet 10 inches.

(2) The sum of the heights of the n people is 178 feet 9 inches.

what is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet and 2.5 inches and the average height of the rest of the people in the group is 5 feet 10 inches

(2) the sum of the heights of the n people is 178 feet 9 inches

pranrasvij wrote:

zisis wrote:

pranrasvij wrote:

A is easily the right choice since it gives info about the rest (1-n/3) and n/3 => we dont need the final value of "n" in that case.

B gives us total height but no way to get the mean without more on "n".

so the mean height is the heights given at a ration 1:2 ????

please explain....

yep... all you have to do is the add the 2 heights and divide by 2 to get the mean height => easy to calculate (IMHO!)

Answer to the question is A, but you shouldn't divide the "sum" by 2, you should divide by \(n\).

\(Weighted \ average=\frac{sum \ of \ weights}{# \ of \ data \ points}\), or in our case \(average \ height=\frac{sum \ of \ heights}{# \ of \ people}\).

(1) The average height of \(\frac{n}{3}\) people is 74.5 inches and the average height of \(\frac{2n}{3}\) people (the res of the people in the group \(n-\frac{n}{3}=\frac{2n}{3}\)) is 70 inches --> \(average \ height=\frac{sum \ of \ heights}{# \ of \ people}=\frac{74.5*\frac{n}{3}+70*\frac{2n}{3}}{n}\) --> \(n\) cancels out --> \(average \ height=74.5*\frac{1}{3}+70*\frac{2}{3}\). Sufficient.

(2) Sum of heights equals to 178 feet 9 inches --> only nominator is given. Not sufficient.

Re: What is the average (arithmetic mean) height of the n people [#permalink]

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21 Mar 2010, 11:35

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nifoui wrote:

What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet 2(1/2) inches, and the average height of the rest of the people in the group is 5 feet 10 inches.

(2) The sum of the heightsof the n people is 178 feet 9 inches.

Stmt1: Avg of n/3 people= 6feet 2(1/2) inches = n/3 * 6feet 2(1/2) inches Avg of 2n/3 people = 5feet 10 inches = 2n /3*5feet 10 inches If we add both above quantities and divide it by n we will get the avg since n will cancel out. So, sufficient.

Stmt2: if sum is given to calculate avg we have to divide it by n. But we dont know the value of n so insufficient. Hence A is the answer
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Re: What is the average (arithmetic mean) height of the n people [#permalink]

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21 Mar 2010, 23:49

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Socker121314 wrote:

IMO E....from the information provided we don't know what N is.

but if u see statement 1 you can find out avg without knowing n Avg = (n/3 * 6feet 2(1/2) inches + 2n /3*5feet 10 inches ) / n = 1/3 * 6feet 2(1/2) inches + 2 /3*5feet 10 inches we dont need to convert it and calculate but we can find the value. So answer is A
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What is the average (arithmetic mean) height of the n people [#permalink]

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14 Jul 2010, 13:35

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What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet and 2.5 inches and the average height of the rest of the people in the group is 5 feet 10 inches (2) the sum of the heights of the n people is 178 feet 9 inches

Bunel - I need one help. This is not a difficult question and it's easy to see that A is sufficient. However I thought B is suf too because the stimulus says N. Now N could be anything. Is it not sufficient to say avg height = sum of heights (given in the second option)/N - N is mentioned in the stem. Why do we have to concern with the actual value of N?

Official Guide:

In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.

(1) The average height of \(\frac{n}{3}\) people is 74.5 inches and the average height of \(\frac{2n}{3}\) people (the res of the people in the group \(n-\frac{n}{3}=\frac{2n}{3}\)) is 70 inches --> \(average \ height=\frac{sum \ of \ heights}{# \ of \ people}=\frac{74.5*\frac{n}{3}+70*\frac{2n}{3}}{n}\) --> \(n\) cancels out --> \(average \ height=74.5*\frac{1}{3}+70*\frac{2}{3}\). Sufficient.

(2) Sum of heights equals to 178 feet 9 inches --> only nominator is given. Not sufficient.

Answer: A.

Hope it helps.

Hi Bunuel, The fact that confused me is the word tallest in statement 1. It says "average height of \(n/3\) [highlight]tallest[/highlight] people in the group is 6 feet 2.5 inches.

Isn't this bit ambiguous? We have no clue how many people to consider in tallest category?

It means that if we order these n people from shortest to tallest and consider \(\frac{n}{3}\) tallest people, then their average height would be 74.5 feet.
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Re: What is the average (arithmetic mean) height of the n people in a cert [#permalink]

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02 Dec 2009, 13:58

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What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet 2 1/2 inches, and the average height of the rest of the people in the group is 5 feet 10 inches.

(2) The sum of the heights of the n people is 178 feet 9 inches.

Last edited by Bunuel on 28 Jul 2015, 07:24, edited 1 time in total.

Renamed the topic, edited the question and added the OA.

Re: What is the average (arithmetic mean) height of the n people in a cert [#permalink]

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04 Dec 2009, 14:00

srini you solved this question correctly however remember that this is a DS question and you don't have to find the right answer so no point converting feet to inches. You could solve the problem even if you approximated their heights to 5 feet and 6 feet.

sum of heights of the group = 5*2n/3 + 6*n/3 Total number of people = n Dividing the above two will gives us a number with no variables. That is sufficient to say that A gives us the answer.
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What is the average (arithmetic mean) height of the n people [#permalink]

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21 Mar 2010, 10:49

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What is the average (arithmetic mean) height of the n people in a certain group?

(1) The average height of the n/3 tallest people in the group is 6 feet and 2.5 inches and the average height of the rest of the people in the group is 5 feet 10 inches (2) the sum of the heights of the n people is 178 feet 9 inches
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