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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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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.
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Re: What is the average (arithmetic mean) height of the n people in a cert [#permalink]
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20 Dec 2005, 10:27
I go for A.
1) 1/3 * 6 feet 2 1/2 inches + 2/3 * 5 feet 10 inches.... SUFF
2) Doesn't give us the value of n (number of elements/people)... INSUFF



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Re: What is the average (arithmetic mean) height of the n people in a cert [#permalink]
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20 Dec 2005, 16:03
A is sufficient,
total height = (n/3)* 74.5 inches + (2/3)n* 70 inches
number of people n
average height = {(n/3)* 74.5 inches + (2/3)n* 70 inches}/n = 68.83 inches.
B insufficient



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Re: What is the average (arithmetic mean) height of the n people in a cert [#permalink]
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20 Dec 2005, 20:13
From (1), (n/3*(6'2.5") + 2n/3*(5'10"))/n > average height. Sufficient.
From (2), we do not know n. Insufficient.
Ans: A



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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 Apr 2007, 16:25
Guys a basic conceptual question.
Suppose we have a set S = {10,20,30,40,50}
If we take individual values as 10,20 and take their av = 15
and the rest 3 values 30,40,50 and avg of these is = 40
So the group average of S {10,20,30,40,50} = 30 is not equal to the sum of individual averages 15+40 = 55 or even the av of the values 55/2 =27.5
Whats the deal here? Explanations needed please



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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.



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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, 14:02
I Think answer is A from S1) Avg of n people = sum of ages of n people/n we are given sum of n people (in inches) as 74.5n/3 + 70*2n/3 ; dividing this by n, n will cancel out and we can calculate the average. S2) insufficient as we dont know the value of n
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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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Re: What is the average (arithmetic mean) height of the n people in a cert [#permalink]
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15 Feb 2010, 07:11
ans should be A
if n/3 is 6 inches then 2n/3 is rest which is 5feet 10 inches
so the avearge height of n people is 6+2*5feet 10/3
so ans is A



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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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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. OA = 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



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Re: Mean of group [#permalink]
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14 Jul 2010, 13:43
A is easily the right choice since it gives info about the rest (1n/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".



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Re: Mean of group [#permalink]
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14 Jul 2010, 13:50
pranrasvij wrote: A is easily the right choice since it gives info about the rest (1n/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....



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Re: Mean of group [#permalink]
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14 Jul 2010, 14:06
zisis wrote: pranrasvij wrote: A is easily the right choice since it gives info about the rest (1n/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!)



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Re: Mean of group [#permalink]
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14 Jul 2010, 15:40
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zisis 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 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 (1n/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. Answer: A. Hope it helps.
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Re: Mean of group [#permalink]
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14 Jul 2010, 16:33
thanks Bunuel.... this is a v good explanation. Sorry I messed up the divide part!....I knew i was wrong somewhere and came back to fix it !!



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Re: Mean of group [#permalink]
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15 Jul 2010, 01:20
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?



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Re: Mean of group [#permalink]
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