What is the average (arithmetic mean) height of the n people : GMAT Data Sufficiency (DS)
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# What is the average (arithmetic mean) height of the n people

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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, 08:03
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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.
[Reveal] Spoiler: OA
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20 Dec 2005, 09:27
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, 15:03
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, 19:13
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, 15:25
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, 12:58
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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, 06:24, 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, 13:02
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, 13:00
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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15 Feb 2010, 06:11
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, 09:49
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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, 10:35
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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 =
[Reveal] Spoiler:
A

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, 22:49
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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 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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14 Jul 2010, 12:43
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".
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Re: Mean of group [#permalink]

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14 Jul 2010, 12:50
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 ????

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14 Jul 2010, 13:06
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 ????

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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14 Jul 2010, 14:40
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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 (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 ????

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.

Hope it helps.
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14 Jul 2010, 15:33
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, 00:20
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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15 Jul 2010, 07:06
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dwivedys wrote:
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.

Hope it helps.
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Re: Mean of group   [#permalink] 15 Jul 2010, 07:06

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