Gmat Prep 2

[Ruben]

What is the average (aritmetic mean) hight of the n people in a certain group?

1 the average hight of the n/3 talles people in the group is 6 feet and 2 1/2 inches and tthe average hight of the people in the group is 5 feet and 10 inches.

2 The sum of the lenghts of the people is 178 feet and 9 inches.


Thanks !!

[StaceyKoprince]

I think you might have missed a word / number in statement 1? It says "the average hight of the people in the group is 5 feet and 10 inches" which appears to answer the question straight out. Is that supposed to say the average height of some subset of the group, as the first half of that statement does? (the first half limits itself to the n/3 tallest people)

[Ruben]

Hi Steacy,

Here is a screen-shot of the actual question. Sorry for the incorrect posting.

[RonPurewal]

Looking at statement (2) first, we see that it is not sufficient, because the average (arithmetic mean) of a group of numbers is defined as (sum of data) / (# of data points). With statement (2), we only have the numerator of this expression (the # of people in the group is unknown), so we can't figure out the average.

Looking at statement (1) alone, we can set up the average as follows:
Average = (sum of data points) / (# of data points)
= [(n/3)(74.5) + (2n/3)(70)] / (n) <-- note that I used inches here, so I won't have to write in more fractions than necessary (trying to write fractions on this forum is not fun)
= [(1/3)(74.5) + (2/3)(70)]
There's no need to simplify further, because the 'n' is gone: you get one number. Therefore, this statement is sufficient.

Answer = A

Note that, if you have the averages of all the FRACTIONS or PERCENTAGES of a group, then you'll be able to calculate the overall average of the group. This is a worthwhile fact to memorize for the data sufficiency problems.

[rkafc81]

I have a question about this...

Quoting Ron "if you have the averages of all the FRACTIONS or PERCENTAGES of a group, then you'll be able to calculate the overall average of the group. This is a worthwhile fact to memorize for the data sufficiency problems. "

how does this actually work (and what's the theory behind it)? does it always work?

thanks!

[RonPurewal]

I have a question about this...

Quoting Ron "if you have the averages of all the FRACTIONS or PERCENTAGES of a group, then you'll be able to calculate the overall average of the group. This is a worthwhile fact to memorize for the data sufficiency problems. "

how does this actually work (and what's the theory behind it)? does it always work?

thanks!

hi,
this is not something that's easily explained in a single forum post, but, fortunately, there's an entire video segment on it. check out the december 17, 2009, video here:
http://www.manhattangmat.com/thursdays-with-ron.cfm
i believe that the weighted average stuff comes at the end of the video, although i don't remember for sure.

[rkafc81]

will check out that vid - thanks Ron

[tim]

:)

[asharma8080]

[pointed out error -- post has been edited]

[RonPurewal]

yep, that was a mistake. fixed. thanks.