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Average mean in a group of people

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Average mean in a group of people

by mehravikas » Wed Jun 04, 2008 2:52 am
S6-22 In a certain group of people, the average (arithmetic mean) weight of the males is 180 pounds and of the females, 120 pounds. What is the average weight of the people in the group?

(1) The group contains twice as many females as males.
(2) The group contains 10 more females than males.


Please explain why the answer is not 'D'
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by molt_llest » Wed Jun 04, 2008 3:08 am
I would choose A

in (2) we can not eliminate the number of male/females variable, and then we don't know the average
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Correct Answer : A

by albertrahul » Wed Jun 04, 2008 3:55 am
A is indeed correct answer as average weight is constant (140) for all examples.
Let Male be 1 and Females be 2, thus:
Total weight of Male = 180
Total weight of Females = 120*2 = 240
total weight = 420, Avg. = 420/3 = 140

You could use any values and result will still be same.

D cannot be correct answer because:
Answers would vary based on values:

If number of males equal 20 then as per statement two females would equal 30 hence average would be (3600 + 3600)/50 = 144.
Example two: Number of males equal 10 and females equal 20:
(1800 + 2400)/30 = 140

Hope this clarifies your doubt.
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by mehravikas » Sat Jun 07, 2008 5:45 pm
Thanks, it does clarifies my doubt.
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Re: Correct Answer : A

by ash_maverick » Thu Jun 11, 2009 10:53 pm
albertrahul wrote:A is indeed correct answer as average weight is constant (140) for all examples.
Let Male be 1 and Females be 2, thus:
Total weight of Male = 180
Total weight of Females = 120*2 = 240
total weight = 420, Avg. = 420/3 = 140

You could use any values and result will still be same.

D cannot be correct answer because:
Answers would vary based on values:

If number of males equal 20 then as per statement two females would equal 30 hence average would be (3600 + 3600)/50 = 144.
Example two: Number of males equal 10 and females equal 20:
(1800 + 2400)/30 = 140

Hope this clarifies your doubt.

isn't this calculation wrong for fact stmt-1

As per the fact stmt-twice as many female as male=> M= 2F.

so the total no of female in terms of Male= 120/2= 60 or total no of Male in term of Female = 180*2= 360F

So, the total average weight= (360F+120F)/2F+F ==> 480F/3F=>160

In terms of Male----> (180M+60M)/M+M/2
240M/1.5M --->160.

Correct me if my calculation is wrong. I was little confused with the calculation of albertrahul. Though i found her approach correct along with the answer.
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by ket » Fri Jun 12, 2009 1:23 am
IMO it's A

Let number of Males be - M and Number of women be W

then what we are searching for is (M*180+W*120)/ (M+W)

In order to solve this we need to find the connection between M and W such that would remove this unknowns and leave us only with numbers.

It is obvious that A offers such connection. (If you plug in 2M instead of W)

While B doesn't, if you plug in M+10 instead of W then there is no way you can get rid of unknown M so you can not solve the problem.

Yeah, I know everybody loves plugging in numbers instead of algebraic solution but still... I think this one is easy this way too. :)
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by tohellandback » Fri Jun 12, 2009 1:42 am
I might be missing something here but don't you guys think we can find the average of the whole lot without any of the options

average of males=180
average of females=120
average of the group=(180+120)/2=150

correct me if i am wrong

ok I got the flaw in my case..
The powers of two are bloody impolite!!
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by ket » Fri Jun 12, 2009 2:06 am
tohellandback wrote:I might be missing something here but don't you guys think we can find the average of the whole lot without any of the options

average of males=180
average of females=120
average of the group=(180+120)/2=150

correct me if i am wrong

ok I got the flaw in my case..

No tohellandback that's exactly GMAT Trap! :)

Look at this :

Set 1 ( 1 2 3) average1=2

Set 2 ( 1 2 3 4) average2=5/2

Combined set ( 1 2 3 1 2 3 4 ) average 16/7


Now if we did this (av1+Av2)/2 then we would have average of 9/2 and that does not equal 16/7, i.e. this method of calculation is wrong.

To calculate the average of combined group correctly you need this steps

1. Av1 * 3 (3 is the number of values in set 1)

2. Av2*4 (4 is the number of values in set 2)

3. (1)+(2) = 16

4. (3)/(3+4) - where 3 and 4 are the number of values in the set1 and set2 respectively, ---- the result will be 16/7
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by tohellandback » Fri Jun 12, 2009 2:27 am
ket wrote:
tohellandback wrote:I might be missing something here but don't you guys think we can find the average of the whole lot without any of the options

average of males=180
average of females=120
average of the group=(180+120)/2=150

correct me if i am wrong

ok I got the flaw in my case..

No tohellandback that's exactly GMAT Trap! :)

Look at this :

Set 1 ( 1 2 3) average1=2

Set 2 ( 1 2 3 4) average2=5/2

Combined set ( 1 2 3 1 2 3 4 ) average 16/7


Now if we did this (av1+Av2)/2 then we would have average of 9/2 and that does not equal 16/7, i.e. this method of calculation is wrong.

To calculate the average of combined group correctly you need this steps

1. Av1 * 3 (3 is the number of values in set 1)

2. Av2*4 (4 is the number of values in set 2)

3. (1)+(2) = 16

4. (3)/(3+4) - where 3 and 4 are the number of values in the set1 and set2 respectively, ---- the result will be 16/7
Thanks ket i got it.

by the way, before you could delete it, I had already seen your flawed post:))
The powers of two are bloody impolite!!
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by ket » Fri Jun 12, 2009 2:30 am
yeah I deleted first post because I made errors in calculation, thats why I hate it plugging numbers! :) I always mess something up :):)
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