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Average age problem

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by gmat009 » Tue Oct 07, 2008 9:04 pm
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
A. 31 B. 31.5 C. 32 D. 32.5 E. 33
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by amitansu » Tue Oct 07, 2008 9:16 pm
'D' is my pick.


Amit
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by vishubn » Tue Oct 07, 2008 9:27 pm
yes it is 32.5 :)


M- number of men
W-number of women

given ----> (22(M)+26(W)/22+26)=35

22(M)/22=38

therefore 22(M)=38*22

sub above we get

(38*22)+26W=35*48

W=((35*48)-(38*22))/26

approximately u get 32.46 which is 32.5

Vishu
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by schakiiieee » Wed Oct 08, 2008 3:25 pm
Similar result but calculated with smaller numbers:

22 men with an average that is 3 higher than the overall average.

--> 22*3 = 66.

26 women who have to drive that average down to 35 again

--> 26*x=66 --> x=66/26=2,something.

--> Women's average age is 35-2,something = 32,5 (only number >32 and <33).
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by linfongyu » Mon Aug 24, 2009 8:40 pm
schakiiieee,

very cool method. I have to leech this technique from you!
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