i dont understand this concept.

[tejal777]

I dont have a particular eg. but i have come across this concept and dont understand.Pls help.Suppose,
Do atleast 20% of the people in city A eat meat?And its given that 18% women and 17% men in city A eat meat.Then how can we conclude the answer as "no"?

[esledge]

This is a neat concept to know: it's Weighted Average (e.g. what is the average number of meat eaters in city A if...). On the GMAT, the weighted average is usually of just two quantities (e.g. % meat eaters for men and for women).

Using your example, the number of people in city A who eat meat is:
0.18M + 0.17W

The percent of people who eat meat is the # of meat eaters/total # of people:
(0.18M + 0.17W)/(M+W)
0.18[M/(M+W)]+0.17[W/(M+W)]

You need to know two principles about this formula.
(1) The result must be between 17% and 18%, inclusive.
(2) If there are more women than men, the result will be closer to 17% (the women's %). If there are more men than women, the result will be closer to 18% (the men's %). If there an equal number of men and women, the result will be exactly 17.5%. Play with some numbers for M and W until this makes sense to you.

Here's bit of an algebraic proof of the principles above. Let's say M + W = T (i.e. total).
% of people who eat meat = 0.18[M/(M+W)]+0.17[W/(M+W)]
% of people who eat meat = 0.18[M/T]+0.17[W/T]
% of people who eat meat = 0.18[M/T]+0.17[(T-M)/T]
% of people who eat meat = 0.18[M/T]+0.17[T/T]-0.17[M/T]
% of people who eat meat = 0.17 + 0.18[M/T] - 0.17[M/T]
% of people who eat meat = 0.17 + 0.01[M/T]

As you can see, since M >=0, the minimum % is 17%. Since the maximum M = T, the maximum % is 18%. 20% is impossible.

[chintanjadwani]

I dont know why you had to complicate it so much :p

Just use simple logic in these examples by assuming nos...

for example, over here, there be 100 men and 100 women in City A.
so 18% i.e. 18 men eat meat and 17% i.e 17 women eat meat.

So out of 200 35 in all men and women eat meat, i.e <20% bcos 20% is 40. ..!!
Voila...ans. is NO..!! :)

[StaceyKoprince]

She complicated it b/c she had to do so in order to prove the answer is always no. You assumed that there are an equal number of men and women. That's one possibility, but it's not the only possibility. So you found one instance in which the answer is no, which is good, but you didn't prove that the answer is ALWAYS no. :)