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A charitable association sold 66 raffle tickets

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by gmatdriller » Tue Feb 26, 2013 5:21 pm
A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What wast he average number of raffle tickets sold by the male members of the association?

Source: Mahattan Quant book6

I'll prefer a shorter method than using the weighted average formula approach;
66 = (mx + fy)/(x+y)....where f=0.7, while x:y is 1:2.
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by Tommy Wallach » Tue Feb 26, 2013 6:35 pm
Hey Gmatdriller,

This is a weighted average question. You can use the concept of weights/residuals to solve it without any annoying equation.

66 is the balance point around which everything must even out.

The women sold an average of 70 tickets each. That's four more than 66, but because there are twice as many women, they create a weight of 8 on the right side of 66 (imagine a number line).

To balance that out, then men need to be 8 to the left of 66, or 58.

Does that work for you?

-t
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by GMATGuruNY » Tue Feb 26, 2013 7:11 pm
gmatdriller wrote:A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What wast he average number of raffle tickets sold by the male members of the association?
Let the number of men = 1 and the number of women = 2, for a total of 3 members.
Total tickets sold by all 3 members = number*average = 3*66 = 198.
Total tickets sold by the 2 women = number*average = 2*70 = 140.
Total tickets sold by the 1 man = 198-140 = 58.
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by PiyushKashyap » Wed Feb 27, 2013 11:10 am
Hi, I tried following method, but not very short method.

As mentioned in question:
Tf total ticket sold to females F.
Tm total ticket sold to males M.

Total Avg is 66 i.e (Tf + Tm)/M+F=66 ----(1)
Tf/F=70 ------(2)

Now divide numerator and denom LHS in eq 1 by F.
(Tf/F + Tm/F) / (M/F) + 1 = 66

(70 + Tm/F) / (1/2) + 1 = 66 M:F=1/2

70 + Tm/F = 3/2 X 66
Tm/F = 99 - 70
Tm/F = 29
Tm = 29F
Divide both side by M.
Tm/M = 29 F/M
Tm / M = 29 X 2 (inverse of male to female ratio)
Thus average ticket sold by males is Tm/M= 58.
Last edited by PiyushKashyap on Wed Feb 27, 2013 11:17 am, edited 2 times in total.
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by Tommy Wallach » Wed Feb 27, 2013 11:14 am
Hey Piyush,

That's definitely not right, but I'm afraid I can't even follow the logic. If you want to explain where each step comes from, that might help. First thing is I'm not sure where you're getting 77. Did you mean 70? If so, try redoing your math with that...

-t
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by vipulgoyal » Wed Feb 27, 2013 8:40 pm
my ans is 78
xy +70(2x)/3x = 66
let y is average of male
xy+140x/3x=66
xy+140x = 218x
hence y = 78
take 70, 66 or .7, .66 ans will be the same
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by Tommy Wallach » Wed Feb 27, 2013 9:43 pm
Hey Vipul,

Do you see how your answer doesn't even make sense? If the average is 66 but the women got 70, which is higher than 66, then we need something lower from the men, to balance it out. If the women got 70 and the men got 78, the overall average would be somewhere between 70 and 78.

-t

P.S. I can't give you any more advice on your method because I don't understand it; you'd have to explain your math piece by piece.
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by gmatdriller » Thu Feb 28, 2013 3:49 pm
The methods as explained by GMATGuru and Tommy Wallace are lucid.
Tommy Wallace: Should the m:f ratio be 2:3 for same question, we
say the female have a spread of 3*4=12; then male = 12/2 = 6 spreads
away from the central mean -in which case men ave = 60?

Kindly refer me to resources I can practice more of such questions.

Regards.
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by Tommy Wallach » Thu Feb 28, 2013 4:25 pm
Hey Gmatdriller,

Absolutely right! Well done!

-t
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