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Math Expert V
Joined: 02 Sep 2009
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A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Difficulty:   15% (low)

Question Stats: 78% (01:54) correct 22% (02:24) wrong based on 179 sessions

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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 was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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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 was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

Solution -

Given that, Total average sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members is X.

(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C.
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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Bunuel 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 was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

Kudos for a correct solution.

For every 1 Male there are two females

Let, Male = 1, Female = 2

i.e. Tickets sold to each male members = x
i.e. Tickets sold to all male members = x*1 = x

Now, Tickets sold to each Female members = 70
i.e. Tickets sold to all Female members = 70*2 = 140

Total Tickets Sold = 140+x

Average Ticket per member = 66
Total Tickets Sold to 1 male and 2 Female (3 members) = 66*3 = 198

140+x = 198

i.e. x = 58

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A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Quote:
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 was the average number of tickets sold by the male members of the association

This is a weighted average question, to solve it quickly, we should realize that the formula is as follows:

$$\frac{X(1) + 70(2)}{1+2}=66$$

But, you don't need to use it like that! This is a sub-600 question, so it's easy to make an actual calculation, but it will still take your time, better to understand the following:

If there are more of X, then weighted average WILL BE closer to X.

70 - 66 = 4, we have 2 of 70, so the overall effect is +8, that is how much X(females) drags average away from Y(males). So, we should take that and divide by number of males and subtract from average.

So the formula:
$$66 - \frac{4*2}{1} = 66 - 8 = 58$$.

And that's why it doesn't matter if we have 2 females and 1 male, or 800 females and 400 males.

This is important, because sometimes absolute values might be huge and many, while differences between the values and averages are usually small on GMAT (my experience).

To better understand the importance of using a deviation from average instead of absolute values see the following question:
if-the-average-of-116741.html
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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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m(1) - A - f(2)
x - 66 - 70

70-66/66-x = 1/2
66-x = 8
x = 56. Ans is C?
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A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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FireStorm wrote:
m(1) - A - f(2)
x - 66 - 70

70-66/66-x = 1/2
66-x = 8
x = 56. Ans is C?

I highlighted your mistake in calc.

66 - x = 8,
x = 58.
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GMAT 1: 660 Q49 V31 Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Bunuel 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 was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

Kudos for a correct solution.

Solution:

Another problem which can be solved with X approach.
Assume, Let the average for Male is x.

Male...............Female
x......................70

.............66...........

4......................x-66

Given, Male: Female => 1: 2

But we know that, 4/ (x-66) = 1/2

Solving for x, x=> 58.

Option C
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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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(X*1)+(2*70) / 1+2 = 66

So , x+140 = 198

hence x = 58

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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Bunuel 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 was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

You can answer this question without doing a lot of calculation. Women sold an average of 70 raffle tickets, which is 4 higher than the total average of 66. Women have a + 4 differential. You also know that the ratio of men to women is 1:2. The women's differential multiplied by 2 will cancel with the men's differential multiplied by 1. If the men's differential is m, then:

1*m + 2*(+4) = 0
m + 8 = 0
m = - 8

The men sold an average of 8 fewer tickets than the total average: 66 - 8 = 58.

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Re: What was the average number of tickets sold by the male members?  [#permalink]

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Assume that the number of male and female members is 1 and 2.

Total tickets = 66 x (1+2) = 198
Tickets sold by the female members = 70 x 2 = 140
So the number of tickets sold by male members = 198 - 140 = 58.

Because we assume the number of male members is 1, this is the average number, too.

The correct answer is E.
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Re: What was the average number of tickets sold by the male members?  [#permalink]

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laveen_g 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 was the average number of tickets sold by the male members of the association?
a. 55
b. 57
c. 56
d. 60
e. 58

Use weighted averages concept discussed here (http://www.veritasprep.com/blog/2011/03 ... -averages/):

W1/W2 = (A2 - Aavg)/(Aavg - A1)
Wm/Wf = 1/2 = (70 - 66)/(66 - Am)
66 - Am = 8
Am = 58

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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Hello Bunuel,

I do not understand the differential method.

Could you please kindly elaborate?

Thank you

The women's differential multiplied by 2 will cancel with the men's differential multiplied by 1. If the men's differential is m, then:

1*m + 2*(+4) = 0
m + 8 = 0
m = - 8

The men sold an average of 8 fewer tickets than the total average: 66 - 8 = 58.
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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Bunuel 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 was the average number of tickets sold by the male members of the association

A. 50
B. 56
C. 58
D. 62
E. 66

Kudos for a correct solution.

Male:Female ratio =1:2
Female average is +4 differential from the total average.
If the average of male is m
The differentials need to cancel out
1*m+2*4=0;
m=-8
So the Male average =66-8=56
Ans:C
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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Avg=sum/#N

1) Total: 66N=Sum
2) Female: 70N=Sum
3) Male to Female = 1:2 multiples of 3
4) 66*3=198 total tickets
5) Female: 70*(2females)=140 tickets
6) Total: 198-140=58 tickets
7) 58*(1male)=58 tickets
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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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ScottTargetTestPrep can you please explain this question?

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Re: A charitable association sold an average of 66 raffle tickets per memb  [#permalink]

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Rocknrolla21 wrote:
ScottTargetTestPrep can you please explain this question?

Posted from my mobile device

Since male to female ratio is 1:2, we can express the number of males and females by x and 2x, respectively, where x is a positive integer. Let m be the average number of tickets sold by the male members.

We can create the following equation:

66 = [(m * x + 70 * 2x)]/(x + 2x)

66 = [(m * x + 70 * 2x)]/3x

66 * 3x = mx + 140x

Dividing by x, we have:

198 = m + 140

58 = m
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