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# I need someone to come up with the formula to this problem.

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Eternal Intern
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I need someone to come up with the formula to this problem.  [#permalink]

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22 Jul 2003, 10:55
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I need someone to come up with the formula to this problem.

In a certain survery of a group of people, 87 people said they found Americans the sexiest, 91 indicated they found Indians the sexiest, and 91 indicated they found Russians the sexiest. Of the people surveyed 9 liked only Americans, 10 liked only Indians, 12 liked only Russians, and 40 liked all three types of girls. How many of the people surveyed liked both Indians and Russians but not American girls?
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22 Jul 2003, 11:11
Draw a venn (or store a picture in your head) and you get the following three equations...

Let Indian & Russian = X
Let Indian & American = Y
Let Russian & American = Z

X + Y = 41
Y + Z = 38
X + Z = 39

Solve away and you get

X = 21
Y = 20
Z = 18

I quickly plugged back in these #'s and they added up - just to check it!!

Answering the question, the girls in question are represented by X, and therefore 21 is the answer.
(time to complete was 1:35)
Eternal Intern
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22 Jul 2003, 12:44
Explain how you came up with equations.

I have no clue and can't follow.
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22 Jul 2003, 13:45
Draw the Venn diagram and it will be clear. Remember that the original numbers that you gave total in each of the nationality "circles". Example: Americans ONLY + Americans & Russians + Americans & Indians + all three = 87. After considering all of the information given, all we need to do is find Americans & Russians, Americans & Indians, and Indians & Russians. Look at the Venn and see what needs to add up. From that we got the three equations with three variables.
Eternal Intern
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23 Jul 2003, 08:46
But it's just not Americans only; thanks, Mciatto little shaky on venns.
Victor
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23 Jul 2003, 09:51
IS = Set representing people who believe Indians are the sexiest = 91
RS= Set representing people who believe Russians are the sexiest = 91
AS= Set representing people who believe Americans are the sexiest = 87

LOI=subset for people who like only Indian girls = 10
LOR=subset for people who like only Russian girls = 12
LOA=subset for people who like only American girls = 9

IRA= people who like all 3 = 40

IR = people liking Indian and Russian girls = x
IA = people liking Indian and American girls = y
RA= people liking Russian and American girls = z

So, from the Venn diagram,

For the circle representing Indians,
x + y + 40 = IS - LOI
=> x + y + 40 = 91 – 10
=> x + y = 41

Similarly, we will get,
y + z = 38
x + z = 39

Now, solving for x will get us 21.

P.S. In the original question, I read "sexiest" as "sexist" and was thinking in the line that if some people think that "Indians are sexist" then they will not like "Indian girls" etc. Sometimes my own carelessness amazes me.
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P K Das

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23 Jul 2003, 10:26

Can't you use the easy way?

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23 Jul 2003, 10:30
This is the Venn diagram which explains how Stolyar got the 3 equations. I did not solve them again. Thanks
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P K Das

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23 Jul 2003, 11:51
WOW, very impressive Diagram.

Pracuda, you are either a math expert or an artist
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