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

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.

But it's just not Americans only; thanks, Mciatto little shaky on venns.
Victor

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.

Help: explain your algebra

Can't you use the easy way?

This is the Venn diagram which explains how Stolyar got the 3 equations. I did not solve them again. Thanks

WOW, very impressive Diagram.


Pracuda, you are either a math expert or an artist :wink: