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Re: At a dinner party, 40% of the guests wore both jackets and t [#permalink]
I am bit confused with the last bit of your answer. If 50% of the guests who wore jackets didn't wear ties, then shouldn't the "No Tie and Jacket" cell be 50? And so the total # of jackets will be 90. So 90%? But 90% is not in the answers so I could be wrong.

SherpaPrep wrote:
This is an overlapping set. You can recognize these because it's possible to do two things at once, or neither, or just one; in this case it's wearing a jacket and/or a tie. Many people use Venn diagrams for these but Venn diagrams can be confusing. An Overlapping Set Table is much easier. Simply draw three vertical and three horizontal lines and then label them with the two possibilities and their opposites. Consult the attached image for an example. Then just fill in the parts of the table. The boxes in every row and column should add to the total.


In this problem, we aren't given any numbers; rather we're given percents. No biggie. Just pretend that the total number of people is 100 and then treat the percents we're given as though they're actually totals. This allows us to fill out the table as illustrated below. Therefore the answer is E.
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Re: At a dinner party, 40% of the guests wore both jackets and t [#permalink]
1
good problem, especially the part when one should make an equation as 40+x(0.5)=x, where x represents the total number of the ones who wore jacket.
then 40=x-0.5x which yields x=80
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At a dinner party, 40 percent of the guests wore both jacket [#permalink]
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gremather wrote:
I am bit confused with the last bit of your answer. If 50% of the guests who wore jackets didn't wear ties, then shouldn't the "No Tie and Jacket" cell be 50? And so the total # of jackets will be 90. So 90%? But 90% is not in the answers so I could be wrong.


If 50% of the guests who wore jackets didn't wear ties means They are only wearing Jackets

Let the total number of people wearing jackets be \(J\)
people wearing only jackets = \(0.5J\)
people wearing both jackets and ties = 0.40(total)

So,
people wearing jackets = people wearing only jackets + people wearing both jackets and ties
\(J = 0.5J + 0.40(total)\)
\(0.5J = 0.40(total)\)
\(J = 0.80(total)\)

Hence, option E
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Re: At a dinner party, 40 percent of the guests wore both jacket [#permalink]
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Re: At a dinner party, 40 percent of the guests wore both jacket [#permalink]
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