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At a dinner party, 40 percent of the guests wore both jacket

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awamy
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At a dinner party, 40 percent of the guests wore both jacket [#permalink] New post   Updated on: 19 Oct 2019, 12:13
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At a dinner party, 40 percent of the guests wore both jackets and ties. If 50 percent of the guests who wore jackets did not wear ties, what percent of the guests wore jackets?

A. 20 percent
B. 40 percent
C. 60 percent
D. 70 percent
E. 80 percent
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E

Originally posted by awamy on 06 Feb 2018, 16:26.
Last edited by sal60 on 19 Oct 2019, 12:13, edited 2 times in total.
Only one answer was selectable
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Re: At a dinner party, 40% of the guests wore both jackets and t [#permalink] New post   06 Feb 2018, 20:08
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awamy wrote:
At a dinner party, 40% of the guests wore both jackets and ties.
if 50% of the guests who wore jackets didn't wear ties, what % of the guests were jackets?
A) 20%
B) 40%
C) 60%
D) 70%
E) 80%


Hello awamy,

I have seen you have posted 16 posts.

Can i request you to read the rules of posting before you post anything. This help to keep the greprep club segregated with the type of Question/Topic and also helps to search the particular topic. Also share the SOURCE of the topic

https://gre.myprepclub.com/forum/rules-for ... -1083.html.

Thanks and keep posting
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Re: At a dinner party, 40% of the guests wore both jackets and t [#permalink] New post   06 Feb 2018, 23:26
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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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gremather
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Re: At a dinner party, 40% of the guests wore both jackets and t [#permalink] New post   23 Feb 2018, 20:42
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] New post   05 Mar 2018, 08:15
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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] New post   24 Feb 2021, 23:38
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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] New post   21 Jul 2022, 05:43
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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