Sets

[anuptvm]

At an university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all students are members of the swim team?

1. 20% 2. 30% 3. 40% 4. 50% 5. 60%

The way I approached this one is...

Let T = total students be 100

Then members of both clubs = 40

Total = Swim Club + Chess Club - Both + neither (since all students are members the neither would be 0)

Chess club members and swimmers = 80% ( as 20% of swimmers are not chess club membersc=32

Swimmers only = 8

chess club = 100 -8 +40 .... kinda lost it here!!!

[anshumishra]

At an university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all students are members of the swim team?

1. 20% 2. 30% 3. 40% 4. 50% 5. 60%

The way I approached this one is...

Let T = total students be 100

Then members of both clubs = 40

Total = Swim Club + Chess Club - Both + neither (since all students are members the neither would be 0)

Chess club members and swimmers = 80% ( as 20% of swimmers are not chess club membersc=32

Swimmers only = 8

chess club = 100 -8 +40 .... kinda lost it here!!!

Let X be the number of swimmers who are not members of chess club

Then as per the question :

(40+x)/ 5 = x
=> x = 10

So, the number of students who are member of swimming team = No. of students who are member of both + No. of students who are member of only Swimming (but not chess club) = 40+10 = 50 %

[Rezinka]

@anuptvm

Your approach :

Let T = total students be 100 : Correct

Then members of both clubs = 40 : Correct

Total = Swim Club + Chess Club - Both + neither (since all students are members the neither would be 0) : Correct

Chess club members and swimmers = 80% ( as 20% of swimmers are not chess club membersc=32 : The problem lies here. When we use this formula, each group i.e. Chess and Swimmers should both include the members present in both groups.

Say, we take 'x' as the number of members in Swim club only.
So members in Chess club only = 100(total) - x (Swim only) - 40 (both)
= 60 - x
Using your formula,
100 = (40+x) + (60-x+40) - 40 + 0
As you see, both sides equal now.

To find the solution to the question we need to take 20% of all Swim members (40 - x) as in the solution above.

Hope that helps.

[diebeatsthegmat]

At an university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all students are members of the swim team?

1. 20% 2. 30% 3. 40% 4. 50% 5. 60%

The way I approached this one is...

Let T = total students be 100

Then members of both clubs = 40

Total = Swim Club + Chess Club - Both + neither (since all students are members the neither would be 0)

Chess club members and swimmers = 80% ( as 20% of swimmers are not chess club membersc=32

Swimmers only = 8

chess club = 100 -8 +40 .... kinda lost it here!!!

Let X be the number of swimmers who are not members of chess club

Then as per the question :

(40+x)/ 5 = x
=> x = 10

So, the number of students who are member of swimming team = No. of students who are member of both + No. of students who are member of only Swimming (but not chess club) = 40+10 = 50 %

where is "5" here?
i dont understand "(40+x)/5" part
can you explain?

[diebeatsthegmat]

At an university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all students are members of the swim team?

1. 20% 2. 30% 3. 40% 4. 50% 5. 60%

The way I approached this one is...

Let T = total students be 100

Then members of both clubs = 40

Total = Swim Club + Chess Club - Both + neither (since all students are members the neither would be 0)

Chess club members and swimmers = 80% ( as 20% of swimmers are not chess club membersc=32

Swimmers only = 8

chess club = 100 -8 +40 .... kinda lost it here!!!

phewwww english!!! i hate english! lol
it says " 20% of S are not in C " = 80%S or 0,8S are in both
or 0.8S=40 so S=400/8=50
50/100*100%=50%

[anshumishra]

At an university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all students are members of the swim team?

1. 20% 2. 30% 3. 40% 4. 50% 5. 60%

The way I approached this one is...

Let T = total students be 100

Then members of both clubs = 40

Total = Swim Club + Chess Club - Both + neither (since all students are members the neither would be 0)

Chess club members and swimmers = 80% ( as 20% of swimmers are not chess club membersc=32

Swimmers only = 8

chess club = 100 -8 +40 .... kinda lost it here!!!

Let X be the number of swimmers who are not members of chess club

Then as per the question :

(40+x)/ 5 = x
=> x = 10

So, the number of students who are member of swimming team = No. of students who are member of both + No. of students who are member of only Swimming (but not chess club) = 40+10 = 50 %

where is "5" here?
i dont understand "(40+x)/5" part
can you explain?

That comes from this statement :

If 20% of members of the swim team are not members of the chess club

20% means 1/5, Since there are 40+x students in the swimming team......
So, (40+x)/5 = x

[HPengineer]

another approach i tried that seems to give correct answer... Comments please


Total = 100

40% of 100 = members of Chess and Swim so 40 people are members of both.


40 people are on the swim team & chess club we can notice that if If 20% of entire swim team is not a member of the chess club then we can say that 80% of the Swim team = 40 members that are in the chess club as well.

So let x = total number of swim team members

.8X = 40 from here we can see that X = 50

50/100 = 50%

Any thoughts?

[anshumishra]

another approach i tried that seems to give correct answer... Comments please


Total = 100

40% of 100 = members of Chess and Swim so 40 people are members of both.


40 people are on the swim team & chess club we can notice that if If 20% of entire swim team is not a member of the chess club then we can say that 80% of the Swim team = 40 members that are in the chess club as well.

So let x = total number of swim team members

.8X = 40 from here we can see that X = 50

50/100 = 50%

Any thoughts?

Perfect !