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anuptvm: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Aug 12, 2009 8:05 amFollowed by: 1 member; GMAT Score:650

by anuptvm » Fri Dec 24, 2010 5:09 pm

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!!!

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Source: Beat The GMAT — Problem Solving | Fri Dec 24, 2010 5:09 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Fri Dec 24, 2010 5:17 pm

anuptvm wrote: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 %

Thanks
Anshu

(Every mistake is a lesson learned )

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Rezinka: Master | Next Rank: 500 Posts; Posts: 131; Joined: Fri Oct 15, 2010 2:39 am; Location: New Delhi, India; Thanked: 11 times

by Rezinka » Fri Dec 24, 2010 9:16 pm

@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.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sat Dec 25, 2010 6:37 pm

anshumishra wrote:
anuptvm wrote: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?

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sat Dec 25, 2010 6:43 pm

anuptvm wrote: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%

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Sat Dec 25, 2010 6:45 pm

diebeatsthegmat wrote:
anshumishra wrote:
anuptvm wrote: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

Thanks
Anshu

(Every mistake is a lesson learned )

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 amFollowed by: 1 member; Thanked: 2 times

by HPengineer » Sat Dec 25, 2010 9:36 pm

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?

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Sat Dec 25, 2010 9:48 pm

HPengineer wrote: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 !

Thanks
Anshu

(Every mistake is a lesson learned )

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