Overlapping sets

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Aug 11, 2012 11:08 pm

Hello,

This is from MGMAT Strategy Guide. However, there is no solution given:

30 people are in a room. 20 of them play golf. 15 of them play golf and tennis. If everyone plays at least one of the two sports, how many of the people play tennis only?

My approach is as follows:

Tennis No Tennis Total
Golf 15 20
No Golf 10 0 10
Total 25 30

I was just wondering if my solution is correct? Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Problem Solving | Sat Aug 11, 2012 11:08 pm

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Sun Aug 12, 2012 12:12 am

gmattesttaker2 wrote:Hello,

This is from MGMAT Strategy Guide. However, there is no solution given:

30 people are in a room. 20 of them play golf. 15 of them play golf and tennis. If everyone plays at least one of the two sports, how many of the people play tennis only?

My approach is as follows:

Tennis No Tennis Total
Golf 15 20
No Golf 10 0 10
Total 25 30

I was just wondering if my solution is correct? Thanks a lot.

Best Regards,
Sri

Only tennis = Total tennis - (both tennis and glof)
the answer should be 10

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gmatwin: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Aug 12, 2012 2:22 am

by gmatwin » Sun Aug 12, 2012 2:26 am

If we use the formula: n(GUT)=n(G) + n(T) - n(G intersection T)

n(GUT)=30
n(G)=20
n(G intersection T)=15

By the formula,n(T) is 25.

Why this approach is wrong?

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niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Sun Aug 12, 2012 5:10 am

gmatwin wrote:If we use the formula: n(GUT)=n(G) + n(T) - n(G intersection T)

n(GUT)=30
n(G)=20
n(G intersection T)=15

By the formula,n(T) is 25.

Why this approach is wrong?

This approach is not wrong..
n(T) = n(only T) + n(Gâˆ©T)
=> n(only T) = n(T) - n(Gâˆ©T) = 25 - 15 = 10

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 12, 2012 7:20 am

gmattesttaker2 wrote:Hello,

This is from MGMAT Strategy Guide. However, there is no solution given:

30 people are in a room. 20 of them play golf. 15 of them play golf and tennis. If everyone plays at least one of the two sports, how many of the people play tennis only?

My approach is as follows:

Tennis No Tennis Total
Golf 15 20
No Golf 10 0 10
Total 25 30

I was just wondering if my solution is correct? Thanks a lot.

Best Regards,
Sri

Hey Sri,
Your setup is correct when I go to post a reply (and see the raw html coding of your solution), but when it shows up as a post, the spacing is off.

Ultimately (using the Double Matrix Method), you should get something like this.

.........Tennis......~Tennis....Total
Golf.......15.............5..........20
~Golf.....10.............0..........10
Total.....25............5

Here's a free video on the Double Matrix method: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Aug 12, 2012 7:33 pm

Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:Hello,

This is from MGMAT Strategy Guide. However, there is no solution given:

30 people are in a room. 20 of them play golf. 15 of them play golf and tennis. If everyone plays at least one of the two sports, how many of the people play tennis only?

My approach is as follows:

Tennis No Tennis Total
Golf 15 20
No Golf 10 0 10
Total 25 30

I was just wondering if my solution is correct? Thanks a lot.

Best Regards,
Sri
Hey Sri,
Your setup is correct when I go to post a reply (and see the raw html coding of your solution), but when it shows up as a post, the spacing is off.

Ultimately (using the Double Matrix Method), you should get something like this.

.........Tennis......~Tennis....Total
Golf.......15.............5..........20
~Golf.....10.............0..........10
Total.....25............5

Here's a free video on the Double Matrix method: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Cheers,
Brent

Hello Brent,

Hope all is well. Thanks for the tip regarding the spacing. I completely overlooked it. Thanks for the Double Matrix explanation and also for the link. It is clear now. Thank you very much again.

Best Regards,
Sri

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kashishh: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Wed Jul 11, 2012 1:49 am; Thanked: 2 times

by kashishh » Tue Aug 14, 2012 1:26 am

Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:Hello,

This is from MGMAT Strategy Guide. However, there is no solution given:

30 people are in a room. 20 of them play golf. 15 of them play golf and tennis. If everyone plays at least one of the two sports, how many of the people play tennis only?

My approach is as follows:

Tennis No Tennis Total
Golf 15 20
No Golf 10 0 10
Total 25 30

I was just wondering if my solution is correct? Thanks a lot.

Best Regards,
Sri
Hey Sri,
Your setup is correct when I go to post a reply (and see the raw html coding of your solution), but when it shows up as a post, the spacing is off.

Ultimately (using the Double Matrix Method), you should get something like this.

.........Tennis......~Tennis....Total
Golf.......15.............5..........20
~Golf.....10.............0..........10
Total.....25............5

Here's a free video on the Double Matrix method: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Cheers,
Brent

Can i solve this way? - 30 = 20+T-15 so, T = 25?
is it correct?

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 14, 2012 6:44 am

kashishh wrote: Can i solve this way? - 30 = 20+T-15 so, T = 25?
is it correct?

Your solution is great. You're using the formula: Total = Group1 + Group2 - Both + Neither
If we let X = the number of tennis players, we get: 30 = 20 + X - 15 + 0
Solve to get: X=25

This method and the Venn Diagram method both work. However, when it comes to more difficult Overlapping Sets questions (like https://www.gmatprepnow.com/module/gmat- ... ems?id=943 ), I find that the Double Matrix method allows for a nice visual approach.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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