NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 01:40 It is currently 25 Apr 2024, 01:40
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

At Rocket Brown Elementary School there are 150 students and three

User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13958
Own Kudos [?]: 32897 [5]
Given Kudos: 5776
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   Updated on: 02 Oct 2023, 13:37
5
Bookmarks
Expert Reply
00:00

Difficulty:

95% (hard)

Question Stats:

29% (03:17) correct 71% (02:59) wrong based on 24 sessions
Hide Show timer Statistics
At Rocket Brown Elementary School there are 150 students and three sports teams – hockey, tennis, and football. Rocket Brown students are allowed to participate in as many of the three sports as they like or to abstain from participation completely, and every student who chooses a team must make that team. At the beginning of the semester, 40 students choose to play on the hockey team, 50 choose to join the tennis team, 90 choose to play on the football team, and exactly 70 elect to play two sports simultaneously.

In the table, select a value that would be the greatest number of students who could choose to play all three sports and the greatest number of students who could choose to play no sports at all. Make only two selections, one in each column.
Play all three
sports 		Play no
sports 		--------
0
20
40
50
70
80
Submit
Click Submit to add this question to your Error log
ShowHide Answer
Official Answer
Play all three
sports: 0
Play no
sports: 40

Originally posted by Sajjad1994 on 27 Sep 2020, 00:16.
Last edited by BottomJee on 02 Oct 2023, 13:37, edited 2 times in total.
Moved to new forum
User avatar
L
kntombat
Retired Moderator
Joined: 28 Feb 2020
Posts: 949
Own Kudos [?]: 485 [0]
Given Kudos: 839
Location: India
WE:Other (Other)
Send PM
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   27 Sep 2020, 11:38
Sajjad1994 Could you provide the Official Explanation for this question as and when possible ?
Thanks.
avatar
B
srishti246
Intern
Intern
Joined: 24 Mar 2018
Posts: 42
Own Kudos [?]: 24 [0]
Given Kudos: 61
Location: India
Concentration: Strategy, Sustainability
GPA: 3.7
WE:Consulting (Consulting)
Send PM
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   02 Oct 2020, 10:57
Don't get your solution. How is 0 the greatest value for all three sports playing students??
User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13958
Own Kudos [?]: 32897 [0]
Given Kudos: 5776
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   11 Oct 2020, 00:38
Expert Reply
kntombat wrote:
Sajjad1994 Could you provide the Official Explanation for this question as and when possible ?
Thanks.


Official Explanation

The question is based on the overlapping sets formula. The equation for three group overlapping sets is:

Group 1 + Group 2 + Group 3 - Overlap Exactly Two Groups - 2(Overlap all Three) + None

Following this convention the equation would be 150 = 40 + 50 + 90 - 70 - 2(x) + None

150 = 40 + 50 + 90 - 70 - 0 + 40

Therefore 40 & 0 are the only acceptable options.
avatar
B
Baps
Intern
Intern
Joined: 02 Jun 2020
Posts: 32
Own Kudos [?]: 13 [0]
Given Kudos: 15
Send PM
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   15 Feb 2021, 12:26
Sajjad1994 wrote:
kntombat wrote:
Sajjad1994 Could you provide the Official Explanation for this question as and when possible ?
Thanks.


Official Explanation

The question is based on the overlapping sets formula. The equation for three group overlapping sets is:

Group 1 + Group 2 + Group 3 - Overlap Exactly Two Groups - 2(Overlap all Three) + None

Following this convention the equation would be 150 = 40 + 50 + 90 - 70 - 2(x) + None

150 = 40 + 50 + 90 - 70 - 0 + 40

Therefore 40 & 0 are the only acceptable options.



Could you explain why can't it be 80 and 20? Thanks.
User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13958
Own Kudos [?]: 32897 [1]
Given Kudos: 5776
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   15 Feb 2021, 23:39
1
Kudos
Expert Reply
Baps wrote:

Could you explain why can't it be 80 and 20? Thanks.


Keep in mind this is an overlapping sets question, we can use the formula given below

Group 1 + Group 2 + Group 3 - Overlap Exactly Two Groups - 2(Overlap all Three) + None

We have total 150 students, if you put 80 and 20 it will exceed 150 and cannot fit into the equation. So we can only pick 40 and 0 and these are only values fits in the formula above.

Thank you
User avatar
B
PC12
Intern
Intern
Joined: 09 Jul 2022
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 10
Location: India
GMAT 1: 600 Q47 V24
Send PM
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   15 Aug 2022, 00:48
150=40+50+90-2*(20)+80

THIS ALSO SATISFIES THE EQUATION. DOESNT IT?
THEN WHY IS NONE=80 AND ALL-3=20 INCORRECT
User avatar
engineered163
Intern
Intern
Joined: 27 Aug 2022
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   27 Aug 2022, 08:50
This is very interesting.. below is my rationale for why it cannot be 20 and 80 for ‘all 3’ and ‘none’ respectively.

Let us take ‘all 3’ as 20. In Group 1,Hockey, there are 40 students. Of this 20 are also on the other 2 sports coz of our assumption.

Let us say that the remaining 20 also play Group 2 sports. That would mean, of the 70 who were in exactly 2 games, 20 are in Group 1 and Group 2. This would leave the remaining 50 to be only in Group 2 and Group 3, but this is not possible since Group 2 had a total of 50 students to begin with and of those 20 are in Group 1 & Group 2..

Similarly if you think about all the different overlaps, there is no way to satisfy the 70 ‘2-group’ overlap at all if we assumed ‘all-three’ to be 20… hence why that has to be 0 and naturally the ‘none’ becomes 40.

Equation wise, we also should have 1&2 + 2&3 + 1&3 = 70 or something like that and that will act as a restraining equation giving us this answer or something.

Posted from my mobile device
User avatar
B
poddarritika98
Intern
Intern
Joined: 02 Apr 2023
Posts: 10
Own Kudos [?]: 10 [0]
Given Kudos: 9
Send PM
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink] New post   25 Dec 2023, 15:45
Why can it be the other way round i.e. none = 40 and all three = 0?
GMAT Club Bot
gmatclubot
Re: At Rocket Brown Elementary School there are 150 students and three [#permalink]
25 Dec 2023, 15:45
Moderators:
Sajjad1994
GRE Forum Moderator
13958 posts
BottomJee
DI Forum Moderator
1031 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions