Find all School-related info fast with the new School-Specific MBA Forum

It is currently 11 Jul 2014, 23:59

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a class of 50 students, 20 play Hockey, 15 play Cricket

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 04 Mar 2012
Posts: 46
Followers: 0

Kudos [?]: 17 [1] , given: 10

In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 01 May 2012, 20:28
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (02:41) correct 40% (02:16) wrong based on 262 sessions
In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

A. 12
B. 10
C. 11
D. 15
E. 14
[Reveal] Spoiler: OA
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18504
Followers: 3189

Kudos [?]: 21282 [4] , given: 2543

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 01 May 2012, 22:27
4
This post received
KUDOS
Expert's post
gmihir wrote:
In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

A. 12
B. 10
C. 11
D. 15
E. 14


Notice that "7 play both Hockey and Cricket" does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Hockey/Football.

{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS

50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;

Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;

Hence, 5+2+3=10 students play exactly two of these sports.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 11 Jul 2012
Posts: 46
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 09 Oct 2012, 10:39
I don't agree with the answer given
If the question is correctly worded the answer ought to be 7 + 5 + 4 = 16
But if the question is: How many students play exactly one of these sports then the answer could be 10 (I haven't checked)
Brother Karamazov
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18504
Followers: 3189

Kudos [?]: 21282 [0], given: 2543

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 11 Jun 2013, 07:24
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 30 Jun 2012
Posts: 84
Location: United States
GMAT 1: 510 Q34 V28
GMAT 2: 580 Q35 V35
GMAT 3: 640 Q34 V44
GMAT 4: 690 Q43 V42
GPA: 3.61
WE: Education (Education)
Followers: 7

Kudos [?]: 78 [0], given: 16

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 07 Jul 2013, 16:07
This question asks for the number of students who played exactly two sports? Why does the second formula not work here?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18504
Followers: 3189

Kudos [?]: 21282 [1] , given: 2543

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 07 Jul 2013, 22:02
1
This post received
KUDOS
Expert's post
josemnz83 wrote:
This question asks for the number of students who played exactly two sports? Why does the second formula not work here?


Notice that "7 play both Hockey and Cricket..." does NOT mean that these 7 students play ONLY Hockey and Cricket, some might play Football too. The same for "4 play Cricket and Football and 5 play Hockey and football". So, we cannot use the second formula directly. Also notice that we don't know the number of students who play all three sports.

But we CAN use the first formula, find the number of students who play all three and then find the number of students who play exactly two of the sports.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 21 Sep 2013
Posts: 18
Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)
Followers: 0

Kudos [?]: 5 [0], given: 62

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 18 Oct 2013, 22:00
Bunuel wrote:
josemnz83 wrote:
This question asks for the number of students who played exactly two sports? Why does the second formula not work here?


Notice that "7 play both Hockey and Cricket..." does NOT mean that these 7 students play ONLY Hockey and Cricket, some might play Football too. The same for "4 play Cricket and Football and 5 play Hockey and football". So, we cannot use the second formula directly. Also notice that we don't know the number of students who play all three sports.

But we CAN use the first formula, find the number of students who play all three and then find the number of students who play exactly two of the sports.

Hope it's clear.




hey bunuel,
if we had to find exactly one sport then how are we suppose to go ahead ?
1 KUDOS received
Intern
Intern
avatar
Status: GMAT Prep. MBA 15-17
Joined: 05 Mar 2013
Posts: 5
Location: Luxembourg
Followers: 0

Kudos [?]: 7 [1] , given: 14

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 04 Nov 2013, 14:29
1
This post received
KUDOS
Bunuel wrote:
josemnz83 wrote:
This question asks for the number of students who played exactly two sports? Why does the second formula not work here?


Notice that "7 play both Hockey and Cricket..." does NOT mean that these 7 students play ONLY Hockey and Cricket, some might play Football too. The same for "4 play Cricket and Football and 5 play Hockey and football". So, we cannot use the second formula directly. Also notice that we don't know the number of students who play all three sports.

But we CAN use the first formula, find the number of students who play all three and then find the number of students who play exactly two of the sports.

Hope it's clear.


Hi All,

That's exactly what I did, started with formula 1 and then used #2 once had "g" (all three):

Formula #1: 50=20+15+11-(7+4+5)+18 --> 2 (all three or "g")
Formula #2: 50=20+15+11-x-(2*2)+18 which leads to 50=60-x ; x=10

Hope this helps.

Cheers,
MJ
Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 598
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 127 [0], given: 160

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 10 Mar 2014, 00:45
Answer = 10
Using Venn Diagram
Bunuel, can you please tell if this method is correct?. Got x -ve in this case
Attachments

set.jpg
set.jpg [ 47.48 KiB | Viewed 1420 times ]


_________________

Kindly press "Kudos" to appreciate

Intern
Intern
avatar
Joined: 27 May 2014
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 1

In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 29 Jun 2014, 13:12
PareshGmat wrote:
Answer = 10
Using Venn Diagram
Bunuel, can you please tell if this method is correct?. Got x -ve in this case



I do not agree with given explanation for the next reason.

If we apply the same logic as we did in previous questions, we get the next....

H=20
C=15
F=11

32 students in game

H and C max 7
C and F max 4
H and F max 5

so,
H=20-7-5=8 max
C=15-7-4= 4 max
F=11-4-5=2 max

at this moment we have the max number of students= 7+4+5+8+4+2=30...2 less than the number of students who participate in any class. If we put any of these students into all three group we will reduce all three numbers of every two classes and can never get the total of 32.

So the formula might be applied well, but this is wrong answer, or even more possible wrong figures in task.

I was surprised that Bunuel did not notice this mistake.
Intern
Intern
avatar
Joined: 22 Feb 2014
Posts: 22
Followers: 0

Kudos [?]: 1 [0], given: 14

GMAT ToolKit User CAT Tests
In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 09 Jul 2014, 07:45
Bunuel wrote:
gmihir wrote:
In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

A. 12
B. 10
C. 11
D. 15
E. 14


Notice that "7 play both Hockey and Cricket" does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Hockey/Football.

[color=#ffff00]{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;



Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;

Hence, 5+2+3=10 students play exactly two of these sports.




Answer: B.



Hi..why did not you use this formula as you have mentioned in the advance set problems..

A+B+C- (ALL TWO GROUPS)- 2(ALL 3 GROUPS)+NEITHER.
I am confuse now. which is correct formula.

Thanks in advance
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18504
Followers: 3189

Kudos [?]: 21282 [0], given: 2543

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] New post 09 Jul 2014, 07:55
Expert's post
GGMAT730 wrote:
Bunuel wrote:
gmihir wrote:
In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

A. 12
B. 10
C. 11
D. 15
E. 14


Notice that "7 play both Hockey and Cricket" does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Hockey/Football.

[color=#ffff00]{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;



Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;

Hence, 5+2+3=10 students play exactly two of these sports.




Answer: B.



Hi..why did not you use this formula as you have mentioned in the advance set problems..

A+B+C- (ALL TWO GROUPS)- 2(ALL 3 GROUPS)+NEITHER.
I am confuse now. which is correct formula.

Thanks in advance


Have you read that post? There are two formulas there and the whole post is about the differences between them.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket   [#permalink] 09 Jul 2014, 07:55
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic After winning 50 percent of the first 20 games it played, Te Bunuel 4 04 Feb 2014, 00:54
After winning 50 percent of the first 20 games it played, rxs0005 3 04 Aug 2010, 03:34
60% of the students in a certain class like playing computer arjtryarjtry 2 04 Sep 2008, 22:55
After winning 50 percent of the first 20 games it played, nfa1rhp 3 22 Jul 2007, 14:58
In a class of 100 students, 20 play Football, 20 do not play cloudz9 3 10 Jun 2005, 17:10
Display posts from previous: Sort by

In a class of 50 students, 20 play Hockey, 15 play Cricket

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.