Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 04 Mar 2012
Posts: 50

In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
01 May 2012, 20:28
3
This post received KUDOS
34
This post was BOOKMARKED
Question Stats:
66% (02:10) correct 34% (02:37) wrong based on 850 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43867

In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
01 May 2012, 22:27
9
This post received KUDOS
Expert's post
14
This post was BOOKMARKED
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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
11 Jun 2013, 07:24



Manager
Joined: 30 Jun 2012
Posts: 83
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)

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
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?



Math Expert
Joined: 02 Sep 2009
Posts: 43867

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
07 Jul 2013, 22:02



Intern
Status: GMAT Prep. MBA 1517
Joined: 05 Mar 2013
Posts: 5
Location: Luxembourg

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
04 Nov 2013, 14:29
3
This post received KUDOS
2
This post was BOOKMARKED
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+11x(2*2)+18 which leads to 50=60x ; x=10 Hope this helps. Cheers, MJ



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1839
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
10 Mar 2014, 00:45
5
This post received KUDOS
Answer = 10 Using Venn Diagram Bunuel, can you please tell if this method is correct?. Got x ve in this case
Attachments
set.jpg [ 47.48 KiB  Viewed 124210 times ]
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 27 May 2014
Posts: 2

In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
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 5so, H=2075=8 max C=1574= 4 max F=1145=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.



Manager
Joined: 28 Aug 2013
Posts: 97
Location: India
Concentration: Operations, Marketing
GMAT Date: 08282014
GPA: 3.86
WE: Supply Chain Management (Manufacturing)

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
17 Aug 2014, 05:21
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 Bunnel, Will you please explain, why you have chosen this formula against exactly 2 formulae.. LS
_________________
Gprep1 540 > Kaplan 580>Veritas 640>MGMAT 590 >MGMAT 2 640 > MGMAT 3 640 > MGMAT 4 650 >MGMAT 5 680  >GMAT prep 1 570
Give your best shot...rest leave upto Mahadev, he is the extractor of all negativity in the world !!



Manager
Joined: 23 Jan 2012
Posts: 75

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
15 Sep 2014, 03:26
lastshot 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 Bunnel, Will you please explain, why you have chosen this formula against exactly 2 formulae.. LS Read the above posts from Bunuel. He has used both the formulas in this problem. Formula no.1 to calculate the no. of students playing all the 3 sports, and then Formula no.2 to calculate the no. of students who play exactly two sports....Hope this helps!



Intern
Joined: 17 Dec 2014
Posts: 1

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
17 Dec 2014, 05:36
Thank you Bunuel. Very much. Posted from my mobile device



Director
Joined: 10 Mar 2013
Posts: 584
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
14 Jun 2015, 04:50
1
This post was BOOKMARKED
I've solved this one with the second formula Let X be the area where all 3 overlap and Exactly 2Groups overlaps = 2Group ovelaps  3*X > 50=20+15+11 (7+4+53X)  2X+18 X=2 and 163X=10
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Intern
Joined: 17 Dec 2016
Posts: 40

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
28 Jan 2017, 09:16
MJ23 wrote: 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+11x(2*2)+18 which leads to 50=60x ; x=10 Hope this helps. Cheers, MJ Dense, but helpful. Somehow, I only noticed my mistake with this explanation and not the one from Bunuel (which is literally the same) thanks



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]
Show Tags
16 Feb 2018, 09:32
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 Since 18 students do not play any of the three sports, 50  18 = 32 students must play at least one of the 3 sports. This total can be formulated as follows: Total = #(H) + #(C) + #(F)  #(H and C)  #(C and F)  #(H and F) + #(H and C and F) Thus, we have: 32 = 20 + 15 + 11  7  4  5 + #(H and C and F) 32 = 30 + #(H and C and F) 2 = #(H and C and F) Since #(H and C) = 7 (which also include those who play Football), but we’ve found that #(H and C and F) = 2, there must be 7  2 = 5 students who play Hockey and Cricket only. Similarly, there must be 4  2 = 2 students who play Cricket and Football only, and 5  2 = 3 students who play Hockey and Football only. Thus, there must be 5 + 2 + 3 = 10 students who play exactly 2 sports. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: In a class of 50 students, 20 play Hockey, 15 play Cricket
[#permalink]
16 Feb 2018, 09:32






