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In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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
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Originally posted by gmihir on 01 May 2012, 20:28.
Last edited by Bunuel on 18 Feb 2019, 04:32, edited 1 time in total.
Renamed the topic and edited the question.




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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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01 May 2012, 22:27
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.
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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11 Jun 2013, 07:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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?



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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07 Jul 2013, 22:02
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.
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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04 Nov 2013, 14:29
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



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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.



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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!



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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17 Dec 2014, 05:36
Thank you Bunuel. Very much. Posted from my mobile device



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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14 Jun 2015, 04:50
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



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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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
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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22 Jan 2019, 08:56
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. \(\{Total\} = \{Hockey\} + \{Cricket\} + \{Football\}  \{HC + CH + HF\} + \{All \ three\} + \{Neither\}\) (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. Hello Bunuel, I am a little confused with the equation. I noticed that sometimes you add the three overlapping sets and sometimes you subtract it. In this case you added all three, whereas in some other examples you would subtract by 2(all three or x if we are trying to find the value). Can you please clarify when I am supposed to use each sign?



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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22 Jan 2019, 09:01
zwander 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. \(\{Total\} = \{Hockey\} + \{Cricket\} + \{Football\}  \{HC + CH + HF\} + \{All \ three\} + \{Neither\}\) (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. Hello Bunuel, I am a little confused with the equation. I noticed that sometimes you add the three overlapping sets and sometimes you subtract it. In this case you added all three, whereas in some other examples you would subtract by 2(all three or x if we are trying to find the value). Can you please clarify when I am supposed to use each sign? Please follow the link highlighted above.
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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29 Jan 2020, 01:20
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 BunuelCould you tell why are we considering, from the given statement ' 7 people who play both hockey and cricket', there are possibly people also playing football. In your post https://gmatclub.com/forum/advancedove ... 44260.html in eg 6, which, I think, is similar to this problem  it is given that the roster had 9 names in common between E & M. Why then are we not considering the possibility of the common names on the E&M roster include people who have also taken statistics ? Thanks



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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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29 Jan 2020, 01:31
ankitprad 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 BunuelCould you tell why are we considering, from the given statement ' 7 people who play both hockey and cricket', there are possibly people also playing football. In your post https://gmatclub.com/forum/advancedove ... 44260.html in eg 6, which, I think, is similar to this problem  it is given that the roster had 9 names in common between E & M. Why then are we not considering the possibility of the common names on the E&M roster include people who have also taken statistics ? Thanks 1. Let me ask you back: how does the phrase "7 play both Hockey and Cricket..." could mean that those 7 does not play any other sports? 2. In the example, you give, it's the same: "E and M had 9 names in common" does not mean that any from those 9 do not belong to S. If you check solutions here: https://gmatclub.com/forum/whenprofess ... 43149.html, you'll see that it can be a case. For example:
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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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18 Mar 2020, 12:45
This type of 3 overlapping set problem, where we are given the number of each 2 group overlap I find you need to use a venn diagram in addition to one of the formulas. First 20 +15 +11(7+4+5)2all 3 +18 = 50> 4616+18*all3 =50
>48 all3 = 50 > all 3 =2 Now we have values for every position in the venn diagram. If we label the section of the three overlapping spots b,c,d,f, we can quickly note that we are adding b+c+d+c+c+f = b+d+f+3c . What we want is b+d+f. So we must subtract 3(2) = 6 therefore 166 =10, play exactly two sports. Also worth noting. If you are not super fast at these type of problems, get about a minute in, and realize there is still a substantial amount of work left to do, it might be in your best interest to drop a problem like this. Its good to be able to get the points from a question like this but it is not worth more than 2 and a half minutes of your time on the real CAT.




Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
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