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Of the 36 students in a certain class, 10 are in the chess club and 13

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Bunuel
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Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink] New post   24 Oct 2019, 00:18
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Of the 36 students in a certain class, 10 are in the chess club and 13 are in the bridge club. If 20 of the students are not in either club, how many of the students are in only one of the two clubs?

A. 7
B. 9
C. 14
D. 16
E. 23
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B
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Re: Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink] New post   24 Oct 2019, 00:27
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Bunuel wrote:
Of the 36 students in a certain class, 10 are in the chess club and 13 are in the bridge club. If 20 of the students are not in either club, how many of the students are in only one of the two clubs?

A. 7
B. 9
C. 14
D. 16
E. 23



Total = C + B - Both + Neither

36 = 10 +13 - Both + 20

Both = 7,

Only chess = 10 - 7 = 3

Only Bridge = 13 - 7 = 6.

Members playing single games = 6 + 3 = 9.

B is the option.
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Re: Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink] New post   24 Oct 2019, 00:34
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All=chess+bridge-bith+neither
36=10+13-both+20
both=7

only one club=all-neither-both
only one club=36-20-7=9

IMO
Ans: B
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Re: Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink] New post   31 Oct 2019, 03:58
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Solution



Given
    • In a class, there are 36 students.
      o 10 of them are in chess club
      o 13 are in high bridge.

To find
    • The number of student that are in only one of the two clubs if 20 of the students are not in either club

Approach and Working out
Total students of the class – Students who are not part of any club = Students part of chess club + Students part of High bridge - Students part of both the clubs

    • 36 – 20 = 10 + 13 - Students part of both the clubs
    • 16 = 23 - Students part of both the clubs
    • Students part of both the clubs = 7
So, 16 students were part of clubs. And 7 of them were in both of them.
Hence, 16-7 =9 were part of only1 club.

Thus, option B is the correct answer.

Correct Answer: Option B
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Re: Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink] New post   03 Nov 2019, 00:36
Members in only chess + members in only bridge + members in both + members in neither =36
Members in chess + members in bridge + members in both =20
Let the number of members in both = x
10-x +13-x + x =16
x =7
Members in in only one of the two clubs = Members in only chess + members in only bridge = 3+6 =9
Hence B
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Re: Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink] New post   09 Dec 2020, 00:59
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Total - neither = Chess + Bridge - Both

=> 36 - 20 = 10 + 13 - Both

=> Both = 10 + 13 - 16 = 7

Chess - Both = Only chess = 10 - 7 = 3

Bridge - Both = Only bridge = 13 - 7 = 6

Total: 3 + 6 = 9

Answer B
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Re: Of the 36 students in a certain class, 10 are in the chess club and 13 [#permalink]
09 Dec 2020, 00:59
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