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In a class of 33, every student plays at least one game.

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KarunMendiratta
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In a class of 33, every student plays at least one game. [#permalink] New post   14 Sep 2021, 21:14
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In a class of 33, every student plays at least one game.
20 students play cricket, 25 play football and 18 play hockey.
15 play both cricket and football, 12 play football and hockey and 10 play cricket and hockey.

Quantity A
Quantity B
Students who play only cricket
2


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
ShowHide Answer
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C
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motion2020
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In a class of 33, every student plays at least one game. [#permalink] New post   15 Sep 2021, 02:32
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To start, it's not known how many students play all three games (denoting cricket=C, football=F, hockey=H), and we introduce this as a variable \(x\). Those who play exclusively C&F, F&H and C&H are \(15-x\), football \(12-x\), and hockey \(10-x\) respectively. Solve for \(x\) by setting an equation below

\(33=20+25+18-(15-x+12-x+10-x+2x)\), \(x=7\).

Hence, \(C&F=15-7=8\) and \(C&H=10-7=3\)

The number of students who play only cricket is \(F-C&F-C&H-C&F&H=20-8-3-7=2\).

Answer must be C :)

KarunMendiratta, thanks for posting


KarunMendiratta wrote:
In a class of 33, every student plays at least one game.
20 students play cricket, 25 play football and 18 play hockey.
15 play both cricket and football, 12 play football and hockey and 10 play cricket and hockey.

Quantity A
Quantity B
Students who play only cricket
2


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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KarunMendiratta
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Re: In a class of 33, every student plays at least one game. [#permalink] New post   15 Sep 2021, 04:34
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motion2020 wrote:
To start, it's not known how many students play all three games (denoting cricket=C, football=F, hockey=H), and we introduce this as a variable \(x\). Those who play exclusively C&F, F&H and C&H are \(15-x\), football \(12-x\), and hockey \(10-x\) respectively. Solve for \(x\) by setting an equation below

\(33=20+25+18-(15-x+12-x+10-x+2x)\), \(x=7\).

Hence, \(C&F=15-7=8\) and \(C&H=10-7=3\)

The number of students who play only cricket is \(F-C&F-C&H-C&F&H=20-8-3-7=2\).

Answer must be C :)

KarunMendiratta, thanks for posting


KarunMendiratta wrote:
In a class of 33, every student plays at least one game.
20 students play cricket, 25 play football and 18 play hockey.
15 play both cricket and football, 12 play football and hockey and 10 play cricket and hockey.

Quantity A
Quantity B
Students who play only cricket
2


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given


motion2020
Happy to help!
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arjunbir
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Re: In a class of 33, every student plays at least one game. [#permalink] New post   17 Sep 2021, 13:26
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33=20+25+18−(15−x+12−x+10−x+2x)33=20+25+18−(15−x+12−x+10−x+2x) , x=7
Sir what does 2x in this equation stands for?I always get confused with 3 overlapping sets
Thank you
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Re: In a class of 33, every student plays at least one game. [#permalink] New post   20 Oct 2024, 06:19
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a class of 33, every student plays at least one game. [#permalink]
20 Oct 2024, 06:19
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