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Retired Moderator
Joined: 16 Apr 2020
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Location: India
WE:Education (Education)
In a class of 33, every student plays at least one game.
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14 Sep 2021, 21:14
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.
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
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
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
In a class of 33, every student plays at least one game.
[#permalink]
15 Sep 2021, 02:32
15 Sep 2021, 02:32
1
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
\(33=20+25+18-(15-x+12-x+10-x+2x)\), \(x=7\).
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.
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
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
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: In a class of 33, every student plays at least one game.
[#permalink]
15 Sep 2021, 04:34
15 Sep 2021, 04:34
1
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
\(33=20+25+18-(15-x+12-x+10-x+2x)\), \(x=7\).
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.
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
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!
