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In Milton school, the number of students who play Badminton is thrice

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Bunuel
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In Milton school, the number of students who play Badminton is thrice [#permalink] New post   13 Apr 2021, 03:00
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Question Stats:

81% (02:10) correct 19% (02:39) wrong based on 70 sessions
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In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120
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D
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stne
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Re: In Milton school, the number of students who play Badminton is thrice [#permalink] New post   20 Apr 2021, 09:17
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Bunuel wrote:
In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120


Let \(3x\) play Badminton

Let \(x\) play tennis

\(60\) Play both sports , so ONLY badminton \(3x-60\) and ONLY tennis \(x-60\)

The number of students who play both the sports is thrice the number of students who play only Tennis.

\(3(x-60)=60 -> 3x-180 =60 \), \(3x=240\) , \(x=80\)

Only Badminton \(3*80 -60 = 180\)

Ans- D

Bunuel , can you please check , whether the OA is correct, Thank you

Hope it's clear.
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Re: In Milton school, the number of students who play Badminton is thrice [#permalink] New post   20 Apr 2021, 09:39
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stne wrote:
Bunuel wrote:
In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120


Let \(3x\) play Badminton

Let \(x\) play tennis

\(60\) Play both sports , so ONLY badminton \(3x-60\) and ONLY tennis \(x-60\)

The number of students who play both the sports is thrice the number of students who play only Tennis.

\(3(x-60)=60 -> 3x-180 =60 \), \(3x=240\) , \(x=80\)

Only Badminton \(3*80 -60 = 180\)

Ans- D

Bunuel , can you please check , whether the OA is correct, Thank you

Hope it's clear.

_____________________
Edited the OA. Thank you.
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Re: In Milton school, the number of students who play Badminton is thrice [#permalink] New post   20 Apr 2021, 21:18
Bunuel wrote:
stne wrote:
Bunuel wrote:
In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120


Let \(3x\) play Badminton

Let \(x\) play tennis

\(60\) Play both sports , so ONLY badminton \(3x-60\) and ONLY tennis \(x-60\)

The number of students who play both the sports is thrice the number of students who play only Tennis.

\(3(x-60)=60 -> 3x-180 =60 \), \(3x=240\) , \(x=80\)

Only Badminton \(3*80 -60 = 180\)

Ans- D

Bunuel , can you please check , whether the OA is correct, Thank you

Hope it's clear.

_____________________
Edited the OA. Thank you.


Bunuel,
Is Algebra the best way to solve this question? I tried on a matrix, though it took me more than 3 minutes. Looking for more ways to solve this question (rather these types of questions).
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Re: In Milton school, the number of students who play Badminton is thrice [#permalink] New post   20 Apr 2021, 23:05
Bunuel wrote:
In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120

Venn Diagram works best here.
t = students who play only tennis
3t = students who play both games
Total tennis playing students = 3t + t = 4t
b = students who play badminton only
Total badminton playing students = b + 3t
\(\implies\) b + 3t = 3(4t)
b = 9t

Also, 3t = 60
t = 20
Therefore, b = 9t = 180

Answer D.
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Re: In Milton school, the number of students who play Badminton is thrice [#permalink] New post   21 Apr 2021, 03:42
AnkitSingh2020 wrote:
In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120


Let \(3x\) play Badminton

Let \(x\) play tennis

\(60\) Play both sports , so ONLY badminton \(3x-60\) and ONLY tennis \(x-60\)

The number of students who play both the sports is thrice the number of students who play only Tennis.

\(3(x-60)=60 -> 3x-180 =60 \), \(3x=240\) , \(x=80\)

Only Badminton \(3*80 -60 = 180\)

Ans- D


Bunuel,
Is Algebra the best way to solve this question? I tried on a matrix, though it took me more than 3 minutes. Looking for more ways to solve this question (rather these types of questions).[/quote][/quote]

Hey AnkitSingh2020, for me personally drawing out a 2*2 matrix works best and I was able to solve this in under a minute using the same approach.
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Re: In Milton school, the number of students who play Badminton is thrice [#permalink] New post   21 Apr 2021, 19:40
Brian123 wrote:
AnkitSingh2020 wrote:
In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120


Let \(3x\) play Badminton

Let \(x\) play tennis

\(60\) Play both sports , so ONLY badminton \(3x-60\) and ONLY tennis \(x-60\)

The number of students who play both the sports is thrice the number of students who play only Tennis.

\(3(x-60)=60 -> 3x-180 =60 \), \(3x=240\) , \(x=80\)

Only Badminton \(3*80 -60 = 180\)

Ans- D


Bunuel,
Is Algebra the best way to solve this question? I tried on a matrix, though it took me more than 3 minutes. Looking for more ways to solve this question (rather these types of questions).
[/quote]

Hey AnkitSingh2020, for me personally drawing out a 2*2 matrix works best and I was able to solve this in under a minute using the same approach.[/quote]

Hi Brian, that's what I thought. Thanks for confirming. Maybe with practice I can get it under 2 mins. :)
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In Milton school, the number of students who play Badminton is thrice [#permalink] New post   23 Apr 2021, 06:04
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Solution


Given:
    • The number of students who play Badminton is thrice the number of students who play Tennis.
    • The number of students who play both the sports is thrice the number of students who play only Tennis.
    • The number of students who play both the sports = 60

To find:
    • The number of students who play only badminton.

Approach and Working:
    • Let the number of students who play only badminton = b
    • Let the number of students who play only tennis = t
    • Let the number of students who play both the sports = s

Translating the information given in the question, we get:
    • b + s = 3(t + s)
    • s = 3t = 60
      o Thus, t = 20

Substituting the value of t and s in the first equation, we get
    • b + 60 = 3(20 + 60)
    • b = 180

Hence the correct answer is Option D

Answer: D
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In Milton school, the number of students who play Badminton is thrice [#permalink]
23 Apr 2021, 06:04
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