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In a competition, a school awarded medals in different categories

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In a competition, a school awarded medals in different categories  [#permalink]

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New post Updated on: 06 Apr 2020, 04:09
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In a competition, a school awarded medals in different categories. 36 medals in dance, 12 medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons and only 4 persons got medals in all the three categories, how many received medals in exactly two of these categories?

a. 12
b. 13
c. 14
d. 15
e. 16

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Originally posted by zs2 on 05 Apr 2020, 12:40.
Last edited by zs2 on 06 Apr 2020, 04:09, edited 1 time in total.
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Re: In a competition, a school awarded medals in different categories  [#permalink]

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New post 05 Apr 2020, 15:01
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Assume 'x' number of persons received medals in exactly two of these categories

Number of persons that received medals in exactly one of these categories= 45-x-4 = 41-x

41-x + 2*x + 3*4 = 36+18+12= 66

x = 13

All the options are wrong imo


zs2 wrote:
In a competition, a school awarded medals in different categories. 36 medals in dance, 12 medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons and only 4 persons got medals in all the three categories, how many received medals in exactly two of these categories?

a. 2
b. 3
c. 4
d. 5
e. 6
Senior Manager
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Joined: 18 Dec 2017
Posts: 295
Re: In a competition, a school awarded medals in different categories  [#permalink]

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New post 05 Apr 2020, 20:00
Let number of people getting award in exactly one category =x
Number of people getting award in exactly 2 category = y
66= x +2y+ 3×4 ----(1)
45= x + y + 4 ----(2)
Subtracting 2nd equation from 1st
Y=13

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Re: In a competition, a school awarded medals in different categories  [#permalink]

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New post 06 Apr 2020, 04:10
nick1816 wrote:
Assume 'x' number of persons received medals in exactly two of these categories

Number of persons that received medals in exactly one of these categories= 45-x-4 = 41-x

41-x + 2*x + 3*4 = 36+18+12= 66

x = 13

All the options are wrong imo


zs2 wrote:
In a competition, a school awarded medals in different categories. 36 medals in dance, 12 medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons and only 4 persons got medals in all the three categories, how many received medals in exactly two of these categories?

a. 2
b. 3
c. 4
d. 5
e. 6


Options corrected. Thanks
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Please highlight if you found this helpful, Thanks in advance
GMAT Club Bot
Re: In a competition, a school awarded medals in different categories   [#permalink] 06 Apr 2020, 04:10

In a competition, a school awarded medals in different categories

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