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# The Mathematics Club in a school held an open house on three afternoon

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Joined: 23 Feb 2015
Posts: 1454
The Mathematics Club in a school held an open house on three afternoon  [#permalink]

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28 Nov 2019, 06:44
1
5
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:52) correct 31% (03:24) wrong based on 36 sessions

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The Mathematics Club in a school held an open house on three afternoons. 115, 75 and 110 students attended on the first, second and third afternoons respectively. 30 attended only on the first day, 35 on the first and second days. 70 attended the first and the third days and 35 attended on the second and third
days. How many attended on all the three days?
(A) 15
(B) 25
(C) 21
(D) 20
(E) 30

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Math Expert
Joined: 02 Aug 2009
Posts: 8344
Re: The Mathematics Club in a school held an open house on three afternoon  [#permalink]

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29 Nov 2019, 20:01
1
The Mathematics Club in a school held an open house on three afternoons. 115, 75 and 110 students attended on the first, second and third afternoons respectively. 30 attended only on the first day, 35 on the first and second days. 70 attended the first and the third days and 35 attended on the second and third
days. How many attended on all the three days?
(A) 15
(B) 25
(C) 21
(D) 20
(E) 30

The students who attended on first day are 115.
There are 30 who attended on just the first day, 35 on 1st and 2nd and 70 on 1st and 3rd. If we total up the three there will be repetition in 35 and 70 as there will be certain number who attended on all three days and are common to 35 and 70.
So all three days = 30+35+70-115=135-115=20

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Intern
Joined: 22 Oct 2018
Posts: 18
Re: The Mathematics Club in a school held an open house on three afternoon  [#permalink]

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06 Dec 2019, 20:38
This looks like a sets problem. Can someone give me a brief explanation for this. Would appreciate it !
Re: The Mathematics Club in a school held an open house on three afternoon   [#permalink] 06 Dec 2019, 20:38
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