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Two family reunions are happening at the same hotel, the Oates reunion
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Bunuel
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Two family reunions are happening at the same hotel, the Oates reunion [#permalink] New post  24 Aug 2015, 22:31
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Two family reunions are happening at the same hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?

(A) 2
(B) 5
(C) 10
(D) 16
(E) 22


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Re: Two family reunions are happening at the same hotel, the Oates reunion [#permalink] New post  25 Aug 2015, 00:25
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Bunuel wrote:
Two family reunions are happening at the same hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?

(A) 2
(B) 5
(C) 10
(D) 16
(E) 22


Ans: A

Solution: Total = O+H-both
100 = 62+40-x
x=2
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Two family reunions are happening at the same hotel, the Oates reunion [#permalink] New post  25 Aug 2015, 03:50
Bunuel wrote:
Two family reunions are happening at the same hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?

(A) 2
(B) 5
(C) 10
(D) 16
(E) 22


Kudos for a correct solution.


Refer to the attached image for the matrix method. Text in black : given, text in red: calculated.
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Re: Two family reunions are happening at the same hotel, the Oates reunion [#permalink] New post  25 Aug 2015, 10:31
Total =100, O=40 ,H=62, both = x
Total = o+h-x =>100=40+62-x
=> x=2
hence answer is A
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Re: Two family reunions are happening at the same hotel, the Oates reunion [#permalink] New post  25 Aug 2015, 10:35
Bunuel wrote:
Two family reunions are happening at the same hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?

(A) 2
(B) 5
(C) 10
(D) 16
(E) 22


Kudos for a correct solution.


No of people in Oates reunion=40
No of people in Hall reunion=62
Attending both=x
All guests attend at least one.
Therefore, 100=40+62-(Both)
Both=2
Answer A
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Re: Two family reunions are happening at the same hotel, the Oates reunion [#permalink] New post  13 Oct 2019, 00:28
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