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A certain one-day seminar consisted of a morning session and

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A certain one-day seminar consisted of a morning session and [#permalink] New post 09 Jul 2012, 02:31
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A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 attending the seminar attended at least one of the two sessions, how many of the people attended the morning session only?

(1) 3/4 of the people attended both sessions.
(2) 7/8 of the people attended the afternoon session.
[Reveal] Spoiler: OA

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Re: A certain one-day seminar consisted of a morning session and [#permalink] New post 09 Jul 2012, 02:47
Expert's post
Stiv wrote:
A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 attending the seminar attended at least one of the two sessions, how many of the people attended the morning session only?

(1) 3/4 of the people attended both sessions.
(2) 7/8 of the people attended the afternoon session.


A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 people attending the seminar attended at least one of the two sessions, how many of the people attended the morning session only.

Since "each of the 128 people attending the seminar attended at least one of the two sessions", then there are no one who attended neither of sessions. So, we have that: {Total} = {Morning} + {Afternoon} - {Both}.

(1) 3/4 of the people attended both sessions. 3/4 of 128 is 96. So we know that 96 people attended both seminars. If you draw Venn diagram you'll see that 96 is the intersection of the people who attended morning session and the evening session. This only tells that minimum # of people for the morning session is 96. Morning only could be from 0 to 32. Not sufficient.

(2) 7/8 of the people attended the afternoon session. 7/8 of 128 is 112. So, 112 people attended the afternoon session. Since each of the 128 people attending the seminar attended at least one of the two sessions hence rest of the people 16, must have been attending the morning session and not attending the evening, which IS only morning session attendant #. Sufficient. ({Total} = {Morning} + {Afternoon} - {Both} --> 128 = {Morning} + 112 - {Both} --> {Morning} - {Both} = 16).

Answer: B.
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Re: A certain one-day seminar consisted of a morning session and [#permalink] New post 09 Jul 2012, 03:26
B.

Given: Morning, Evening. 128 guys at least one of the sessions.

1. 3/4 - both sessions - insuff
2. 7/8 - Afternoong sessions = Only Afternoon+both => 1/8 left = only morning. Hence, suff
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A certain one-day seminar consisted of a morning session and an [#permalink] New post 02 Dec 2012, 00:41
balajinaik wrote:
While i got the answer right, I always gt confused with the wording "Atleast in Venn Diagrams". How do i associate this word with the " both" and "Neither" regions in the venn diagram,

Pls explain,
Thanks


If you have 2 events. Create a Venn diagram having 2 intersecting circles.
Then, in a Venn diagram.

At least is one of the 2 circles
Both is the intersection
Neither is outside of the two circles
A certain one-day seminar consisted of a morning session and an   [#permalink] 02 Dec 2012, 00:41
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