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.

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

(1) 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 after noon session=112 people. This directly tells that 112 attended after noon session, as 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 #.

Again on Venn diagram 112 would be: only afternoon + intersection of morning and afternoon, so the third part which is morning only would be: total-(Afternoon and intersection)=128-112=16.

Answer: B.

P.S. You can attach the file directly to the question, so that everyone see it on the page.
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Actually, just the reverse would be correct. Please see the attached picture.



Morning Session Only = Grey Color = M
Both (Morning Session+Afternoon) = Orange Color = M&A
Afternoon Session Only = Yellow Color = A

Q: If M+M&A+A=128
M=?

St1:
M&A=96
Not Sufficient.

St2:
M&A+A=112
Now, we know M&A+A+M=128
M&A+A=112
So, M=16(Morning Session only)
Sufficient.

Ans: "B"

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Now, if the question were: How many people attended morning session, we are asked to find M+M&A

St1:
M&A=96
Not Sufficient.

St2:
M&A+A=112
Now, we can't find "M&A+M" using this information and the stem.
Not Sufficient.

Together:
We can find "A" and eventually "M&A+M".
Sufficient.

Ans: "C"

Dear Fluke
were "only" not there
then B would have been a straight away answer (why would we need St A)

M only = M - both ?

1. Not sufficient

both = (3/4)*128 = 96

Total = M + A - both

M-both = 128- A

we still need to know either M or A to find M only.

2. Sufficient

A = (7/8)*128 = 112

Total = M + A - both

=>M-both = Total - A = 128-112 = 16.

Answer is B.
128 =

Bunuel,
Statement 2 says that 7/8 attended the afternoon session (i.e. 112 ppl). From these, we don't know how many attended afternoon only or morning + afternoon, hence how can we say for sure that 16 attended morning only?

Consider this: we are asked to find how many of the people attended the morning session only. So, we need to find {Morning} - {Both}. Now:

{Total} = {Morning} + {Afternoon} - {Both};
{128} = {Morning} + 112 - {Both};
{Morning} - {Both} = 16.

Does this make sense?
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I tried solving this prob. by using double set matrix. Is that a wrong approach for this problem? I got (C) by doing that.

Hi arkle,

The question asks us to find the number of people who attended the morning session only i.e. who attended the morning session but did not attend the afternoon session.

Even when using the double set matrix you will get option B as the answer. Please refer the diagram of the matrix below for statement-II:



We are given that 7/8 of the people attended the afternoon session i.e. number of people who attended afternoon session irrespective of whether they attended morning session or not is 112. Since the total number of people who attended the session is 128, we get the number of people who did not attend the afternoon session as 128 - 112 = 16.

As everyone attended at least one session there were 0 number of people who did not attend any of the session. That leaves us with 16 number of people who did not attend the afternoon session but attended only the morning session which is what the question asks us .

Hence st-II is sufficient to answer the question.

Hope this helps

Regards
Harsh
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