A certain one-day seminar consisted of a morning session

[gmat_s]

Please help in answering the following question from GMATPrep Ques 1:
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

I chose ans C but that is wrong :--(

[Guest]

The answer is (B)

From (2) total no of participants attended afternoon session = (7/8)* 128 = 112. Out of 128, 112 attended afternoon session. Hence the no. of people who did not attend afternoon session or who attended morning session = 128-112 = 16. Sufficient

From (1) 3/4 of 128 = 96 people attended both the sessions. But we have no information about rest of the people.

[gmat_s]

Thanks "Guest".

I missed the keyword "only" in the end and made mistake.
Thanks for correct and clear answer!

[kannan_m_80]

Can somebody draw the double set matrix for this, we have been told to stick to Venn diagrams for 3 sets but this is 2 parameters and I'm finding it difficult creating a matrix to solve this question.

[kannan_m_80]

It seems it will be much easier to solve this using a Venn diagram, i set up the double set matrix and was confused.
morning session not morning session Total
afternoon session Stat A- 3/4*128 stat B - 7/8*128
not afternoon session ? 0 (given)
total 128(given)

[esledge]

The key to setting up the Double Set Matrix is that the two columns are opposite, mutually exclusive qualities (A and not-A). Same for the rows.

The trick here is recognizing that morning session is NOT the opposite of the afternoon session. Attending the morning session IS the opposite of not attending the morning session.

Here's what the matrix would look like for statement (2):
------------AM----not-AM------Total
PM---------unk------unk----(7/8)128 = 112
not-PM-----16-------0-------(1/8)128 = 16
Total-------unk------unk------128

By "unk" I mean the value is unknown--you could write alg expressions for these boxes, but wouldn't be able to solve. But you don't need to: We have the AM/not-PM box populated with the answer, which is 16.

If you solve this way, it's a good idea to circle the AM/not-PM box in the matrix before you start putting numbers in. I think C is a trap answer because (a) there are still so many unknowns in the chart when filled in for (2), and (b) the temptation to use the numbers you would already have put in a separate chart for (1).

I think you could use a Venn for this one. The Venn gets tricky when you have to consider the space OUTSIDE the circles. But in this problem, everyone attended one of the seminars or both, so everyone will be assigned to either the morning circle, the afternoon circle, or both.

[sanyalpritish]

Hi,
In the Double Matrix How do we know that "No one attended both the sessions" if we assume that no attended then correctly it has been put to 0 else..

[RonPurewal]

Hi,
In the Double Matrix How do we know that "No one attended both the sessions" if we assume that no attended then correctly it has been put to 0 else..

that 0 is in the box that corresponds to attending NEITHER of the sessions.

this zero is justified by the following text in the question:
each of the 128 people attending the seminar attended at least one of the two sessions

[sanyalpritish]

Thx

[mschwrtz]

Glad that Emily and Ron were able to help. Get comfortable with that DSM (double-set matrix, not Diagnostic and Statistical Manual of Mental Disorders). It's a great tool.