The organizers of a conference offered a certain number

Question

The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees. How many seminars were there?

10
11
15
20
26

(A) 10
(B) 11
(C) 15
(D) 20
(E) 26

GMATinsight · Accepted Answer

18x  >  15(x-4)+93

i.e. 3x  >  33
i.e. x  >  11

x min = 11

Answer option B

SVP482 · Answer

Four Seminars were attended by 93 people. Since the intention was to accommodate 18 per seminar. The possible number of seminars should be a multiple of 18. Also, the organizers were able to accommodate only 15 per seminar. Those who could not be accommodated in these seminars, were part of the 93 people who were adjusted for 4 seminars. 
 
18 * 4 = 72

93 - 72 = 21 people were from the schedule seminars.

Diving 21 / (18 - 15), we get 7 seminars.

7 + 4 = 11 seminars

Skywalker18 · Answer

Number of attendees per Seminar as per original plan = 18
Due to space limitations, max number of attendees = 15
Also, there are 4 seminars without any seating constraints and have total attendees of at least = 93
As per original plan, these 4 seminars would have had = 18*4 = 72 
So , there are 21 extra attendees in these 4 seminars without space limitations 
Therefore, number of seminars with seating limitation = (93-72)/3 = 7
Total number of seminars = 4+7 =11
Answer B

AdityaHongunti · Answer

Algebraic approach-

# of seminar= s
# of seminar with space limitations= x

Now remaining seminar without limitation: 
s-x = 4 ..... (1)

Total number of INTENDED attendees= 18*s
Total number of attendees in seminar with limitations= 15*X

Number of remaining attendees = intended attendees-attendees with limitations >=93

18s-15x >=93 .....(2)

Solving (1) and (2)
X=7
s=4+7
s=11.... option B

Posted from my mobile device

EMPOWERgmatRichC · Answer

Hi All,

We're told that the organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees. We're asked for the total number of seminars that were planned. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

Let's TEST Answer D: 20 seminars 
With an expectation of 18 attendees/seminar, (18)(20) = 360 attendees. 
16 seminars can hold only 15 attendees each, accounting for (16)(15) = 240 attendees. 
360 - 240 = 120 additional attendees, but the remaining 4 seminars are only expected to hold 93 attendees. 
In this situation, we have too many attendees, so this number is TOO BIG. We need fewer attendees, thus we need fewer seminars

Let's TEST Answer B: 11 seminars 
With an expectation of 18 attendees/seminar, (18)(11) = 198 attendees. 
7 seminars can hold only 15 attendees each, accounting for (7)(15) = 105 attendees. 
198 - 105 = 93 additional attendees. This is an exact match for what we were told, so this must be the answer!

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

dabaobao · Answer

Let T = total number of attendees
Let S = total number of seminars

Initial Plan: T = 18S
Actual: T = 15(S-4) + 93

So we have 2 equations and 2 unknowns.

18S = 15S - 60 + 93
3S = 33
S =11

ANSWER: B

Basshead · Answer

Four seminars were attended by 93 people. These four seminars should have  only  been attended by 72 people.

93 - 72 = 21 extra people.

Since 3 people were left out of each seminar, the 21 extra people came from 21 / 3 = 7 seminars.

7 seminars + 4 seminars = 11 seminars.

Answer is B.

AndrewN · Answer

Can anyone confirm, preferably with a screenshot of the actual GMAT Prep question, that the problem states   at least  93 conference attendees  (highlighted above)?

Thank you.

- Andrew

Bunuel · Answer

Could not find the actual screenshot but several other sites, which have this question, all have "at least 93 conference attendees".

AndrewN · Answer

Thank you,   Bunuel  , for the prompt reply. Yes, I found the same when I googled the question. But does such phrasing not change the nature of the question? That is, if there is no restriction on the upper limit to the number of conference attendees who are to be placed in these 4 remaining seminars, then why could some other answer not be justified? For instance, tracing the same line of logic that Rich from EMPOWERgmat has outlined above, we could say that there were originally 20 scheduled seminars (answer choice (D)).

18 * 20 = 360

Thus, there would be 360 attendees. If all but 4 of these seminars held 15 people, well, we can do the math on that one quite easily:

15 * 16 = 240

But the difference between the two numbers of attendees is 120, which is, of course,   at least   93. It is quite possible that within the constraints of the question, the one that is written above, these 120 remaining attendees could be equally divided among the 4 other seminars.

I find myself wondering whether this is, in fact, a GMAT Prep question, since it was only more recently posted in this forum and elsewhere. Perhaps one site copied from another, and the source got lost in the mix, or the person who originally transcribed the question did not do so correctly. What do you think?

I can appreciate that (B)  can be  the answer, but I cannot ignore this nagging thought that something is off.

- Andrew

AndrewN · Answer

Hello,  IanStewart . I am writing as a student of this test, as someone who genuinely wishes to understand the core of a matter, and I trust your Expert opinion (just as I trust that of   Bunuel  , but I have not received a response, and one does not seem forthcoming). If you will take a moment to review my above post, please tell me, am I off-base, or is the problem lacking something as written? I am not disputing that 11 is a valid answer. I simply find the phrasing at the end of the setup problematic.

Thank you for taking the time to consider my request.

- Andrew

Rickooreo · Answer

gmatophobia  can you please help me with this question

gmatophobia · Answer

Hi  Rickooreo

We'll take the information one at a time -

1) We know that the organizers accounted for 18 people who would attend each seminar and taking that into account they had organized say "n" seminars.

2) Due to space constraints, only 15 people could attend each seminar.  Inference: So every seminar had 3 people who were in excess.

3) In the last 4 seminars there were at least 93 attendees.

Let's try to visualize this

__ __ - - - - __ __  __ __ __ __

Had everything gone according to the plan (i.e. the space constraint hadn't been an issue), there would have been 72 (18 * 4) people attending the last 4 seminars.

However we that there are at least 93 who have turned up now. Let's take 93 for now, the excess 21 (93 - 72) are those people who were not able to attend their seminars due to space constraints and have landed in the last four.

We know each seminar has 3 people who are in excess, so the extra, 21 people, accounts from 7 seminars.

Therefore total seminars = 7 + 4 = 11

Note: Each seminar room added, merely adds 3 more people to the extra count. As 11 is a valid option we can go it.

Hope this clarifies.

Rickooreo · Answer

Hi  gmatophobia , 
Thankyou for sharing your approach

I have two doubts, more related to the interpretation of what is mentioned in the question

Sentence 1 : The organizers of a conference offered a certain number of simultaneous seminars with the intention that  each seminar would be attended by 18 conference attendees .
>> I thought that this is the capacity of the conference room, maybe there are more participant but each seminar would be attended by 18 attendees

Sentence 2 : leaving 4 remaining seminars that together would be attended by  at least  93 conference attendees

The question says atleast so had it been more than 93, the count of 21 will change and hence the number of seminar. The questions is asking for "How many seminars were there?" not minimum number of seminar.

Can you please correct me

Engineer1 · Answer

MartyMurray   KarishmaB   chetan2u  - It's a confusing question, IMO. I get both B and C as the correct answers. What am I missing?
Don't mind the handwriting. : ) Thank you!

chetan2u · Answer

Hi,

The moment we get x greater than 11 after forming the equation, there is no reason why other options cannot be the answer.
Even if you substitute the values back in equation, the options B to E would fit in

I would surely not advise you to mull over the question any further. It is best left alone. In all probability, this may not be a GMAT prep question.

Kinshook · Answer

paidlukkhha   Bunuel

Answers B-E all are correct. Please check OA.
Given: The organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of the seminars, leaving 4 remaining seminars that together would be attended by at least 93 conference attendees.
Asked: How many seminars were there?
Let the number of seminars be x.

18x >= 15(x-4) + 93
3x >= 33
x >= 11

IMO B-E

KarishmaB · Answer

Total number of attendees = 18n (where n is the number of seminars)

Each of the (n-4) seminars can accommodate at most 15 attendees and there will be 93 attendees leftover (if each seminar accommodates 15 attendees). More than 93 will be leftover only if the (n-4) don't all accommodate 15 each.

Hence, 18n = 15(n-4) + 93
n = 11

Answer (B)

KarishmaB · Answer

How is (C) the answer? Why do you have a ">" sign? There are only simple equations involved in the question and the answer is simply (B) i.e. 11. As for handwriting, who am I to judge? I can't write straight for the life of me!!

The organizers of a conference offered a certain number

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The organizers of a conference offered a certain number

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