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The cost of registration at a professional association meeti

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The cost of registration at a professional association meeti [#permalink]

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New post 29 Jun 2014, 02:48
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A
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D
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  55% (hard)

Question Stats:

71% (02:25) correct 29% (02:22) wrong based on 84 sessions

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The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 100 more than the number who did not, and if receipts for registration and lunch totaled $92,600, how many people paid just for registration at the meeting?

(A) 700
(B) 800
(C) 1,300
(D) 1,500
(E) 1,800
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Jun 2014, 08:03, edited 1 time in total.
Edited the question and added the OA.

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Re: The cost of registration at a professional association meeti [#permalink]

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New post 29 Jun 2014, 06:08
manideepgre wrote:
The cost of registration at a professional association meeting was $50 per person; a lunch for
registrants only was available for an additional $22 per person. If the number of registrants
who paid for lunch was 100 more than the number who did not, and if receipts for registration
and lunch totaled $92,600, how many people paid just for registration at the meeting?
(A) 700
(B) 800
(C) 1,300
(D) 1,500
(E) 1,800


Hello manideepgre,

Welcome to Gmatclub!!

The question is a good option for plugging in where in you try answer choices...It is always a good idea to start with option C..

As per the question we need to find how many people paid just for registration at the meeting..

Let that no. be X =1300. Now since X+100=1400 people registered for lunch as well, 1400+1300=2700 would have registered for sure...and total amount for registration will be 2700*50= 135,000 which is more than the total collection and hence C is not the answer...You can also eliminate D and E as the those numbers are even higher and thus make the collection much more..

Option B : X=800, X+100=900...So total 1700 people registered and paid 1700*50=85000 and 900*22=19800...Again 85000+19800> Total collection of $92600...hence no. people will be less than 800...

Ans is A...

What is the official answer and source of the question??

Here are some posts which you will find useful and I suggest you go through them...


rules-for-posting-please-read-this-before-posting-133935.html
all-you-need-for-quant-140445.html
rules-for-posting-in-verbal-gmat-forum-134642.html

ATB
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The cost of registration at a professional association meeti [#permalink]

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New post 01 Jul 2014, 22:00
manideepgre wrote:
The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 100 more than the number who did not, and if receipts for registration and lunch totaled $92,600, how many people paid just for registration at the meeting?

(A) 700
(B) 800
(C) 1,300
(D) 1,500
(E) 1,800



Bunuel / Experts, is the wording correct for this question? I'm trying to solve using Venn Diagram & going nowhere.. :(

Suggestions please....
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Last edited by PareshGmat on 02 Jul 2014, 18:18, edited 1 time in total.

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Re: The cost of registration at a professional association meeti [#permalink]

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New post 01 Jul 2014, 23:00
Hi paresh,

I think the lunch representation will be in entirely in the registration circle...ie people who opt for lunch will be a subset of people who register. There will have to be 2 circle one inside the another

Try that if u can

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we have two equations to solve the problem:
50x+72y=92600
y-x=100

solving for x gives us 700, so the answer is A

we can consider picking but for me it is better to solve equations than put one or two answer choice

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New post 01 Jul 2014, 23:55
Temurkhon wrote:
we have two equations to solve the problem:
50x+72y=92600
y-x=100

solving for x gives us 700, so the answer is A

we can consider picking but for me it is better to solve equations than put one or two answer choice


Thanks. This line created confusion for me. Can you elaborate as to how the two equations were formed?

Does it mean that every registered person had the Lunch? Also Lunch was attended by other non-registered persons.

If the number of registrants who paid for lunch was 100 more than the number who did not,
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Last edited by PareshGmat on 02 Jul 2014, 18:19, edited 1 time in total.

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New post 02 Jul 2014, 01:24
PareshGmat wrote:
Temurkhon wrote:
we have two equations to solve the problem:
50x+72y=92600
y-x=100

solving for x gives us 700, so the answer is A

we can consider picking but for me it is better to solve equations than put one or two answer choice


Thanks. This line created confusion for me. Can you elaborate as to how the two equations were formed?

Does it mean that every registered person had the Lunch? Also Lunch was attended by other non-registered persons.

If the number of registrants who paid for lunch was 100 more than the number who did not,



Logic for the equations is that X means number of people only registered but not paid for lunch (50 USD), Y means people who registered and paid for lunch (50+22=72 USD). We do not have people who did not register but had the lunch.

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Re: The cost of registration at a professional association meeti [#permalink]

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New post 02 Jul 2014, 01:27
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PareshGmat wrote:
Temurkhon wrote:
we have two equations to solve the problem:
50x+72y=92600
y-x=100

solving for x gives us 700, so the answer is A

we can consider picking but for me it is better to solve equations than put one or two answer choice


Thanks. This line created confusion for me. Can you elaborate as to how the two equations were formed?

Does it mean that every registered person had the Lunch? Also Lunch was attended by other non-registered persons.

If the number of registrants who paid for lunch was 100 more than the number who did not,


Attachment:
Untitled.png
Untitled.png [ 19.52 KiB | Viewed 1907 times ]

Everybody registered for the conference but people who also opted for food coupons were 100 more than those who did not opted for coupons..

So Ideally, Overlap should be like this
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New post 12 Jul 2014, 20:33
Not sure if this the most efficient method.. but this how I did it

from the statement, given that registration fees = 50 and lunch = 22. Hence registration +lunch = 72.
if x=no. of registrations and y=no. of ppl paid for lunch then

50x+72(x+y)=92600... we know that y = 100. Hence, the equation is

50x+72(x+100)=92600

On solving for x, we get 700 which is answer choice A.

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Re: The cost of registration at a professional association meeti [#permalink]

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New post 13 Jul 2014, 03:04
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PareshGmat wrote:
Temurkhon wrote:
we have two equations to solve the problem:
50x+72y=92600
y-x=100

solving for x gives us 700, so the answer is A

we can consider picking but for me it is better to solve equations than put one or two answer choice


Thanks. This line created confusion for me. Can you elaborate as to how the two equations were formed?

Does it mean that every registered person had the Lunch? Also Lunch was attended by other non-registered persons.

If the number of registrants who paid for lunch was 100 more than the number who did not,



Hello PareshGmat.
Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 100 more than the number who did not. That means, total number of people who registered and paid for lunch = 100 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(100 + x) = 7200 + 72x
Now, total amount received was 92,600.
Thus, from the above data,
50x + 7200 + 72x = 92600
122x = 92600 - 7200
122x = 85400
x = 700.

Hence the correct Ans is A
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