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For a certain event, 148 people attended. If all 148 had pai

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Carcass
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For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   02 Dec 2018, 09:55
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For a certain event, 148 people attended. If all 148 had paid full admission price, the total revenue would be three times the cost of sponsoring the event. (Admission price was the only source of revenue.) As it happens, only 50 paid the full admission price, and the others paid nothing.

Quantity A
Quantity B
The total revenue
The cost of sponsoring the event


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
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A
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Fatemeh
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   02 Dec 2018, 22:11
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Answer: B (Not sure)
148 attended
If 148 paid full admission price : total_revenue = 3* sponsoring_money
Paid the full admission price: 50
Paid nothing: 148 - 50 = 98

A: The total revenue
B: The cost of sponsoring the event

If 148 paid full admission price : total_revenue = 3* sponsoring_money
148 * full_admission_price = 3* sponsoring_money = total_revenue

And as admission price is the only source of revenue then :
50 *full_admission_price = Total_paid_money

148 * full_admission_price = 3* sponsoring_money divide by 3:
148/3 * full_admission_price = sponsoring_money
Then we know that total paid money is 50*full_admissions_price and sponsoring_money is 148/3 * full_admission_price then the revenue will be (50-148/3)* full_admission_price = 2/3 * full_admission_price (Less than one person’s admission price)
So A is 2/3 * per_person_full_admission_price
B is 148/3 * per_person_full_admission_price
And B is bigger.
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   03 Dec 2018, 12:34
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Revenue = 148*P and this are 3 times the costs

\(C=\frac{148}{3}\)*P

The revenue of column A are 50*P

\(R > C\)

A in the answer
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   03 Dec 2018, 12:41
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Just wondering if we can pick values in such a question like $2 or $10 for one ticket?
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   03 Dec 2018, 12:44
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yeah, sure. It is one of your strategy in your arsenal. Of course, you can.

However, picking numbers is one of the most powerful ways to tackle a question yet is not among my favorite.

Often is better working conceptually and reaching faster the solution that waste time with numbers.

It depends.

Regards
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   03 Dec 2018, 12:48
Carcass wrote:
yeah, sure. It is one of your strategy in your arsenal. Of course, you can.

However, picking numbers is one of the most powerful ways to tackle a question yet is not among my favorite.

Often is better working conceptually and reaching faster the solution that waste time with numbers.

It depends.

Regards


I agree with this because sometimes there are fractions and decimals and negatives (FR O ZE N) that need to be taken into account and picking whole positive numbers can be deceptive. I use picking numbers strategy mainly when I am unable to work it out conceptually or I am sure that it is a positive integer
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   03 Dec 2018, 19:18
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kruttikaaggarwal wrote:
Carcass wrote:
yeah, sure. It is one of your strategy in your arsenal. Of course, you can.

However, picking numbers is one of the most powerful ways to tackle a question yet is not among my favorite.

Often is better working conceptually and reaching faster the solution that waste time with numbers.

It depends.

Regards


I agree with this because sometimes there are fractions and decimals and negatives (FR O ZE N) that need to be taken into account and picking whole positive numbers can be deceptive. I use picking numbers strategy mainly when I am unable to work it out conceptually or I am sure that it is a positive integer



hi..
picking a number is a good way to tackle a question easily and with speed.
But as you say it is quite deceptive and you should be careful..

As a rule never substitute a value when two quantities are interlinked..

Here the two values are constant, so you can use it
revenue from 50 = 50A
sponsoring cost = \(\frac{148A}{3}=49.33*A\)
so whatever you take A, revenue and sponsoring cost will have same relationship that is R>S

But say I told you the sponsoring cost was a constant amount 20.
or sponsoring amount was 1$ dollar for each person attending.
here you cannot take a value for admission price
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   24 Jun 2019, 12:27
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That's my explanation, it is slightly different than all of the above. Please, correct me if I am wrong:

Potential revenue would be 3 times sponsoring expenses: r0 = 3 * s => s = r0 / 3; This is B.
So the ticket price was potential revenue divided by number of attendees: t = r0 / 148;
Real revenue is number of people who paid multiplied by ticket price: r = 50 * t = 50 / 148 * r0; And this is A.

Here we see that while B is r0 divided by 3, A is r0 divided by less than 3, therefore, A is greater.

Answer A
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   26 Jun 2019, 05:05
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Carcass wrote:
For a certain event, 148 people attended. If all 148 had paid full admission price, the total revenue would be three times the cost of sponsoring the event. (Admission price was the only source of revenue.) As it happens, only 50 paid the full admission price, and the others paid nothing.

Quantity A
Quantity B
The total revenue
The cost of sponsoring the event




If all 148 had paid full admission price, the total revenue would be three times the cost of sponsoring the event.
Let C = cost of sponsoring the event
Let T = cost of 1 full price ticket

So, revenue from 148 full price tickets = 3C
In other words, 148T = 3C

We can also say that revenue from 150 full price tickets is MORE THAN three times the cost of sponsoring the event.
This means that 150T > 3C
Divide both sides by 3 to get: 50T > C

Answer: A

Cheers,
Brent
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   05 Jul 2019, 03:39
let's divide 148 by 3 to get the sponsoring cost-- 148/3 = 49.33 which is less than 50.

Suppose that each one paid $1, thus 50 people paid $50.

Thus, Column A, the total revenue, is $50 which is greater than Column B, the sponsoring cost, which is $49.33.
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   24 Aug 2019, 15:50
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revenue generated when 148 people paid full price is thrice the cost.
i.e. revenue, R=148P=3C
now, a single ticket price P=(3/148)C

so if only 50 people pay the full price, then new revenue R’=50*(3/148)C = (150/148)C
this shows that R’>C.
the answer is A.


extra note:
if only 49 people paid the full price then, r= 49*(3/148)C = (147/148)C
here r<C
still, the answer is not B, as full revenue R is amount accumulated from people paying full price + amount accumulated from payment by remaining people (who haven't paid in full yet paid something).
info about remaining people is not given that's why in that case answer is D.
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   04 Oct 2019, 15:17
Doesn't this parenthesis "(Admission price was the only source of revenue.)" suggest that you do not have enough information to answer? What if, for instance, the 50 people bought thing inside? If there are other sources of revenue answer must be D.
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   04 Oct 2019, 15:50
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Implicitly you answered your own question.

The portion inside the parenthesis is to clarify that people DO NOT bring in other sources of money aside from the revenue.

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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   14 Jan 2020, 19:57
Carcass wrote:
For a certain event, 148 people attended. If all 148 had paid full admission price, the total revenue would be three times the cost of sponsoring the event. (Admission price was the only source of revenue.) As it happens, only 50 paid the full admission price, and the others paid nothing.

Quantity A
Quantity B
The total revenue
The cost of sponsoring the event


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given


The important crux to be learned here is THAT--------

Deciphering language to form an equation can be confusing, so it's often helpful to take certain keywords and replace them with math symbols. For example, forms of the word "to be" can be replaced with an equal sign. This means that we could take this line from the passage

"The total revenue for an event would be three times the cost" and form this equation:

SO, total revenue = 3 × cost

HAVE A LOOK HERE --Click
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink] New post   17 Aug 2023, 08:30
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Conceptual Answer:

We are told that if 148 pay the full price (F), then the total revenues will be 3 times the total cost

So we have:
148F=3C

We know that 50 people paid the full ticket price, and that the remaining 98 paid a partial price.

We can convert the prior statement to get a relative value of 50 full price tickets to the full cost:

148F=3C
F=3/148 C
50F=150/148C

We can clearly see that 50F will be slightly over C. Therefore, no matter how much the remainder of the people paid, the revenues from the 50F more than cover the cost of the event itself.

QA is larger.
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