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For a certain event, 148 people attended. If all 148 had pai : Quantitative Comparison Questions

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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink]
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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]
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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]
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]
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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]
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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]
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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]
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]
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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]
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]
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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.

Regards
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Re: For a certain event, 148 people attended. If all 148 had pai [#permalink]
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]
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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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