Every attendee at a monster truck rally paid the same direct

Question

Every attendee at a monster truck rally paid the same admission fee. How many people attended the rally?

(1) If the admission fee  had been raised to $20  and twice as many people had attended, the total admission fees collected would have been three times greater.

(2) If the admission fee  had been raised to $30  and two-thirds as many people had attended, the total admission fees collected would have been 150% of the actual admission fees collected.

asethi100 · Answer

Initially,

No of people attending = x
Price per ticket = y
Revenue collected = (No. of tickets sold)*(Price per ticket) = x*y.

Condition 1:

No of people attending = 2x
Price per ticket = 20
Revenue for condition 1 = 2x*20 = 40x

This revenue is 3 times the original revenue,

Thus, 40x = 3xy

x cancels out, hence insufficient

Condition 2:

No of people attending = 2x/3
Price per ticket = 30
Revenue for condition 1 = 2x*30/3 = 20x

This revenue is 3 times the original revenue,

Thus, 20x = 1.5xy

x cancels out, hence insufficient

1 & 2 together donot give the value of x either. Hence OA is E.

Bunuel · Answer

Every attendee at a monster truck rally paid the same admission fee. How many people attended the rally?

Number of attendees = n;
Fee = x.

(1) If the admission fee  had been raised to $20  and twice as many people had attended, the total admission fees collected would have been three times greater.

20*2n = 3xn --> x = 40/3. Not sufficient.

(2) If the admission fee  had been raised to $30  and two-thirds as many people had attended, the total admission fees collected would have been 150% of the actual admission fees collected.

30*2/3*n = 3/2*xn --> x = 40/3. Not sufficient.

(1)+(2) From both statements we have that x = 40/3, which is not sufficient to get the value of n.

Answer: E.

Hope it's clear.

Ameya85 · Answer

Bunuel ,

Thanks for the explaination, I marked D for this question and below was my method

1 -> Admission Fee be X and total number of people attended be N so initially Total = XN

Now, with St.1, we have 2N * (X+20) = 3XN > 20XN + 40N = 3XN > 40N = XN > X = 40. Hence sufficient. What did I do wrong here?

Ameya

Bunuel · Answer

First of all, we need to find n, not x.

Next, your equation is not correct. (1) says "If the admission fee had been raised  to  $20" not " by  $20". Thus it should be 20*2n = 3xn.

Bakervai · Answer

Dear  Bunuel

You wrote, 
 Number of attendees = n;
Fee = x.

(1) If the admission fee had been raised to $20 and twice as many people had attended, the total admission fees collected would have been three times greater.

20*2n = 3xn --> x = 40/3. Not sufficient.

why x can not be 40/3 ? (It appeared okay to me, since a fee can be 13.33)

can you please tell me, what am i missing here ?

Bunuel · Answer

When combining we can get that x IS 40/3, but we need the value of n (the number of attendees), which we cannot determine.

Bakervai · Answer

Thanks, I got that.
Just tell me one more thing, does this problem belong to the criteria "two variable, one equation.. no solution..." ?

stonecold · Answer

hey  Bunuel 
i have a slight doubt in this question
in the first statement it says the collection would have been 3 times greater
what does 3 times greater mean?
i initially wrote => XN+3XN
then Changed it to 3XN as it looked messier in the first place.
can you help me out here..
thanks

stonecold · Answer

Abhishek009 Need some help with this one. This question although is straight forward but i cannot seem to get the statement 1 I have this doubt for over a 1 months now ..!!! Bunuel is a busy man

chetan2u · Answer

Hi  stonecold ,

3 different ways - 
 1)two times greater than MEANS 2x BUT will be x+200% of x if it reads y is 200% greater than x
2) two times as many MEANS 2x again
3) BUT two times more than MEANS x+2x = 3x

Hope it clears the doubt

Regards,
Chetan

stonecold · Answer

Cool ..! I get the difference now .!

Regards 
StoneCold

chetan2u · Answer

Hi,
i think there was a typo in my post above --
two times Greater than should be same as more than so it should be x+2x = 3x..

examples--
x is 200% more/ greater than y -- x = y+2y..
But if it says x is two times greater than y it will be x=2y..
x is 2 times as much as y -- x=2y

stonecold · Answer

THATS What my Doubt is..
Okay so i am more confused now.

Statement 1 of yours is not clear chetan
I have no doubt in one and two.
What does y is two times greater than x represent mathematically

regards
StoneCold

chetan2u · Answer

Hi,

let me talk of greater than, as I have seen its usage..
greater than is used to compare numbers , % etc..

lets see the %.. 
x is 20% greater than y MEANS x = y+0.2y..
x is 100% greater than y means x= y+y =2y..
here the value of % greater than is added over and above initial value..

Now numbers in terms of radius, height etc.. 
height is two times greater than radius of the cylinder..
h = 2r..
Prob of doing x is two times greater than prob of doing y..
so prob of x = 2* prob of doing y..

so these are the two different variations which I wanted to speak of..

ethanhunt007 · Answer

Hi, I have an issue with the phrase "greater than"

If I say X is twice of Y, then it should mean --> X = 2Y
If I say X is two times greater than Y, shouldn't it mean --> X = 3Y

Here, in the above question based on statement (1) shouldn't it be 4xn instead of 3xn as the phrase uses the term "three times greater than" instead of "three times" alone.

IanStewart · Answer

There seems to be some confusion about this earlier in this thread. The phrase "X is 2 times greater than Y" simply means that X = 2Y. It's understandable that this might seem confusing, because if instead we say "X is 200% greater than Y" we definitely mean that X = 3Y, but this all boils down to idiomatic usage in English. If you think of smaller numbers, it might be clear this is how the phrase is used in the language (there's a reason you've never heard anyone say "X is 1 times greater than Y" to mean that X is twice as big as Y), and it's also what the dictionary says, as quoted at this link: https://mathforum.org/library/drmath/view/61774.html

JDF · Answer

I don’t understand... what you showed us, you can cancel the x. So you can solve for y. Why can’t you plug in for y and solve for x, then solve for n?

Posted from my mobile device

DSBlender · Answer

We are asked to find the real number of people that attended the rally. In each statement, we can use "n" to represent the number of people, and "p" to represent the actual price of each ticket.

Let's start by testing Statement 1). We can translate this sentence into the equation 15*2n=3pn. We have two variables outstanding. We need to find "n", but we don't know what p is. We can't cancel out n. Statement 1 is INSUFFICIENT.

Statement 2). Similarly, we can translate this sentence into the equation 22.50*(2/3)n=(3/2)pn. Like Statement 1), we still have two variables. INSUFFICIENT.

Let's try to combine Statement 1) and Statement 2). We have 15*2n=3pn and 22.5*(2/3)n=(3/2)pn. Let's break each statement down to its core by simplifying them. The first statement turns into 30n=3pn. The second statement turns into 15n=1.5pn. Wait a minute, we need to use algebraic theory to recognize that these two equations are identical. If we multiply the second equation by 2, we get 30n=3pn, which is identical to the revised Statement 1). We can't solve a system of equations with two identical equations, so C is INSUFFICIENT.

The answer is E.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Every attendee at a monster truck rally paid the same direct

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Every attendee at a monster truck rally paid the same direct

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards