At a certain symphonic concert, tickets for the orchestra

Modeled on PS N. 198 OG 13th edition.

It is a really hard problem. Eventually, all the new problems provided by the new OG are harder than before, this is general.

Here the best strategy is to follow a conceptual approach. soon a picking number strategy is quite cumbersome, and you get in trouble.

Ciao Mike
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ok here is how i did it
i picked numbers of two kinds of tickets as 3 and 5 respectively (for purpose of easy calculation), so we got 50*3=150, and 30*5=150 for balcony tickets.
total revenue=150+150=300, so R=(150/300)*100=50 and B=(5/8)*100=500/8
then all we have to do is test following options by inserting R=50 into them and see if we yield B=500/8

Here is that question: last-sunday-a-certain-store-sold-copies-of-newspaper-a-for-101739.html

All OG13 questions: the-official-guide-quantitative-question-directory-143450.html

Hope it helps.
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Yeah very tough to pick numbers indeed!

What approach do you suggest Mike?

Cheers!
J

Dear jlgdr,
I don't know if you followed that link to the blog article, but in that article, I show a full solution using picking numbers.

For starters, we know that if B = 0, then R = 0. Here, all the answers satisfy that. We also know that if B = 100, then R = 100. Right there, we can plug in and eliminate some answers. Those are two particular easy choices to make for numbers to pick.

A little more challenging, but not so hard --- suppose they sell just as many balcony tickets as orchestra tickets, a 50/50 split. Then, of course, B = 50. For simplicity, suppose they sold 10 of each. That's $500 for the ten orchestra tickets, and $300 for the ten balcony tickets, for a grand total of $800 in revenue. Then, the balcony accounts for 300/800 = 3/8 of the revenue or 37.5 percent. R = 37.5 --- that's a little harder to plug in, but after we eliminate the first batch of answers, we don't have so many to check.

Does all this make sense?
Mike
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From what we have so far, we get this:

50x+30y=T (Total Revenue)
30y=RT/100
y= B(x+y)/100

Fro these equations above, we get this:
30y= (50x+30y)R/100 and y= (x+y)B/100 OR

3000y= 30Bx+30By and 3000y= 50Rx+ 30Ry

by subtracting from each other we get this: (*) x/y= (30B-30R)/(50R-30B)
Stop here! We need x/y. Right. We already have this: x/y= {B(x+y)/100}/{(100-B)(x+y)/100}
by reducing, we get this (**) x/y= B/(100-B)!

By replacing (*) with (**) we can easily find the solution:

B= 500R/(2R+300)!!!

Let x=no. of orchestra tickets
y=no. of Balcony tickets
We know,50x+30y=T(Total Revenue) (1)

Also,RT/100=30y OR T/y=3000/R

And B/100*(x+y)=y OR x/y=100-B/B

Divide (1) by y

We get, 50*(100-B/B) + 30=3000/R

Simplifying,100/B=(3000-30R+50R)/50R

B=500R/(300+2R)

I am not sure if this question is worded incorrectly. Refer to " If R% of the revenue for the concert was from the sale of balcony tickets, and B% of the tickets sold were balcony tickets,

Both R and B refer to Balcony tickets hence its adding to the confusion.

Dear Epex
I'm happy to help. The percent R is a percent of money, a percent of revenue, so that's a dollar amount. The percent B is a percent of the number of tickets, so that's a number of tickets.

Suppose the symphony sold ten balcony ticket and ten orchestra tickets. That's 20 tickets, and ten are balcony tickets, which is B = 50%. Meanwhile, from those sales, they take in $300 from the balcony tickets and $500 from the orchestra tickets, for a total revenue of $800. Of this $800, $300 came from balcony tickets: that's a R = (3/8)*100 = 37.5%.

Does this distinction make sense?
Mike
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Thanks. It does help. "R" used in question stem makes the reader feel that it's related to total revenue not the revenue of sale from B tickets.

Dear Epex,
I don't know about this. It says, "R% of the revenue for the concert was from the sale of balcony tickets." That quite clearly states that R% is a percent of the total revenue. If you mean that the choice of the letter "R" is confusing, then you really have to move past your attachment to the letters used for variables. For example, usually a problem will use D for distance and T for time, but it would mathematically perfectly legal to use T for distance and D for time, as long as that was clearly specified in the problem. The meaning of variables is determined exclusively from how they are mathematically defined, and the letter chosen for the variable is 100% arbitrary. In general, the GMAT usually is not trying to fool test-takers with cheap tricks such as reversing familiar variables (the D-T switch above), but in a problem in which there are not standard variables, any letters could be used. Don't be attached to the choice of letter. Always pay attention to the mathematical definition of the variable.
Does this make sense?
Mike
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fell for the number picking first...but then algebra worked for me fast..
+1 for the question.

Hi Mike, are you saying that in order to solve this question you suggest to try an easy technique (testing extremes) and if that does not give us the answer, then try a relatively harder technique of a 50/50 split for # of tickets.

I read your post on how to eliminate some answers using easy technique smart numbers. Using extremes? is that the correct name for the technique you described? I was able to eliminate A and C when I tried r= 100% and b=100%. When I tried r=0% and b=0% gave me nothing to eliminate. Just as you said it would.

Then I tried the little harder technique. Using smart numbers at 50/50 split for number of tickets. In my example I used 1 ticket for O and 1 ticket for B. This little harder work gave me the answer I was looking for.

$PPU # = T
O => 50 (1) = 50
B => 30 (1) = 30
Total 2 = 80

R=30/80 = 0.375 =37.5%
B = 1/2 = 0.50 = 50%

Only D gives you B in terms of R

(500(37.5))/(300 + (2(37.5))) = 50

Dear lalania1

I'm happy to respond. Precisely! We use extremes, such as R = 0 and R = 100%, to eliminate "low-hanging fruit"---those answer choices that can be easily eliminated.

I think you would make you job even easier by using fractions rather than decimals. If we have a percent of (3/8)*100%, there's no law that says we have to convert that to a decimal. We can lever it exactly like that, and all our multiplication is much easier.

Does all this make sense?
Mike
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This is my solution.

\(R = \frac{(30y)}{(50x+30y)} * 100 - (1)\)
\(B = \frac{(y)}{(x+y)} * 100- (2)\)

From (1)

\(R(50x+30y) = 3000y\)
\(50Rx + 30Ry = 3000y\)
\(50Rx = 3000y - 30Ry\)
\(x = \frac{(3000y - 30Ry)}{50R}\)
\(x =\frac{(300y - 3Ry)}{5R}\)

From (2)

\(B = \frac{y}{(x+y)} * 100\)
\(B = \frac{100y}{[(300y - 3Ry)/(5R) + y]}\)
\(B = \frac{100}{[( 300-3R)/5R] + 1}\)
\(B = \frac{5R*100}{(300 - 3R + 5R)}\)
\(B = \frac{500R}{(300 + 2R)}\)
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Hi y'all,

Can someone please let me know if I approached this correctly, or just got lucky?

I struggle with percent/fraction/decimal problems (for some reason) so I try to choose smart numbers whenever I can.

Here, I imagined a theatre with 10 balcony seats and 10 orchestra seats. So R would be 3/8, or 37.5%. B would be 50%. So I'm looking for an answer that gives me 1/2 or 50%.

Looking at the answers, I know I can immediately eliminate A and B, because the numerator will be larger than the denominator (i.e., more than 1/2). I also notice that C would not be close enough to 1/2, so I eliminate that one too.

Then I'm down to D and E, and even here, I don't try to do any complicated computations. If we round R to 40%, we can turn the numerator of both D and E to about 200 (knowing it will be a little less). The denominator then is either 380 (ish...) or 320 (ish...). From these estimates, D looks closest to 1/2 with 200/380, so I choose this.

So am I completely lucky or did I approach this correctly? It seems a bit strange to me that I plugged a whole number in for R (37.5), but was looking for an overall fraction of 1/2 for B. Obviously if I was looking for a whole number of 50, I would not find any of the answers to be correct. I'm hoping some of you might be able to let me know how I'm tackling these types of questions!

Posted from my mobile device

This took me time but here's how I did it:

Orchestra (O) + Balcony (B) = Total Number of Tickets --> O+B = Total Number of Tickets.

I will now assume O+B = 100

meaning, O = 100-B

Now onto Revenue:

R% of Revenue = Price of Balcony * Number of Balcony Seats

Total Revenue = (30B*100)/R

Now Total Revenue is also equal to Price of B * Balcony seats + Price of O * Orchestra seats

Total Revenue = 30B +(100-B) *50

5000-20B

Now equate:

5000-20B=(30B*100)/R

We simplify and get Option D.

Tricky, tough, and time consuming. I hope to get better at this.