This question is very similar in structure to another OG question:
https://www.beatthegmat.com/og2016-ds-wh ... tml#797219
(You'll note similarities in the solution).
Total revenue can be defined as:
Revenue = (# of full-price tickets)x(full-ticket price) + (# of reduced-price tickets)x(reduced-ticket price)
I'll assign the following variables for clarity:
number of full-price tickets = F
price of each full-ticket = f
number of reduced-price tickets = R
price of each reduced-ticket = r
Revenue = (F)(f) + (R)(r)
We're given the total # of tickets, so we know that F + R = 400. If we knew a proportion between F and R, we could infer the values.
We are also given that r (the price of reduced-price tickets) is x% of f (price of full-priced tickets). We would need the value of x and the value of either f or r to infer the price of each.
Target question: what are the values of F, f, R, and r?
(1) x = 50
The reduced-price tickets are half the price of the full-priced ones, but what are those prices? $5 and $10? Or $100 and $200? We also don't know anything about F and R. Insufficient.
(2) Full-price tickets sold for $20 each.
By itself, this gives us only 1 of the 4 values we need to solve. Insufficient.
(1) & (2) together
We can infer that f = $20 and r = $10. However, we still don't know how many of each were sold. If the theater sold mostly full-price tickets (if F is close to 400), the total revenue could be close to $8000. If they sold almost all reduced-price tickets (if R is close to 400), the total revenue would be closer to $4000.
Since we still don't know the values of F and R, we cannot answer the question. The answer is
E.
