Last Saturday, the Aurora Theatre sold two types of tickets for the

Question

Last Saturday, the Aurora Theatre sold two types of tickets for the same show: Front Row tickets and Upper Level tickets. Each Front Row ticket sold for the same price, and each Upper Level ticket sold for the same price. What was the ratio of the theatre’s total revenue from Front Row tickets to its total revenue from Upper Level tickets?

(1) Last Saturday, the theatre sold 3 times as many Front Row tickets as Upper Level tickets.

(2) Last Saturday, each Upper Level ticket cost 20 euros more than each Front Row ticket.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Last Saturday, the Aurora Theatre sold two types of tickets for the same show: Front Row tickets and Upper Level tickets. Each Front Row ticket sold for the same price, and each Upper Level ticket sold for the same price. What was the ratio of the theatre’s total revenue from Front Row tickets to its total revenue from Upper Level tickets?

Let x be the price of a Front Row ticket and y be the price of an Upper Level ticket.
Let a be the number of Front Row tickets sold and b be the number of Upper Level tickets sold.

We want to find the value of (xa)/(yb).

(1) Last Saturday, the theatre sold 3 times as many Front Row tickets as Upper Level tickets.

This gives a = 3b, so the ratio becomes (x * 3b)/(y * b) = 3x/y. Not sufficient.

(2) Last Saturday, each Upper Level ticket cost 20 euros more than each Front Row ticket.

This gives y = x + 20, so the ratio becomes (xa)/((x + 20)b). Not sufficient.

(1) + (2) When taken together, the ratio becomes (xa)/(yb) = (x*3b)/((x + 20)b) = 3x/(x + 20), which still depends on x, so it is not determined. Not sufficient.

Answer: E.

Adit_ · Answer

Ratio1:Ratio2
= Price1*Total1 : Price2*Total2

Statement 1:
Clearly INSUFFICIENT

Statement 2:
INSUFFICIENT as well

Combining the 2:

When it comes to ratio you need only multiples.
The number of tickets are in multiple form 
BUT
Prices are 20 more or less than the other.
INSUFFICIENT

Answer:  Option E

Edskore · Answer

This is a clean Data Sufficiency question testing Ratios and Word Problems — specifically, whether you can determine a ratio when you know either the number ratio or the price difference, but not both.

Key concept being tested: To find a revenue ratio, you need BOTH the quantity ratio AND the price ratio. One without the other leaves you with an expression that can take multiple values.

Step 1 — Define variables.
Let F = price per Front Row ticket, U = price per Upper Level ticket, f = number of Front Row tickets sold, u = number of Upper Level tickets sold. Revenue ratio = (F · f) / (U · u).

Step 2 — Evaluate Statement (1): f = 3u.
Substituting: Ratio = (F · 3u) / (U · u) = 3F/U. We still don't know the prices F and U. Pick F=10, U=10 → ratio = 3. Pick F=10, U=20 → ratio = 1.5. Not sufficient.

Step 3 — Evaluate Statement (2): U = F + 20.
Substituting: Ratio = (F · f) / ((F + 20) · u). We still don't know f/u. Pick f=u=1, F=10 → ratio = 10/30 = 1/3. Pick f=3u, F=10 → ratio = 30/30 = 1. Not sufficient.

Common trap: Students often combine the two statements and assume they now have "enough information" because each statement fills a gap. The key insight is that even combined, F remains unknown.

Step 4 — Evaluate both together.
Combined: ratio = 3F / (F + 20). This expression changes with F: if F=10 → ratio = 30/30 = 1; if F=40 → ratio = 120/60 = 2. Different values of F give different ratios, so we cannot determine a unique answer. Not sufficient.

Answer: E

Takeaway: For any revenue ratio question in DS, ask yourself: do I know BOTH the price ratio AND the quantity ratio? If you only know one, that is almost never sufficient on its own — and a price difference (not price ratio) rarely pins things down either.

Last Saturday, the Aurora Theatre sold two types of tickets for the

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Last Saturday, the Aurora Theatre sold two types of tickets for the

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