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06 Aug 2026, 05:29
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A concert venue’s ticket revenue increased by 15% from 2023 to 2024, while its operating costs increased by 10% over the same period. If net income is defined as ticket revenue minus operating costs, by what percent did the venue’s net income increase from 2023 to 2024?
(1) The venue’s net income in 2023 was $120,000.
(2) In 2023, the venue’s ticket revenue was twice its operating costs.
(1) The venue’s net income in 2023 was $120,000.
(2) In 2023, the venue’s ticket revenue was twice its operating costs.
06 Aug 2026, 05:29
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Official Solution:
A concert venue’s ticket revenue increased by 15% from 2023 to 2024, while its operating costs increased by 10% over the same period. If net income is defined as ticket revenue minus operating costs, by what percent did the venue’s net income increase from 2023 to 2024?
Let \(R\) be the venue’s ticket revenue in 2023, and let \(C\) be its operating costs in 2023.
The net income in 2023 was \(R - C\).
The net income in 2024 was \(1.15R - 1.10C\).
The increase in net income was \((1.15R - 1.10C) - (R - C) = 0.15R - 0.10C\).
The question asks for the percent increase in net income:
\(\frac{0.15R - 0.10C}{R - C} * 100\)
(1) The venue’s net income in 2023 was $120,000.
This gives \(R - C = 120,000\), which is not enough to get the value of \(\frac{0.15R - 0.10C}{R - C} * 100\).
Not sufficient.
(2) In 2023, the venue’s ticket revenue was twice its operating costs.
This gives \(R = 2C\).
Substitute into the expression:
\(\frac{0.15R - 0.10C}{R - C} =\)
\(= \frac{0.15 * 2C - 0.10C}{2C - C} =\)
\(= \frac{0.20C}{C}=\)
\(= 0.20\)
So the venue’s net income increased by \(20\%\).
Sufficient.
Answer: B
A concert venue’s ticket revenue increased by 15% from 2023 to 2024, while its operating costs increased by 10% over the same period. If net income is defined as ticket revenue minus operating costs, by what percent did the venue’s net income increase from 2023 to 2024?
Let \(R\) be the venue’s ticket revenue in 2023, and let \(C\) be its operating costs in 2023.
The net income in 2023 was \(R - C\).
The net income in 2024 was \(1.15R - 1.10C\).
The increase in net income was \((1.15R - 1.10C) - (R - C) = 0.15R - 0.10C\).
The question asks for the percent increase in net income:
\(\frac{0.15R - 0.10C}{R - C} * 100\)
(1) The venue’s net income in 2023 was $120,000.
This gives \(R - C = 120,000\), which is not enough to get the value of \(\frac{0.15R - 0.10C}{R - C} * 100\).
Not sufficient.
(2) In 2023, the venue’s ticket revenue was twice its operating costs.
This gives \(R = 2C\).
Substitute into the expression:
\(\frac{0.15R - 0.10C}{R - C} =\)
\(= \frac{0.15 * 2C - 0.10C}{2C - C} =\)
\(= \frac{0.20C}{C}=\)
\(= 0.20\)
So the venue’s net income increased by \(20\%\).
Sufficient.
Answer: B
