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Deciphering Percentage Changes in Revenue

Learn how to analyze year-over-year percentage changes without knowing absolute base values. We explore compounding percentages, weighted averages of combined revenues, and the relationship between revenue, price, and quantity.

C2023=C2020×(1+0.05)×(1+0.04)×(1−0.03)C_{2023} = C_{2020} \times (1 + 0.05) \times (1 + 0.04) \times (1 - 0.03)
C2023=C2020×1.05×1.04×0.97C_{2023} = C_{2020} \times 1.05 \times 1.04 \times 0.97
1.05×1.04×0.97=1.059241.05 \times 1.04 \times 0.97 = 1.05924
Let's look at the percentage change from 2020 to 2023. A common trap is to just add the percentages together. For CandyBursts, five plus four minus three is six percent. But watch what happens when we multiply the multipliers instead.
Step-by-step solver
1

Analyze Statement 1

We only have year-over-year percentage changes, not absolute dollar amounts. Therefore, we cannot compare the total revenue generated by the two products.

2

Analyze Statement 2

From 2022 to 2023, CandyBursts revenue decreased (-3%) and BerryBonbons revenue increased (+6%). Without the base revenues, we don't know if the net total increased or decreased. Thus, it is true that we don't have enough information.

3

Analyze Statement 3

Calculate the compound multipliers from 2020 to 2023. CandyBursts: 1.05 * 1.04 * 0.97 = 1.05924. BerryBonbons: 1.08 * 0.92 * 1.06 = 1.053216. They are not exactly the same.

1.05924≠1.0532161.05924 \neq 1.053216
4

Analyze Statement 4

Revenue = Price * Quantity. In 2022, Revenue increased by 4% (multiplier 1.04), while Price increased from 0.20 to 0.22 (multiplier 1.10). Quantity multiplier = 1.04 / 1.10 = ~0.945, which means quantity dropped.

Q22=1.041.10Q21Q_{22} = \frac{1.04}{1.10} Q_{21}
5

Analyze Statement 5

No absolute dollar amounts are provided in the data, so any specific dollar bound is purely speculative.

6

Analyze Statement 6

The 2023 revenue growth relative to 2020 is 5.92% for CandyBursts and 5.32% for BerryBonbons. Since the combined growth is a weighted average of these two values, it must be less than 6%.

5.32%<Total Growth<5.92%5.32\% < \text{Total Growth} < 5.92\%
7

Analyze Statement 7

In 2021, both CandyBursts (+5%) and BerryBonbons (+8%) increased in revenue. The combined total must therefore also increase.

8

Analyze Statement 8

In 2022, one increased (+4%) and one decreased (-8%). Without base values, we cannot know the direction of the total.

Original question

Exam Questions Compilation All questions from the assessment (revenue, database, and probability sections). Part A – Revenue Changes (CandyBursts & BerryBonbons) In the table, each numerical value represents the percentage change in the product’s revenue relative to the preceding year. For simplicity, we’ll assume that the percentage changes reported are exact. Table (year-over-year % change): CandyBursts: 2021 +5%, 2022 +4%, 2023 –3% BerryBonbons: 2021 +8%, 2022 –8%, 2023 +6% Question 1: Which of the following sentences are certainly true, given the information currently available? Select all that apply. 1. If we exclude 2022, BerryBonbons have generated more revenue than CandyBursts on average in the given period 2. We don’t have enough information to say whether the total revenues have increased or decreased from 2022 to 2023 3. The percentage change in 2023 revenue from 2020 is exactly the same for CandyBurst and BerryBonbons 4. If the price of a single CandyBurst was $0.20 in 2021 and $0.22 in 2022, then we know that the number of CandyBursts sold in 2022 was lower than the previous year 5. In 2020, BerryBonbons generated less than $3.52 million in revenues 6. The total revenues (of CandyBursts and BerryBonbons combined) increased by no more than 6% in 2023 compared to 2020 7. Total revenues (that is, the revenues of CandyBurst and BerryBonbons combined) increased in 2021 compared to 2020 8. Total revenues decreased in 2022 compared to 2021

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