In Year 1, a retail company's total revenue was generated by two divisions: Division X, wh… — GRE General Test

In Year 1, a retail company's total revenue was generated by two divisions: Division X, which accounted for $40\%$ of total revenue, and Division Y, which accounted for the remaining $60\%$ . From Year 1 to Year 2, revenue from Division X increased by $20\%$ , while revenue from Division Y decreased by $10\%$ . From Year 2 to Year 3, revenue from Division X decreased by $10\%$ , while revenue from Division Y increased by $20\%$ . Which of the following statements must be true? Select all such statements.

Total company revenue in Year 3 was $8\%$ greater than total company revenue in Year 1.Answer
From Year 1 to Year 3, revenue from Division X increased by $8\%$ .Answer
C
In Year 2, Division X accounted for more than $50\%$ of total company revenue.
D
Total company revenue in Year 2 was $10\%$ greater than total company revenue in Year 1.
From Year 1 to Year 3, revenue from Division Y increased by $8\%$ .Answer

Answer

The correct statements are: total company revenue in Year 3 was 8% greater than in Year 1; revenue from Division X increased by 8% from Year 1 to Year 3; and revenue from Division Y increased by 8% from Year 1 to Year 3.

The statements confirming an 8% overall increase for total company revenue, Division X revenue, and Division Y revenue from Year 1 to Year 3 are all correct. A 20% increase followed by a 10% decrease (and vice versa) multiplies the starting amount by

1.20 \times 0.90 = 1.08

, which represents a net 8% increase on each respective division's initial base.

Step-by-Step Solution

Assign a variable to initial total revenue and calculate division revenues for Year 1.

Let total revenue in Year 1 be

R

. Revenue from Division X is

0.40 R

and revenue from Division Y is

0.60 R

Establishing initial quantities provides the base for computing percentage changes across subsequent years.

Calculate division revenues and total revenue for Year 2.

Division X revenue in Year 2 =

0.40 R \times 1.20 = 0.48 R

. Division Y revenue in Year 2 =

0.60 R \times 0.90 = 0.54 R

. Total Year 2 revenue =

0.48 R + 0.54 R = 1.02 R

Applying the respective 20% increase and 10% decrease to Year 1 base values yields Year 2 amounts.

Calculate division revenues and total revenue for Year 3.

Division X revenue in Year 3 =

0.48 R \times 0.90 = 0.432 R

. Division Y revenue in Year 3 =

0.54 R \times 1.20 = 0.648 R

. Total Year 3 revenue =

0.432 R + 0.648 R = 1.08 R

Applying the respective 10% decrease and 20% increase to Year 2 values yields Year 3 amounts.

Evaluate the percent changes from Year 1 to Year 3 for each division and the total company.

Division X change:

\frac{0.432 R - 0.40 R}{0.40 R} = 8\%

. Division Y change:

\frac{0.648 R - 0.60 R}{0.60 R} = 8\%

. Total revenue change:

\frac{1.08 R - 1.00 R}{1.00 R} = 8\%

. Also, Division X proportion in Year 2 was

\frac{0.48 R}{1.02 R} \approx 47.06\%

Determines which of the given statements hold true based on accurate relative changes.

Key Concept

Weighted and Successive Percent Change

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic