Was Store K's profit last month at least 10 percent greater than its profit the previous month?

[BTGModeratorVI]

Was Store K's profit last month at least 10 percent greater than its profit the previous month?

(1) Store K's expenses last month were 5 percent greater than its expenses the previous month.
(2) Store K's revenues last month were 10 percent greater than its revenues the previous month.


Answer: C
Source: official guide

[Brent@GMATPrepNow]

Was Store K's profit last month at least 10 percent greater than its profit the previous month?

(1) Store K's expenses last month were 5 percent greater than its expenses the previous month.
(2) Store K's revenues last month were 10 percent greater than its revenues the previous month.


Answer: C
Source: official guide

Target question: Was Store K's profit last month at least 10 percent greater than its profit the previous month?

IMPORTANT: Profit = Revenue - Expenses

Statement 1: Store K's expenses last month were 5 percent greater than its expenses the previous month.
Since we have no information about revenue, there is no way to compare profits.
Statement 1 is NOT SUFFICIENT

Statement 2: Store K's revenues last month were 10 percent greater than its revenues the previous month.
Since we have no information about expenses, there is no way to compare profits.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Important concepts: If X is 5% greater than Y, then X = 1.05Y, and if X is 10% greater than Y, then X = 1.10Y.
If we let R = the revenue from the previous month, then (from statement 2), 1.1R = the revenue from last month.
If we let E = the expenses from the previous month, then (from statement 1), 1.05E = the expenses from last month.

The target question asks Was Store K's profit last month at least 10 percent greater than its profit the previous month?
In other words, Was Store K's profit last month greater than or equal to a value that's 10 percent greater than its profit the previous month?
In other words: Is 1.10R - 1.05E ≥ 1.10(R - E)?
Expand the right side to get: Is 1.10R - 1.05E ≥ 1.10R - 1.10E?
Add 1.10E to both sides of the inequality to get: Is 1.10R + 0.05E ≥ 1.10R?
Subtract 1.10R from both sides to get: Is 0.05E ≥ 0?
The answer to this rephrased target question is a definite YES (since we can assume E ≥ 0, which means 0.05E ≥ 0)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent