Percents: Ballparking Percents

Donna gets a 10% increase in salary every two years. If her annual salary in 2004 was $121,000, what was her annual salary in 2000?

Incorrect. [[snippet]] This answer choice can be __POE__'d immediately, as the question clearly states that she earned 121,000 in 2004, after two salary increases of 10%.

Incorrect. [[snippet]] Start with the middle choice. If Donna earned 110,000 in 2000, her salary increased by $$10\%\times 110{,}000 = 11{,}000$$ in two years, so she earned $121,000 in 2002. You can stop right here, as the question clearly states that she reached 121,000 in 2004, after another 10% increase in salary. This answer choice is too big, so __POE__ it, as well as D and E, and go check A or B.

Correct. [[snippet]] If Donna earned 100,000 in 2000, her salary increased by $$10\%\times 100{,}000 = 10{,}000$$ in two years, so she earned $110,000 in 2002. In the next two years her salary increased by another $$10\%\times 110{,}000 = 11{,}000$$, so in 2004 she earned $121,000. Hence, this is the correct answer.

Incorrect. [[snippet]] If Donna earned 116,000 in 2000, her salary increased by $$10\%\times 116{,}000 = 11{,}600$$ in two years, so she earned $127,600 in 2002. You can stop right here, as that is already greater than the $121,000 the question states that she earned in 2004. You're looking for a smaller answer choice, so eliminate anything greater than D and go check A, B, or C.

Incorrect. [[snippet]] If Donna earned 95,000 in 2000, her salary increased by $$10\% \times 95{,}000 = 9{,}500$$ in two years, so she earned $104,500 in 2002. In the next two years her salary increased by another $$10\%\times 104{,}500 = 10{,}450$$. No need to calculate her resulting salary in 2004, as the $50 at the end ensures that this answer choice will not equal the required $121,000 set by the question stem. __POE__ A and look for something higher.

$95,000

$100,000

$110,000

$116,000

$121,100