Question: The price of a certain painting increased by 20% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price?
- 102%
- 105%
- 120%
- 135%
- 140%
Correct Answer: A
Solution and Explanation:
Approach Solution 1:
Let the initial price = 100 $
Price after 1st year = 120 (20% increase)
Price after 2nd year = 15% decrease
= 120 - 15/100*120 = 102 $
= 102%
Approach Solution 2:
Let’s assume the original price of the painting was $100. At the end of the first year, after the 20% increase, it was worth $120. At the end of the second year, after a 15% drop, it was worth $102. Thus, the price of the painting at the end was 102/100 x 100% = 102% of the original price.
Approach Solution 3:
Given:
- The price of a certain painting,
- Increased by 20% during the first year
- And decreased by 15% during the second year.
To find:
- The price of the painting at the end of the 2-year period was what percent of the original price
Approach and Working Out:
- Let the initial price of the painting be x
- Price at the end of first year = x + 20% of x = 1.2x
- Price at the end of second year = 1.2x – 15% of 1.2x = 1.2x – 0.15 * 1.2x = 1.02x = 102 % of x
Therefore, the price of the painting at the end of the 2-year period was 102% percent of the original price.
“The price of a certain painting increased by 20% during the first year”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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