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?

1. 102%
2. 105%
3. 120%
4. 135%
5. 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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