The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
The value of a collectible comic book increased by \(167\%\) from the end of 2011 to the end of 2012 and then decreased by \(16\%\) from the end of 2012 to the end of 2013. What was the net percentage increase in the value of the collectible comic book from the end of 2011 to the end of 2013?
1. TRANSLATE the problem information
- Given information:
- Comic book value increased by 167% from end 2011 to end 2012
- Value then decreased by 16% from end 2012 to end 2013
- Need: Net percentage change from end 2011 to end 2013
- Let's call the initial value at end 2011: \(\mathrm{x}\) dollars
2. INFER the approach
- Key insight: Percentage changes must be applied sequentially, not just subtracted (167% - 16%)
- We need to calculate the actual value after each change, then find the overall percentage change
- Strategy: Track the value through each year, then compare final to initial
3. Calculate the value at end of 2012
- TRANSLATE: "Increased by 167%" means the new value = original + 167% of original
- End 2012 value = \(\mathrm{x + 1.67x = 2.67x}\) dollars
4. Calculate the value at end of 2013
- TRANSLATE: "Decreased by 16%" means subtract 16% of the 2012 value
- End 2013 value = \(\mathrm{2.67x - 0.16(2.67x) = 2.67x(1 - 0.16) = 2.67x(0.84)}\)
- SIMPLIFY: \(\mathrm{2.67 \times 0.84 = 2.2428x}\) dollars (use calculator)
5. Find the net percentage increase
- Net change = Final value - Initial value = \(\mathrm{2.2428x - x = 1.2428x}\)
- Net percentage increase = \(\mathrm{(1.2428x ÷ x) \times 100\% = 124.28\%}\)
Answer: A. 124.28%
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students think they can simply subtract the percentages: \(\mathrm{167\% - 16\% = 151\%}\)
They miss that the 16% decrease applies to the already-increased 2012 value, not the original 2011 value. Since 151% appears as Choice C, this misconception leads directly to a wrong answer.
This may lead them to select Choice C (151.00%)
Second Most Common Error:
Poor TRANSLATE reasoning: Students misread "decreased by 16%" as "increased by 16%" due to rushing or anxiety
When they calculate \(\mathrm{(2.67x)(1.16) = 3.0972x}\), they get a net increase of 209.72%, which matches exactly with the wrong calculation described in the solution explanation.
This may lead them to select Choice D (209.72%)
The Bottom Line:
This problem tests whether students understand that sequential percentage changes compound - the second percentage applies to the result of the first change, not the original amount. Many students want to treat percentages like simple addition/subtraction, which works for some problems but fails here.