This CAT-level Future Year Question tests percentage change and the effect of independent linear percentage changes on a quantity.
The question requires you to carefully account for two opposing effects on the same economic index and determine their combined impact.
Studies suggest that a 1% increase in the income share of a country's top 10% earners causes a certain economic index Z to fall by 0.15%, while a 1% increase in the income share of the bottom 10% earners causes Z to rise by 0.45% (these effects are independent and linear). In a given year, the top 10%'s income share falls by 4% while the bottom 10%'s income share rises by 6%. Find the net percentage change in Z.
A. 2.7%
B. 3.9%
C. 3.3%
D. 3.0%
Before watching the solution, identify the effect of each change separately.
Remember that a fall in the top 10%'s income share produces the opposite effect on Z from an increase in that share.
Then combine the two independent effects.
The primary concept tested is Percentages, specifically percentage change and combining independent linear effects.
The question also tests:
This question belongs to:
Quantitative Aptitude → Arithmetic → Percentages
Calculate the change in Z caused by the change in the top 10%'s income share separately.
Then calculate the change caused by the bottom 10%'s income share separately.
Pay close attention to the direction of each change.
Since the effects are explicitly stated to be independent and linear, combine the two resulting changes to obtain the net percentage change.
A common CAT trap is getting the sign of a percentage effect wrong.
Here, an increase in the top 10%'s income share causes Z to fall. Therefore, a decrease in that income share produces the opposite effect on Z.
Similarly, an increase in the bottom 10%'s income share causes Z to rise.
The key skill is translating the direction of each change correctly before combining the effects.
Difficulty: Easy
The mathematical operations are straightforward. The main challenge is correctly interpreting the direction and magnitude of the two independent effects and combining them without making a sign error.
Have you solved it?
Watch the complete video solution for the step-by-step approach and final answer.
https://www.youtube.com/watch?v=LMEo5wsJobM
The primary concept tested is percentage change, particularly combining independent linear percentage effects.
This question belongs to CAT Quantitative Aptitude, specifically the Arithmetic → Percentages area.
The key challenge is correctly identifying the direction of each effect. A decrease in a variable that negatively affects Z produces a positive effect on Z.
When the question explicitly states that the effects are independent and linear, calculate each effect separately and then combine the resulting changes with their appropriate signs.
This is an Easy difficulty CAT-level Future Year Question. The calculation is simple, but careful interpretation of positive and negative effects is required.