If the diameter of a circle increases by 50 percent, by what percent GMAT Problem Solving

Question: If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?

  • 25%
  • 50%
  • 100%
  • 125%
  • 225%

Approach Solution (1)

If the diameter of a circle increases by 50 percent, the radius also increases by 50 percent. If we let the original radius = 10, the new radius = 15. Thus, we have:
Area of the original circle = 102 * π = 100π
Area of the new circle = 152 * π = 225π
We use the percent change formula: (New - Old) / Old * 100. Therefore, the area of the circle increases by
(225π - 100π) / (100π) x 100 = 125 π / π = 125 percent
Correct option:
D

Approach Solution (2)

If the diameter increases by 50%, then radius will also increase by 50%
The area will remain the same.
Therefore, Area = π * (r2)
Let the radius increases from 10 to 15
Then, the area would increase from 100π to 225π
Therefore, there will be an increase of 125%
Correct option:
D

Approach Solution (3)

Let the original number be 100%
Successive percentage = a% + b% + (ab/100)%
50% + 50% + (50*50/100)%
= 100% + 25%
= 125%
Correct option:
D

“If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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