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GRE Quantitative Reasoning QUESTION #8113
Question 1

A cake recipe requires a round pan that is 8 inches in diameter. If someone wants to make a cake of the same depth but using a pan that is 12 inches in diameter instead, by what factor should the recipe ingredients be multiplied?

  • $2\dfrac{1}{2}$
  • $2\dfrac{1}{4}$✔️
  • $1\dfrac{1}{2}$
  • $1\dfrac{4}{9}$
Correct Answer Explanation

The volume of a cake (same depth) is proportional to the area of the base, which is proportional to the square of the diameter (or radius).

Factor $= \left(\dfrac{12}{8}\right)^2 = \left(\dfrac{3}{2}\right)^2 = \dfrac{9}{4} = 2\dfrac{1}{4}$

The recipe ingredients should be multiplied by $2\dfrac{1}{4}$.