The positive number a is 230 % of the number b , and a is 60 % of the number

Question

The positive number a is 230 % of the number b , and a is 60 % of the number c . If c is p % of b , which of the following is closest to the value of p ?

Accepted Answer

Choice D is correct. It's given that a is 230 % of b . It follows that a = 230 100 b . It's also given that a is 60 % of c . It follows that a = 60 100 c . Since a = 230 100 b and a = 60 100 c , it follows that 230 100 b = 60 100 c . Multiplying each side of this equation by 100 60 yields 23 6 b = c . If c is p % of b , then c = p 100 b . It follows that 23 6 = p 100 . Multiplying each side of this equation by 100 yields 2,300 6 = p . It follows that the value of p is approximately 383.33 . Therefore, of the given choices, 383 is closest to the value of p . Choice A is incorrect. This is closest to the value of p if b is 230 % of a , rather than if a is 230 % of b , and if b is p % of c , rather than if c is p % of b . Choice B is incorrect. This is closest to the value of p if a is 230 % greater than b , rather than 230 % of b . Choice C is incorrect. This is closest to the value of p if c is p % greater than b , rather than p % of b .

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