If \(a, b,\) and \(c\) are positive integers such that \(a < b < c,\) is \(a\%\) of \(b\%\) of \(c\) an integer?

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If \(a, b,\) and \(c\) are positive integers such that \(a < b < c,\) is \(a\%\) of \(b\%\) of \(c\) an integer?

(1) \(b = \left(\dfrac{a}{100}\right)^{-1}\)

(2) \(c = 100^b\)

Answer: B

Source: Manhattan GMAT
Source: — Data Sufficiency |