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If a% of a + b% of b = 2% of ab, then what percent of a is b?

b is 100% of a. The condition reads \(\frac{a^{2}}{100} + \frac{b^{2}}{100}\) \(= \frac{2ab}{100}\), so \(a^{2} - 2ab + b^{2} = 0\), i.e. \((a - b)^{2} = 0\) and a = b. A…

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If a% of a + b% of b = 2% of ab, then what percent of a is b?

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Correct answer D

b is 100% of a. The condition reads a2100+b2100\frac{a^{2}}{100} + \frac{b^{2}}{100} =2ab100= \frac{2ab}{100}, so a2−2ab+b2=0a^{2} - 2ab + b^{2} = 0, i.e. (a−b)2=0(a - b)^{2} = 0 and a = b. A number equal to a is 100% of a, so 25%, 50% and 75% are all impossible here.

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