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Difficulty 2.0 Junior Find the answer
In the expression x y 2 xy^2 x y 2 x x x y y y 25 25 25 (A) decreased 50 % \textbf{(A)}\ \text{decreased } 50\% (A) decreased 50% (B) decreased 75 % (C) decreased 37 64 of its value \textbf{(B)}\ \text{decreased }75\%\\ \textbf{(C)}\ \text{decreased }\frac{37}{64}\text{ of its value} (B) decreased 75% (C) decreased 64 37 of its value (D) decreased 27 64 of its value (E) none of these \textbf{(D)}\ \text{decreased }\frac{27}{64}\text{ of its value}\\ \textbf{(E)}\ \text{none of these} (D) decreased 64 27 of its value (E) none of these
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Solution x y 2 xy^2 x y 2 ( 3 4 x ) ( 3 4 y ) 2 (\frac{3}{4}x)(\frac{3}{4}y)^2 ( 4 3 x ) ( 4 3 y ) 2 ( 3 4 ) 3 x y 2 (\frac{3}{4})^3xy^2 ( 4 3 ) 3 x y 2 27 64 x y 2 \frac{27}{64}xy^2 64 27 x y 2 x y 2 − 27 64 x y 2 = 37 64 x y 2 ⟹ (C) xy^2-\frac{27}{64}xy^2 = \frac{37}{64}xy^2 \implies \textbf{(C)} x y 2 − 64 27 x y 2 = 64 37 x y 2 ⟹ (C)
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