# CAT 2006 | Question: 57

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What are the values of $x$ and $y$ that satisfy both the equations?

• $2^{0.7x} \cdot 3^{-1.25y} = 8\sqrt{6} / 27$
• $4^{0.3x} \cdot 9^{0.2y} = 8.(81)^{\frac{1}{5}}$
1. $x=2, y=5$
2. $x=2.5, y=6$
3. $x=3, y=5$
4. $x=3, y=4$
5. $x=5, y=2$

The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:$7$$13$$14$$18$$20$
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