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Official 2018 Paper 2 · Q19

Paper 2Logic & proof

Three real numbers xx, yy and zz satisfy x>y>z>1x>y>z>1.

Which one of the following statements must be true?

A2z+12x>2x+2z2y\frac{2^{z+1}}{2^x}>\frac{2^x+2^z}{2^y}
B2>3x+3z3y2>\frac{3^x+3^z}{3^y}
C2×5x5z>5x+5z5y\frac{2\times5^x}{5^z}>\frac{5^x+5^z}{5^y}
D2<7x+7z7y2<\frac{7^x+7^z}{7^y}

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