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MathNet 2000 — Math Olympiad Vault Question 112

Math Olympiad Vault · MathNet 2000 — Math Olympiad Vault

Question 112

Let $X=a+7b$, $Y=2a+5b$, and $Z=4a+2b$, where $a,b$ are positive real numbers. Then:
(A) $X\lt Y\lt Z$
(B) $Z\lt Y\lt X$
(C) $Y\lt X\lt Z$
(D) $Y\lt Z\lt X$
(E) The order of $X,Y,Z$ depends on the values of $a,b$.