$$x-y>\frac{\left(x+y\right)}{2}$$
$$2\left(x-y\right)>x+y$$ $$2x-2y>x+y$$
$$2x>x+y+2y$$ $$2x-x>y+2y$$ $$Is\ x>3y\ \ \ \ ?$$
Statement 1
$$y<x$$ $$This\ means\ \ x\ >y$$ $$But\ it\ doesnt\ infer\ that\ \ x>3y$$
because, if x = 2 and y = 1 then x < 3y but if x=5 and y = 1 then x > 3y then x - y is NOT SUFFICIENT.
Statement 2
$$x<2y$$
If x is less than 2y then x must be less than 3y
$$x<2y<3y\ \sin ce\ x<3y\ $$ $$then,\ x-y<\frac{\left(x+y\right)}{2}$$
Statement 2 alone is SUFFICIENT.
$$Answer\ is\ OPTION\ B$$
If \(x\) and \(y\) are positive integers, is \(x - y > \dfrac{x+y}2?\)
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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