Question

Given the condition $\frac{5}{6}<\frac{1}{2}x-\frac{1}{2}y<\frac{3}{2}$, find one possible value of $x-y$?

• A. $\frac{5}{3}<x-y<3$
• B. $\frac{2}{3}<x-y<3$
• C. $\frac{4}{3}<x-y<2$
• D. $\frac{5}{3}<x-y<6$

Answer 1

Answer: (A)

$\frac{5}{3}<x-y<3$

Given, $\frac{5}{6}<\frac{1}{2}x-\frac{1}{2}y<\frac{3}{2}$

Multiply all sides by $2$, we get

$\frac{5}{6}\times 2<(\frac{1}{2}x-\frac{1}{2}y)\times 2<\frac{3}{2}\times 2$

$\Rightarrow \frac{5}{3}<x-y<3$