Test 8
1.
\(x,y\in\mathbb{R}\)
\((x+y)\in\mathbb{Z}\)
\(\left.\begin{aligned}-5<x<-1\\-3<y<9\end{aligned}\right\}\)
\(\Rightarrow \max(x+y)=?\)
A) \(5\)B) \(6\)C) \(7\)D) \(8\)E) \(9\)
2.
\(x,y\in\mathbb{Z}\)
\(\left.\begin{aligned}-3<x<4\\-4<y<5\end{aligned}\right\}\)
\(\Rightarrow \max(3x-y)=?\)
A) \(16\)B) \(12\)C) \(8\)D) \(6\)E) \(2\)
3.
\(x,y\in\mathbb{Z}\)
\(\left.\begin{aligned}-1<x<8\\-5<y<6\end{aligned}\right\}\)
\(\Rightarrow \min(2x-5y)=?\)
A) \(-31\)B) \(-29\)C) \(-28\)D) \(-26\)E) \(-25\)
4.
\(x,y,z\in\mathbb{Z}\)
\(\left.\begin{aligned}-2<x<4\\-1<y<3\\2<z<8\end{aligned}\right\}\)
\(\Rightarrow \max(x-y+z)=?\)
A) \(13\)B) \(12\)C) \(10\)D) \(8\)E) \(6\)
5.
\(x,y\in\mathbb{Z}\)
\(\left.\begin{aligned}-4<x\le4\\-3\le y<5\end{aligned}\right\}\)
\(\Rightarrow \max(x-y)=?\)
A) \(-1\)B) \(0\)C) \(3\)D) \(6\)E) \(7\)
6.
\(x,y\in\mathbb{Z}\)
\(\left.\begin{aligned}-2<x<5\\-7<y<3\end{aligned}\right\}\)
\(\Rightarrow \max(3x-2y)=?\)
A) \(8\)B) \(10\)C) \(18\)D) \(24\)E) \(28\)
7.
\(x,y\in\mathbb{R}\)
\((2x-3y)\in\mathbb{Z}\)
\(\left.\begin{aligned}-7<x<3\\-4<y<5\end{aligned}\right\}\)
\(\Rightarrow \min(2x-3y)=?\)
A) \(-30\)B) \(-28\)C) \(-26\)D) \(-24\)E) \(-22\)
8.
\(x,y\in\mathbb{R}\qquad(2x+3y)\in\mathbb{Z}\)
\(\left.\begin{aligned}-4<x<3\\-2<y<4\end{aligned}\right\}\)
\(\Rightarrow \max(2x+3y)=?\)
A) \(4\)B) \(6\)C) \(12\)D) \(17\)E) \(18\)