Test 7
1.
\(a\cdot b>0\)
\(a<b\)
Which of the followings is true?
A) \(\samefrac{1}{a}<\samefrac{1}{b}\)B) \(\samefrac{1}{a}>\samefrac{1}{b}\)C) \(a+b>0\)D) \(a+b<0\)E) \(\samefrac{a}{b}<0\)
2.
\(\samefrac{x}{2}-\samefrac{x-1}{3}<\samefrac{x}{5}\)
\(x\in\mathbb{Z}\)
\(\Rightarrow\min(x)=?\)
A) \(9\)B) \(10\)C) \(11\)D) \(12\)E) \(13\)
3.
\(x\in\mathbb{R}\)
\(-7<x<-2\)
\(\Rightarrow ?<x^2<?\)
A) \(0<x^2<49\)B) \(0<x^2<4\)C) \(4<x^2<49\)D) \(2<x^2<7\)E) \(14<x^2<21\)
4.
\(x\in\mathbb{R}\)
\(-3<x<5\)
\(\Rightarrow ?<x^2<?\)
A) \(9<x^2<25\)B) \(0<x^2<9\)C) \(0\le x^2<25\)D) \(3<x^2<5\)E) \(9\le x^2<25\)
5.
\(x\in\mathbb{R}\)
\(-9<x<4\)
\(\Rightarrow ?<x^2<?\)
A) \(16<x^2<81\)B) \(0\le x^2<16\)C) \(0\le x^2<81\)D) \(4<x^2<9\)E) \(0\le x^2<9\)
6.
\(x,y\in\mathbb{R}\)
\(\left.\begin{aligned}-7<x<5\\-3<y<8\end{aligned}\right\}\)
\(\Rightarrow ?<x\cdot y<?\)
A) \(21<x\cdot y<40\)B) \(-15<x\cdot y<21\)C) \(-56<x\cdot y<40\)D) \(-56<x\cdot y<21\)E) \(-15<x\cdot y<40\)
7.
\(x,y\in\mathbb{R}\)
\(\left.\begin{aligned}-4<x<3\\-7<y<4\end{aligned}\right\}\)
\(\Rightarrow ?<x\cdot y<?\)
A) \(12<x\cdot y<28\)B) \(-12<x\cdot y<28\)C) \(-28<x\cdot y<28\)D) \(-21<x\cdot y<28\)E) \(0<x\cdot y<28\)
8.
\(x,y\in\mathbb{Z}\)
\(\left.\begin{aligned}-5<x<-1\\-3<y<9\end{aligned}\right\}\)
\(\Rightarrow \max(x+y)=?\)
A) \(5\)B) \(6\)C) \(7\)D) \(8\)E) \(9\)