Test 11
1.
\(a,b,c\in\mathbb{Z}^{+}\)
\(\left.\begin{aligned}2\cdot a=3\cdot b\\2\cdot b=5\cdot c\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(24\)B) \(29\)C) \(32\)D) \(36\)E) \(39\)
2.
\(a,b\in\mathbb{Z}^{+}\)
\(a^2-b^2=17\)
\(\Rightarrow a\cdot b=?\)
A) \(17\)B) \(20\)C) \(36\)D) \(45\)E) \(72\)
3.
\(a,b\in\mathbb{Z}^{+}\)
\((a+2b)\cdot(a-b)=19\)
\(\Rightarrow a\cdot b=?\)
A) \(42\)B) \(35\)C) \(30\)D) \(28\)E) \(24\)
4.
\(a,b\in\mathbb{Z}^{+}\)
\(a^2-4b^2=13\)
\(\Rightarrow a\cdot b=?\)
A) \(42\)B) \(21\)C) \(18\)D) \(13\)E) \(6\)
5.
\(a,b,c,d\in\mathbb{Z}^{+}\)
\(a\ne b\ne c\ne d\)
\(a\cdot b\cdot c\cdot d=273\)
\(\Rightarrow a+b+c+d=?\)
A) \(20\)B) \(21\)C) \(22\)D) \(23\)E) \(24\)
6.
\(a,b,c\in\mathbb{Z}^{+}\)
\(\left.\begin{aligned}a\cdot b=21\\b\cdot c=14\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(6\)B) \(10\)C) \(12\)D) \(19\)E) \(35\)
7.
\(a,b,c\in\mathbb{Z}^{-}\)
\(\left.\begin{aligned}a\cdot b=20\\b\cdot c=12\end{aligned}\right\}\)
\(\Rightarrow \max(a+b+c)=?\)
A) \(-33\)B) \(-32\)C) \(-12\)D) \(-1\)E) \(0\)
8.
\(a,b,c\in\mathbb{Z}^{+}\)
\(\left.\begin{aligned}a\cdot b=20\\b\cdot c=12\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(12\)B) \(16\)C) \(18\)D) \(32\)E) \(33\)