Test 12
1.
\(a,b,c\in\mathbb{Z}\)
\(\left.\begin{aligned}a\cdot b=20\\b\cdot c=12\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(-33\)B) \(-32\)C) \(0\)D) \(12\)E) \(33\)
2.
\(a,b,c\in\mathbb{Z}^{+}\)
\(\left.\begin{aligned}2\cdot a=3\cdot b\\5\cdot b=6\cdot c\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(11\)B) \(13\)C) \(16\)D) \(18\)E) \(20\)
3.
\(a,b,c\in\mathbb{Z}^{+}\)
\(\left.\begin{aligned}2\cdot a=3\cdot b\\2\cdot b=5\cdot c\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(24\)B) \(29\)C) \(32\)D) \(36\)E) \(39\)
4.
\(a,b,c\in\mathbb{Z}^{+}\)
\(\left.\begin{aligned}4\cdot a=5\cdot b\\3\cdot b=6\cdot c\end{aligned}\right\}\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(1\)B) \(8\)C) \(11\)D) \(14\)E) \(31\)
5.
\(a,b,c\in\mathbb{Z}^{-}\)
\(12\cdot a=20\cdot b=24\cdot c\)
\(\Rightarrow \max(a+b+c)=?\)
A) \(-21\)B) \(-20\)C) \(-14\)D) \(-11\)E) \(-1\)
6.
\(a,b,c\in\mathbb{Z}^{+}\)
\(20\cdot a=36\cdot b=35\cdot c\)
\(\Rightarrow \min(a+b+c)=?\)
A) \(136\)B) \(134\)C) \(130\)D) \(128\)E) \(120\)
7.
\(a,b,c\in\mathbb{Z}^{-}\)
\(12\cdot a=16\cdot b=18\cdot c\)
\(\Rightarrow \max(a+b+c)=?\)
A) \(-21\)B) \(-25\)C) \(-27\)D) \(-29\)E) \(-32\)
8.
\(A,x,y,z\in\mathbb{Z}^{+}\)
\(A=5\cdot x+4=7\cdot y+6=8\cdot z+7\)
\(\Rightarrow \min(A)=?\)
A) \(274\)B) \(276\)C) \(278\)D) \(279\)E) \(281\)