KCET · Maths · Basic of Mathematics
If \((24,92)=24 m+92 n\), then \((m, n)\) is
- A \((-1,4)\)
- B \((4,-1)\)
- C \((4,-3)\)
- D \((-4,3)\)
Answer & Solution
Correct Answer
(B) \((4,-1)\)
Step-by-step Solution
Detailed explanation
Since, \(\quad 92=3 \cdot 24+20\)
\(24=1 \cdot 20+4\)
\(20=4 \cdot 5+0\)
\(\therefore \quad(24,92)=4\)
\(=24-1 \cdot 20\)
\(=24-1 \cdot(92-3 \cdot 24)\)
\(=24-92+3 \cdot 24\)
\(=4 \cdot 24-92\)
But \((24,92)=24 m+92 n\)
\(\therefore\) From Eqs. (i) and (ii), we get
\[
\begin{aligned}
\mathrm{m} &=4 \text { and } \mathrm{n}=-1 \\
\therefore \quad(\mathrm{m}, \mathrm{n}) &=(4,-1)
\end{aligned}
\]
\(24=1 \cdot 20+4\)
\(20=4 \cdot 5+0\)
\(\therefore \quad(24,92)=4\)
\(=24-1 \cdot 20\)
\(=24-1 \cdot(92-3 \cdot 24)\)
\(=24-92+3 \cdot 24\)
\(=4 \cdot 24-92\)
But \((24,92)=24 m+92 n\)
\(\therefore\) From Eqs. (i) and (ii), we get
\[
\begin{aligned}
\mathrm{m} &=4 \text { and } \mathrm{n}=-1 \\
\therefore \quad(\mathrm{m}, \mathrm{n}) &=(4,-1)
\end{aligned}
\]
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