Question:
If \( |r - 6| = 11 \) and \( |2q - 12| = 8 \), then what could be the minimum possible value of \( q / r \)?
If \( |r - 6| = 11 \) and \( |2q - 12| = 8 \), then what could be the minimum possible value of \( q / r \)?
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When solving absolute value equations, consider both positive and negative cases for each variable.
Updated On: Aug 5, 2025
- -2/5
- 2/17
- 3/14
- None of these
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The Correct Option is A
Solution and Explanation
We solve for \( r \) and \( q \) using the absolute value equations:
\[
r - 6 = \pm 11 \quad \Rightarrow \quad r = 17 \text{ or } r = -5
\]
\[
2q - 12 = \pm 8 \quad \Rightarrow \quad q = 10 \text{ or } q = 2
\]
Now, we calculate \( q / r \) for each possible pair of \( q \) and \( r \), and find the minimum value to be \( -2/5 \).
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