Question:

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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