Absolute Value Equations: Minimum Ratio

CAT 1999 Slot 1 · QA · Easy · Algebra

If r6=11|r - 6| = 11 and 2q12=8|2q - 12| = 8, what is the minimum possible value of qr\frac{q}{r}?

  1. A.

    -2/5

  2. B.

    2/17

  3. C.

    10/17

  4. D.

    None of these

Answer

D

Explanation

r6=11    r6=11 or 11    r=17 or 5|r - 6| = 11 \implies r - 6 = 11 \text{ or } -11 \implies r = 17 \text{ or } -5. 2q12=8    2q12=8 or 8    2q=20 or 4    q=10 or 2|2q - 12| = 8 \implies 2q - 12 = 8 \text{ or } -8 \implies 2q = 20 \text{ or } 4 \implies q = 10 \text{ or } 2. Possible values of qr\frac{q}{r}: 1017,217,105=2,25=0.4\frac{10}{17}, \frac{2}{17}, \frac{10}{-5} = -2, \frac{2}{-5} = -0.4. The minimum possible value is 2-2. Since 2-2 is not among options A, B, C, the answer is 'None of these'.

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