MBApyq

Absolute Value Equations: Minimum Ratio

CAT 1999 Slot 1 · Quantitative Ability · Easy · Algebra

This is an easy Quantitative Ability question from the CAT 1999 Slot 1 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 1999 Slot 1 questionsMore Algebra questionsAll CAT QA

If ∣r−6∣=11|r - 6| = 11 and ∣2q−12∣=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

∣r−6∣=11  ⟹  r−6=11 or −11  ⟹  r=17 or −5|r - 6| = 11 \implies r - 6 = 11 \text{ or } -11 \implies r = 17 \text{ or } -5. ∣2q−12∣=8  ⟹  2q−12=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}: 1017,217,10−5=−2,2−5=−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'.

Related Algebra questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace