CAT 2023 Slot 1 QA Q8 Time, Speed & Distance

Question 8 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.

Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of \(x \mathrm{~km}\) till then, where \(x\) is a whole number and is palindromic, i.e., \(x\) remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of \(26862 \mathrm{~km}\) till then, this number again being palindromic. If Brishti never drove at more than \(110 \mathrm{~km} / \mathrm{h}\), then the greatest possible average speed at which she drove during the trip, in \(\mathrm{km} / \mathrm{h}\), was
  1. A
    90
  2. B
    100
  3. C
    80
  4. D
    110

Answer: (B) 100 Time, Speed & Distance MCQ

Solution

  1. In 8 hours at most \(110\) km/h she covers at most 880 km, so \(x \ge 26862 - 880 = 25982\).
  2. Palindromes just below 26862 are 26762, 26662, ..., 26062 (form \(26a62\)), then 25952, which is 910 km away (too far).
  3. The largest feasible distance is \(26862 - 26062 = 800\) km.
  4. Greatest average speed \(= \frac{800}{8} = 100\) km/h.

More Time, Speed & Distance questions from CAT

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