CAT 2023 Question Paper | Quant Slot 1

CAT Previous Year Paper | CAT Quant Questions | Question 8

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 8 : 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. 90
  2. 100
  3. 80
  4. 110

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Explanatory Answer

The distance travelled before the trip (x in km.) is a palindrome.
Let the average speed of Brishti be s kmph.
The total distance covered by Brishti after the trip is 26862 km.
The distance covered by Brishti during the trip is 8×s = 8s km.
x = 26862 – 8s
For x to be a palindrome, of the given options, s can only be 100.
Therefore, the average speed of Brishti during the trip is 100 kmph.

The answer is '100'

Choice B is the correct answer.

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