Time, Speed and Distance Question 3 - CAT 2023
Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x 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 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was:
Step-by-Step Explanation
Establish bounds using the options:
The final odometer reading is 26862 km. The trip lasted 8 hours.
Distance Covered = 8 × Average Speed (s)
The initial reading x = 26862 − 8s must be a palindrome. We are looking for the greatest possible average speed where s ≤ 110 km/h.
Test the maximum available choice:
Try Option A (s = 110 km/h):
Distance = 8 × 110 = 880 km
x = 26862 − 880 = 25982 (Not a palindrome)
Try Option C (s = 100 km/h):
Distance = 8 × 100 = 800 km
x = 26862 − 800 = 26062 (This is a palindrome!)
Since 100 km/h satisfies all constraints and is the largest remaining option, it is the correct answer.
Correct Option: C
💡 FundaMakers Tip:
For optimization problems with explicit numerical choices, always test the options starting from the most extreme condition requested. Because the problem asks for the greatest possible speed, checking 110 first and then 100 ensures you locate the maximum bound immediately without needing to test smaller numbers like 90 or 80.