CAT (QA) PYQs

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is

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 traveled a total of $26862 \mathrm{~km}$ till then, this number again being palindromic. If Brishti never drove at more than $110 \mathrm{~km} / \mathrm{hr}$, then the greatest possible average speed at which she drove during the trip, in km/hr, was

For some natural number $n$, assume that $(15000)!$ is divisible by $(n!)!$. The largest possible value of $n$ is