IPMAT Indore Number System > Miscellaneous PYQs

If $a$, $b$, and $c$ are three prime numbers such that $abc = 23(a + b + c)$, then the maximum possible value of $a + b - c$ is

A natural number $n$ lies between $100$ and $400$, and the sum of its digits is $10$. The probability that $n$ is divisible by $4$, is

In a four-digit number, the product of the thousands digit and units digit is zero while their difference is 7. Product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is __________.

The number of pairs of integers whose sums are equal to their products is