List of top Quantitative Aptitude Questions on Number Theory asked in IBSAT

What is the difference between the sum of the cubes and that of the sum of the square of first twenty natural numbers?
If 'y' is a number such that \( y = x^{x/2} \), where x is a positive integer, what is the difference between the largest possible four-digit value of y and the smallest possible three-digit value of y?
'abcd' is a four-digit number. It has only two factors excluding 1 and itself. In addition, the first two digits form a perfect square and the next two digits form a number which is one more than a perfect square. Which of the following could be the number?
Harsha received price money in a jackpot. He expressed the price money in the following way. Consider a number 'N' that can be expressed in the form of prime factors 3, 5, 7 and 11. The total number of factors of N is 32. The difference between the largest and the smallest such number possible, given that each of these prime factors occur at least once, is the price money that Harsha won. What is the price money that Harsha won in the jackpot?
What is the remainder obtained when the smallest prime number, when raised to the ninety second multiple of sixteen, is divided by two hundred and fifty seven?
On a cardboard there are 32 squares. 1 coin is kept on the first box, 2 coins on the second box and so on. Collect all the coins and add some more coins to them. These coins are equally distributed on all the squares of the cardboard. What is the minimum number of coins that are added?