Number System T...

Raju had to divide 1080 by N, a two-digit number. Instead, he performed the division using M which is obtained by reversing the digits of N and ended up with a quotient which was 25 less than what he should have obtained otherwise. If 1080 is exactly divisible both by N and M, find the sum of the digits of N.

A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

A teacher wrote a number on the blackboard and the following observations were made by the students. The number is a four-digit number.The sum of the digits equals the product of the digits. The number is divisible by the sum of the digits.The sum of the digits of the number is

The sum of the factorials of the three-digits of a 3-digit number is equal to the three-digit number formed by these three digits, taken in the same order. Which of the following is true of the number of such three-digit numbers, if no digit occurs more than once?

Let S be a two-digit number such that both S and S² end with the same digit and none of the digits in S equals zero. When the digits of S are written in the reverse order, the square of the new number so obtained has the last digit as 6 and is less than 3000. How many values of S are possible?

Let N be a positive integer not equal to 1. Then none of the numbers 2, 3,...., N is a divisor of (N! - 1). Thus, we can conclude that

16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?

What is the least number of soldiers that can be drawn up in troops of 12, 15, 18 and 20 soldiers and also in form of a solid square?

What is the remainder when (10³ + 9³)⁷⁵² is divided by 123?

When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes?

Every element of S1 is made greater than or equal to every element of S2 by adding to each element of SI an integer x. Then, x cannot be less than

The History teacher was referring to a year in the 19th century. Rohan found an easy way to remember the year. He found that the number, when viewed in a mirror, increased 4.5 times. Which year was the teacher referring to?

N is a number which when divided by 10 gives 9 as the remainder, when divided by 9 gives 8 as the remainder, when divided by 8 gives 7 as the remainder, when divided by 7 gives 6 as the remainder, when divided by 6 gives 5 as the remainder, when divided by 5 gives 4 as the remainder, when divided by 4 gives 3 as the remainder, when divided by 3 gives 2 as the remainder, when divided by 2 gives 1 as the remainder.What is N?

How many different four digit numbers are there in the octal (Base 8) system, expressed in that system?

When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

Find the unit digit:
346 ⁷⁶⁵ * 768 ⁹⁸³ * 987 ⁵⁹⁹

If a number when successively divided by 9, 7, and 5 leaves the remainders 8, 5, and 1 respectively. Find the smallest such 4-digit number.

A number when divided by 841 gives a remainder of 87. What will be the remainder when we divide the same number by 29?

A number when divided by 703 gives a remainder of 75. What will be the remainder when we divide the same number by 37?

Find the remainder when a number is divided by 49. The same number when divided by 147 leaves 53 as remainder.