Number system: practice set 4

What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?

A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A − B is a multiple of 27, where A > B, how many such different A’s are possible?

Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4?

Consider a set of 11 numbers:

1. Value-I: Minimum value of the average of the numbers of the set when they are consecutive integers ≥ −5.
2. Value-II: Minimum value of the product of the numbers of the set when they are consecutive non-negative integers.

Which one of the following is correct?

421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?

If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?

A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?

40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again?

The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?

If

15 × 14 × 13 × ··· × 3 × 2 × 1 = 3ᵐ × n

where m and n are positive integers, then what is the maximum value of m?

Consider the following addition problem:

3P + 4P + PP + PP = RQ2; where P, Q and R are different digits.

What is the arithmetic mean of all such possible sums?

Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?

For what value of n, the sum of digits in the number (10ⁿ + 1) is 2?

Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next?

Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. The only possible value of B is

If x − y = 8, then which of the following must be true?

1. 1.Both x and y must be positive for any value of x and y.
2. 2.If x is positive, y must be negative for any value of x and y.
3. 3.If x is negative, y must be positive for any value of x and y.

Select the correct answer using the code given below.

What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150?