Without performing actual addition and division write the quotient when the sum of 69 and 96 is divided by

(i) 11 (ii) 15

Without performing actual computations, find the quotient when 94-49 is divided by

(i) 9 (ii) 5

If sum of the number 985 and two other numbers obtained by arranging the digits of 985 in cyclic order is divided by 111,22 and 37 respectively. Find the quotient in each case.

Find the quotient when the difference of 985 and 958 is divided by 9.

Given that the number is divisible by 3, where a is a digit, what are the possible values of a?

If x is a digit such that the number is divisible by 3, find possible values of x.

If x is a digit of the number such that it is divisible by 9, find possible values of x.

Given that the number is divisible by 9, where y is a digit, what are the possible values of y?

If is a multiple of 11, where x is a digit, what is the value of x?

If is a number with x as its tens digit such that it is divisible by 4. Find all possible values of x.

If x denotes the digit at hundreds place of the number such that the number is divisible by 11. Find all possible values of x.

Find the remainder when 981547 is divided by 5. Do that without doing actual division.

Find the remainder when 51439786 is divided by 3. Do that without performing actual division.

Find the remainder, without performing actual division, when 798 is divided by 11.

Without performing actual division, find the remainder when 928174653 is divided by 11.

Given an example of a number which is divisible by

1) 2 but not by 4.

2) 3 but not by 6.

3) 4 but not by 8.

4) both 4 and 8 but not by 32

Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.

(ii) If a number is divisible by 9, it must by divisible by 3.

(iii) If a number is divisible by 4, it must by divisible by 8.

(iv) If a number is divisible by 8, it must be divisible by 4.

(v) A number is divisible by 18, if it is divisible by both 3 and 6.

(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.

(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

(viii) If a number divides three numbers exactly, it must divide their sum exactly.

(ix) If two number are co-prime, at least one of them must be a prime number.

(x) The sum of two consecutive odd numbers is always divisible by 4.

Solved each of the following Cryptarithms:

Solved each of the following Cryptarithms:

Solved each of the following Cryptarithms:

Solved each of the following Cryptarithms:

Solved each of the following Cryptarithms:

Solved each of the following Cryptarithms:

Show that the Crptarithm does not have any solution.