R.D. Sharma solutions for Mathematics [English] Class 8 chapter 5 - Playing with Numbers [Latest edition]

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.

Given that the number \[\overline{{35\alpha64}}\] is divisible by 3, where α is a digit, what are the possible values of α?

If x is a digit such that the number \[\overline{{18x71}}\] is divisible by 3, find possible values of x.

If x is a digit of the number \[\overline {{66784x}}\] such that it is divisible by 9, find possible values of x.

Given that the number \[\overline{{67y19}}\] is divisible by 9, where y is a digit, what are the possible values of y?

If \[\overline{{3x2}}\] is a multiple of 11, where x is a digit, what is the value of x?

If \[\overline{{98215x2}}\] is a number with x as its tens digit such that is is divisible by 4. Find all possible values of x.

If x denotes the digit at hundreds place of the number \[\overline{{67x19}}\] such that the number is divisible by 11. Find all possible values of x.

Given an example of a number which is divisible by 2 but not by 4.

Given an example of a number which is divisible by  3 but not by 6.

Given an example of a number which is divisible by 4 but not by 8.

Given an example of a number which is divisible by both 4 and 8 but not by 32.

Which of the following statement is true?
If a number is divisible by 3, it must be divisible by 9.

Which of the following statement is true?
If a number is divisible by 9, it must be divisible by 3.

Which of the following statement is true?
If a number is divisible by 4, it must be divisible by 8.

Which of the following statement is true?
If a number is divisible by 8, it must be divisible by 4.

Which of the following statement is true?
A number is divisible by 18, if it is divisible by both 3 and 6.

Which of the following statement is true?
If a number is divisible by both 9 and 10, it must be divisible by 90.

Which of the following statement is true?
If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

Which of the following statement is true?
If a number divides three numbers exactly, it must divide their sum exactly.

Which of the following statement is true?
If two numbers are co-prime, at least one of them must be a prime number.

Which of the following statement is true?
The sum of two consecutive odd numbers is always divisible by 4.

Solve each of the following Cryptarithms:

  3 7
+ A B
  9 A

Solve each of the following Cryptarithm:

 A B
+3 7
 9 A

Solve each of the following Cryptarithm:

  A 1
+ 1 B
  B 0

Solve each of the following Cryptarithm:

  2 A B
+ A B 1
  B 1 8

Solve each of the following Cryptarithm:

  1 2 A
+ 6 A B
  A 0 9

Solve each of the following Cryptarithm:

  A B 7
+ 7 A B
  9 8 A

Show that the Cryptarithm