Page 72 - ICSE Math 8

AT A GLANCE

¾ A 2-digit number ab can be expressed in generalized form as 10a + b.
¾ The sum of a 2-digit number ab and the number obtained by reversing the digits, when divided by
(a) a + b gives quotient as 11. (b) 11 gives quotient as a + b.
¾ If ab is a 2-digit number, then ab – ba, when divided by
(a) a – b gives remainder as 9. (b) 9 gives remainder as a – b.

¾ A 3-digit number abc can be expressed in generalized form as 100a + 10b + c.
¾ For a 3-digit number abc, abc + bca + cab equals 111 (a + b + c) or 3 × 37 × (a + b + c).
¾ For a 3-digit number abc, abc – cba = 99 × (a – c) or 9 × 11 × (a – c).
¾ A number is divisible by 2 if its ones digit has 0, 2, 4, 6 or 8.

¾ A number is divisible by 3 if the sum of its digits is divisible by 3.
¾ A number is divisible by 4 if the number formed by the tens and ones digits is divisible by 4 or the digits
at tens and ones place are both 0.

¾ A number is divisible by 5 if the ones digit of the number is either 0 or 5.
¾ A number is divisible by 6 if it is divisible by both 2 and 3.
¾ A number is divisible by 9 if the sum of its digits is divisible by 9.
¾ A number is divisible by 10 if the digits at its ones place is 0.
¾ A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of
its digits at even places is either 0 or a multiple of 11.

MENTAL MATHS

1. Choose the correct option.
(a) If A × C × AC = CCC, where A and C are different digits, then the values of A and C are:
(i) A = 3, C = 7 (ii) A = 7, C = 3
(iii) A = 4, C = 7 (iv) A = 7, C = 4
(b) If * and o are two operations such that a * b = a × b + 2 and a o b = a + b – 1, then the value of
{(3 * 3)*3} o 3 is:
(i) 35 (ii) 37 (iii) 38 (iv) 39
(c) If abc is a 3-digit number, then abc – cba when divided by 99 will give quotient as:
(i) a – c (ii) a + b (iii) b + c (iv) b – c

(d) If abc is a 3-digit number, then abc + bca + cab when divided by 37 will give quotient as:
(i) a + b + c (ii) 111 (iii) 3(a + b + c) (iv) a – b – c
(e) For a 2-digit number ab, ab – ba when divided by a – b, gives quotient as:
(i) 111 (ii) 99 (iii) 11 (iv) 9
2. Write True or False.
(a) If a number is divisible by 2, then it must be divisible by 4.
(b) The least value of (x + y) if 4xy7 is exactly divisible by 3 is 1.
(c) The sum of a 2-digit number and its reversing number is always a multiple of 9.

(d) If x5y4z is exactly divisible by 9, then the least value of x + y + z is 6.
(e) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

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