Chapter 13: Playing With Numbers

1:Generalised form of a three-digit number xyz is
(a)x + y + z(b)100x + 10y + z
(c) 100z + 10y + x (d) 100y + 10x + z
Ans: (b).
2:The usual form of 100a + b + 10c is
(a)abc(b)cab(c)bac(d)acb
Ans: (d).
3:If 5 × A = CA then the values of A and C are

(a)A = 5, C = 1(b)A = 4, C = 2
(c)A = 5, C = 2(d)A = 2, C = 5
Ans: (c).
4:If 5 A + 25 is equal to B 2, then the value of A + B is
(a)15(b)10(c)8(d)7
Ans: (a).

1.Generalised form of a four-digit number abdc is
(a)1000 a + 100 b + 10 c + d
(b)1000 a + 100 c + 10 b + d
(c)1000 a + 100 b + 10 d + c
(d)a × b × c × d

2.Generalised form of a two-digit number xy is
(a) x + y(b) 10x + y(c) 10x – y(d) 10y + x
3.The usual form of 1000a + 10b + c is
(a) abc(b) abco(c) aobc(d) aboc
4.Let abc be a three-digit number. Then abc – cba is not divisible by
(a) 9(b) 11(c) 18(d) 33
5.The sum of all the numbers formed by the digits x, y and z of the number xyz is divisible by
(a) 11(b) 33(c) 37(d) 74
6.A four-digit number aabb is divisible by 55. Then possible value(s) of b is/are
(a) 0 and 2(b) 2 and 5(c) 0 and 5(d) 7
7.Let abc be a three digit number. Then abc + bca + cab is not divisible by
(a) a + b + c(b) 3(c) 37(d) 9
8.A four-digit number 4ab5 is divisible by 55. Then the value of b – a is
(a)0(b) 1(c) 4(d) 5
9.If abc is a three digit number, then the number abc – a – b – c is divisible by
(a) 9(b) 90(c) 10(d) 11
10.A six-digit number is formed by repeating a three-digit number. For example 256256, 678678, etc. Any number of this form is divisible by
(a) 7 only(b) 11 only(c) 13 only(d) 1001
11.If the sum of digits of a number is divisible by three, then the number is always divisible by
(a)2(b) 3(c) 6(d) 9
12.If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is
(a) an odd multiple of 3(b) odd multiple of 6
(c) even multiple of 3(d) even multiple of 9

13.If 5 A + B 3 = 65, then the value of A and B is
(a)A = 2, B = 3(b)A = 3, B = 2
(c)A = 2, B = 1(d)A = 1, B = 2
14.If A 3 + 8 B = 150, then the value of A + B is
(a)13(b)12(c)17(d)15
15.If 5 A × A = 399, then the value of A is
(a)3(b)6(c)7(d)9
16.If 6 A × B = A 8 B, then the value of A – B is
(a)–2(b)2(c)–3(d)3
17.Which of the following numbers is divisible by 99
(a)913462(b)114345(c)135792(d)3572406
Fill in the blanks to make the statements true.
18.3134673 is divisible by 3 and ______.
19.20x3 is a multiple of 3 if the digit x is ______ or ______ or ______.
20.3x5 is divisible by 9 if the digit x is __________.
21.The sum of a two–digit number and the number obtained by reversing the digits is always divisible by __________.
22.The difference of a two–digit number and the number obtained by reversing its digits is always divisible by ___________.
23.The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and ___________.
24.If  2BAB8A + then A = ______ and B = ______.
25.If  AB×B96 then A = ______ and B = ______.
26.If B1×B49B then B = _______.

27.1 x 35 is divisible by 9 if x = _______.
28.A four-digit number abcd is divisible by 11, if d + b = _______ or _____
29.A number is divisible by 11 if the differences between the sum of digits at its odd places and that of digits at the even places is either 0 or divisible by ______.
30.If a 3-digit number abc is divisible by 11, then ______ is either 0 or multiple of 11.
31.If A × 3 = 1A, then A = ______.
32.If B × B = AB, then either A = 2, B = 5 or A = ______, B = ______.
33.If the digit 1 is placed after a 2-digit number whose tens is t and ones digit is u, the new number is ______.