Q.1 The HCF of two numbers is 11 and their LCM is 7700. If one of the numbers is 275, then the other is
(A) 279 (B) 283 (C) 308 (D) 318
Q.2 Product of two co-prime numbers is 117. Their LCM should be
(A) 1 (B) 117 (C) equal to their HCF (D) cannot be calculated
Q.3 The LCM and HCF of two numbers are 4125 and 25 respectively. One number is 375. Find by how much is the second number less than the first?
(A) 100 (B) 50 (C) 75 (D) 25
Q.4 Three city tour buses leave the bus stop at 9.00 AM. Bus A returns every 30 minutes, but B returns every 20 minutes and Bus C returns every 45 minutes.
What is the next time, the buses will all return at the same time to the bus stop.
(A) 1:00 PM (B) 12 noon (C) 7:00 PM (D) 11:30 PM
Q.5 The least number of 5-digits which is exactly divisible by 16, 24, 36 and 54 is
(A) 10638 (B) 10368 (C) 13068 (D) 1084
Q.6 Find the greatest number of 5-digit which when divided by 3, 5, 8 and 12 will have 2 as reminder
(A) 99999 (B) 99958 (C) 99960 (D) 99962
Q.7 The length and breadth of a room are 18 m and 28 m respectively. What is the greatest length of the side of a square tile required for pairing the floor of the
room (No space is to be left in the room without a tile)
(A) 2.4 m (B) 4 m (C) 2 m (D) 3.2 m
Q.8 The prime factorisation of 54 is :
(A) 2 × 2 × 3 × 3 (B) 2 × 2 × 2 × 3 (C) 2 × 3 × 3 × 3 (D) 2 × 27
Q.9 Which of the following is a pair of twin primes?
(A) (7, 9) (B) (17, 19) (C) (51, 53) (D) (31, 33)
Q.10 The only even prime number is :
(A) 2 (B) 3 (C) 4 (D) 0
Q.11 LCM of 15, 20 and 30 is :
(A) 50 (B) 20 (C) 60 (D) 15
Q.12 The smallest digit to make the number 5703_2 divisible by 4 is :
(A) 2 (B) 4 (C) 8 (D) 1
Q.13 The largest 3-digit number which is exactly divisible by 3 is :
(A) 998 (B) 992 (C) 999 (D) None of these
Q.14 Which of the following is a pair of co-prime?
(A) (55, 57) (B) (46, 50) (C) (72, 78) (D) none of these
Q.15 Which of the following is a composite number ?
(A) 1 (B) 2 (C) 5 (D) 8
Simplify (1 – 6)
Q.1 8 – (4 × 2) ¸ 8.
Q.2 {3 + (4 × 5) ¸ 2 – 6} ¸ 7.
Q.3 2 – [3 – {6 – (5 – )}]
Q.4 73 of [45 – {6 × 7 + (23 – 4 of 5)}]
Q.5 {5(18 ¸ )– 30} + 20 × 10 ¸ 5
Q.6 What is the value of 64 ¸ 8 ¸ 4 ¸ 2?
Q.7 List all the factors of :
(i) 23 (ii) 48 (iii) 168
Q.8 Write the following :
(i) The first 3-digit even multiple of 7
(ii) Odd multiples of 17, less than 100
(iii) Multiples of 5 between 52 and 76.
Q.9 Write the seven consecutive composite numbers less than 100.
Q.10 Replace the star(*) by the smallest number so that
(i) 78 * 964 many be divisible by 9.
(ii) 75 * may be divisible by 9.
(iii) 2 * 345 may be divisible by 3.
Q.11 What least number should be subtracted from 26492518 so that the resulting number is divisible by 3, but not by 9?
Q.12 Three different tankes contain 496 litres, 403 litres and 713 litres of milk. Find the maximum capacity of a container that can measure the milk of any tanker an exact number of times.
Q.13 Find the largest number that divides 220, 313 and 716 leaving remainders 3 in each case.
Q.14 Find the largest number that will divide 623, 729 and 841 leaving remainders 3, 9 and 1 respectively.
Q.15 Find the LCM of the following by division method :
(i) 20, 25, 30, 50
(ii) 9, 12, 18, 24, 27
(iii) 22, 54, 108, 135, 198
Q.16 Find the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 ?
Q.17 In a walking competition, three person step off together. Their steps measure 85 cm, 90 cm and 80 cm respectively. At what distance from the starting point will they again step off together?
Q.18 Find the greatest number of 4-digit exactly divisible by 12, 16, 24, 28 and 36.
Q.19 Write all the prime numbers between :
(a) 5 and 35 (b) 70 and 100 (c) 40 and 80 (d) 77 and 158
Q.20 Can a composite number be odd ? If yes, write the smallest odd composite number.
Q.21 (a) Is there any natural number having no factor at all ?
(b) Find all the number having exactly one factor.
(c) Find numbers between 1 and 100 having exactly three factors.
Q.22 Express each of the following numbers as sum of two odd primes :
(a) 36 (b) 42 (c) 84 (d) 98
In questions 1 to 38 out of the four options, only one is correct. Write the correct answer.
1. The product of the place values of two 2's in 428721 is
(A) 4 (B) 40000 (C) 400000 (D) 40000000
2. is the same as
(A) 3794 (B) 37940 (C) 37904 (D) 379409
3. If 1 is added to the greatest 7-digit number, it will be equal to
(A) 10 thousand (B) 1 lakh (C) 10 lakh (D) 1 crore
5. When rounded off to nearest thoudands, the number 85642 is
(A) 85600 (B) 85700 (C) 85000 (D) 86000
6. The largest 4-digit number, using any one digit twice, from digits 5, 9,2 and 6
(A) 9652 (B) 9562 (C) 9659 (D) 9965
7. In Indian system of numeration, the number 58695376 is written as
(A) 58,69,53,76 (B) 58,695,376
(C) 5,86,95,376 (D) 586,95,376
8. One million is equal to
(A) 1 Lakh (B) 10 Lakh (C) 1 crore (D) 10 crore
9. The greatest number which on rounding off to nearest thousands gives 5000, is
(A) 5001 (B) 5559 (C) 5999 (D) 5499
10. Keeping the place of 6 in the number 6350947 same, the smallest number obtained by rear- ranging other digits is
(A) 6975430 (B) 6043579 (C) 6034579 (D) 6034759
11. Which of the following numbers in Roman nu- merals is incorrect ?
(A) LXXX (B) LXX (C) LX (D) LLX
12. The largest 5-digit number having three differ- ent digits is
(A) 98978 (B) 99897 (C) 99987 (D) 98799
13. The smallest 4-digit number havein gthree dif- ferent digits is
(A) 1102 (B) 1012 (C) 1020 (D) 1002
14. Number of whole numbers between 38 and 68
(A) 31 (B) 30 (C) 29 (D) 28
15. The product of successor and predecessor of 999 is
(A) 999000 (B) 998000 (C) 989000 (D) 1998
16. THe product of a non-zero whole number and its successor is always
(A) an even number (B) An old number
(C) a prime (D) divisible by 3
17. A whole number is added to 25 and the same number is subtracted from 25. The sum of the resultanting number
(A) 0 (B) 25 (C) 50 (D) 75
18. WHich of the following is not true?
(A) (7 + 8) + 9 = 7 + (8 + 9)
(B) (7 x 8 ) x 9 = 7 x (8 x 9)
(C) 7 + 8 x 9 = (7 + 8) + (7 + 9)
(D) 7 x (8 + 9) = (7 x 8) + (7 x 9)
19. By using dot(.) patterns, which of the follow- ing numbers can be arranged in all the three ways namely a line, a triangle and a rectangle?
(A) 9 (B) 10 (C) 11 (D) 12
20. WHich of the following statements is not true?
(A) Both addition and multiplication of whole numbers.
(B) Zero is the identity for multiplication of whole numbers
(C) Addition and multiplication both are com mutative for whole numbers.
(D) Multiplication is distributive over addition for whole numbers.
21. WHich of the following statements is not true?
(A) 0 + 0 = 0 (B) 0 -0 = 0 (C) 0 x 0 = 0
22. The predecessor of 1 lakh is
(A) 99000 (B) 99999 (C) 999999 (D) 100001
23. The successor of 1 million is
(A) 2 millions (B) 1000001 (C) 100001 (D) 10001
24. Number of even numbers btween 58 and 80 is
(A) (B) 11 (C) 12 (D) 13
25. Sum of the number of primes between 16 to 80 and 90 to 100 is
(A) 20 (B) 18 (C) 17 (D) 16
26. Which of the following statements is not true?
(A) The HCF of two distinct prime numbers is 1
(B) THe HCF of two co-prime numbers is 1
(C) The HCF of two consecutive even num- bers is 2
(D) THe HCF of an even and an odd number is even.
27. The number of distinct prime factors of the largest 4-digit number is
(A) 2 (B) 3 (C) 5 (D) 11
28. The number of distinct prime factor s of the smallest 5 -digit number
(A) 2 (B) 4 (C) 6 (D) 8
29. If the number 7254*98 is divisible by 22, the digit at * is
(A) 1 (B) 2 (C) 6 (D) 0
30. The largest number which alwasy divides the sum of any pair of consecutive odd numbers is
(A) 2 (B) 4 (C) 6 (D) 8
31. A number is divisible by 5 and 6. It may not be divisible by
(A) 10 (B) 15 (C) 30 (D) 60
32. The sum of the prime factor of 1729 is
(A) 13 (B) 19 (C) 32 (D) 39
33. The greatest number which always divides the product of the predecessor and successor of an odd natural number other than 1 is
(A) 6 (B) 4 (C) 16 (D) 8
34. The number of common prime factor of 75, 60, 105 is
(A) 2 (B) 3 (C) 4 (D) 5
35. Which of the following pairs is not coprime?
(A) (B) 11, 12 (C) 1, 3 (D) 31, 33
36. Which of the following numbers is divisible by 11
(A) 1011011 (B) 1111111 (C) 22222222 (D) 3333333
37. LCM of 10, 15 and 20 is
(A) (B) 60 (C) 90 (D) 180
38. LCM of two numbers is 180. Then which of the following is not the HCF of the numbers?
(A) 45 (B) 60 (C) 75 (D) 90
In question 39 to 98 state whether the given statements are true (T) or false(F)
39. In Roman numeration, a sysmbol is not repeated more than three
40. In Roman numberation , if a symbol is repeated, its value is multiplied as many times as it oc- curs.
41. 5555 = 5 x 1000 + 5 x 100 + 5 x 10 + 5 x 1
42. 39746= 3 x 10000 + 9 x 1000 + 7 x 100 + 4 x 10 + 6
43. 82546 = 8 x 1000 + 2 x 1000 + 5 x 100 + 4 x 10 + 6
44. 532235 = 5 x 100000 + 3 x 10000 + 2 x 1000 + 2 x 100 + 3 x 10 + 5
45. XXXIX=31
46. LXXIV=74
47. The number LIV is greater than LVI
48. The number 4578,4587,5478,5487 are in de scending order.
49. The number 85764 rounded off to nearest hundreds is written as 85700.
50. Estimated sum of 7826 and 12469 rounded off to hundreds is 20,000
51. The largest six digit telephone number that can be formed by using digits 5,3,4,7,0,8 only once is 875403
52. The number 81652318 will be read as eighty one crore six lakh fifty two thousand three hundred eighteen
53. The largest 4-digit number formed by the digits 6,7,0,9 using each digit only once is 9760
54. Among kilo,milli and centi, the smallest is centi.
55. Successor of a one digit number is always a one digit numbers.
56. Successor of a 3-digit number is always a 3-digit number.
57. Predecessor of a two digit number is always a two digit number.
58. Every whole number has its successor.
59. Every whole number has its predecessor.
60. Between any two natural numbers, there is one natural number.
61. The smallest 4-digit number is tha successor of the largest 3-digit number.
62. Of the given two natural numbers, the one having more digits is greater.
63. Natural numbers are closed under addition.
64. Natural numbers are not closed under multiplication.
65. Natural numbers are closed under subtraction.
66. Addition is commutative for natural numbers.
67. 1 is the identity for addition of whole numbers.
68. 1 is the identity for multiplication of whole numbers.
69. There is a whole number which when added to a whole number gives the number itself.
70. There is a natural number which when added to a natural number gives the number itself.
71. If a whole number is divided by another whole number, which is greater than the first one, the quotient is not equal to zero.
72. Any non-zero whole number divided by itself gives the quotient 1.
73. The product of two whole numbers need not be a whole number.
74. A Whole number divided by another whole number greater than 1 never gives the quo tient equal to the former.
75. Every multiple of a number is greater than or equal to the number.
76. The number of multiples of a given number is finite.
77. Every number is a multiple of itself.
78. Sum of two consecutive odd numbers is always divisible by 4.
79. If a number divides three numbers exactly , it must divide their sum exactly.
80. If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.
81. If a number is divisible both by 2 and 3, then it is divisible by 12.
82. A number with three or more digit is divisible by 6, if the number formed by its last two digit (i.e.,ones and ten) is divisible by 6.
83. A number with 4 or more digit is divisible by 8, if the number formed by the last three digit is divisible by 8.
84. If the sum of the digit of a number is divisible by 3, then the number itself divisible by 9.
85. All numbers which are divisible by 4 may not be divisible by 8.
86. The Highest common factor of two or more numbers is greater than their lowest common multiple.
87. LCM of two or more numbers is divisible by their HCF.
88. LCM of two numbers is 28 and their HCF us 8.
89. LCM of two or more numbers may be one of the numbers.
90. HCF of two or more numbers may be one of the numbers.
91. Every whole numbers is the successor of an other whole numbers.
92. Sum of two whole numbers is always less than their product.
93. If the sum of two distinct whole numbers is odd, then their difference also must be odd.
94. Any two consecutive numbers are coprime .
95. If the HCF of two numbers is one of the num- bers. them their LCM is the other number.
96. The HCF of two numbers is smaller then the smaller of the numbers
97. THe LCM of two numbers is greater than the larger of the numbers.
98. THe LCM of two coprime numbers is equal to the product of the numbers.
OBJECTIVE :
1.D 2.A 3.B 4.C
5.B 6.C 7.D 8. D
9.D 10.B 11.C 12.A
13.B 14.C 15.B 16.C
17.C 18.B 19.D 20.C
SUBJECTIVE :
1. Predecessor of 7000 = 7000 – 1 = 6999
2. 72389 < 72391
3. 2345, 2435, 2543, 3452, 4325
4. 62, 45, 635
9, 58, 61, 089
5. (a) 2,00,000 + 80,000 + 4,000 + 200 + 30 + 1
(b) 50,00,000 + 2,00,000 + 10,000 + 1,000 + 500 + 60 + 8
(c) 6,00,00,000 + 4,00,000 + 10,000 + 8,000 + 500 + 10 + 7
(d) 8,00,00,000 + 90,00,000 + 1,00,000 + 80,000 + 1,000 + 200 + 10 + 3
6. (a)
(b) one crore thirty lakh seventy nine
thousand six hundred ninty six
Thirty three crore seventy two lakh seventy two thousand one hundred fourten
Seventeen lakh sixty thousand six hundred seven.
(c) Thirten million seventy nine thousand six hundred ninty six.
Three hundred thirty seven million two
hundred seventy two thousand one hundred fourteen
One million seven hundred sixty thousand six hundred seven.
7. Greatest number : 97530
Smallest number : 30579
8.
9. (a) 3228 » 3200 ; 572 » 600
(b) 8010 » 8000 ; 2507 » 3000
(c) 32 » 30 ; 58 » 60
30 × 60 = 1800
(d) 108 × 47 ; 108 » 100
47 » 50
100 × 50 = 5000
10. (a) 46 = XLVI (b) 90 = XC (c) 120 = CXX (d) 150 = CL
11. (a) XX|| = 22 (b) C C X = 210 (c) D C C = 700 (d) L X l l l = 63
12. 7000 ml
13. 95,70,985
14. 9,00,085
15. 2,39,805
16. 1325 children
17. (i) 567, 576, 657, 675, 756, 765
(ii) 209, 290, 902, 920
18. (i) Greatest = 6521 Smallest = 1256
(ii) Greatest = 9870 Smallest = 7089
(iii) Greatest = 6543 Smallest = 3456
(iv) Greatest = 8432 Smallest = 2348
(v) Greatest = 9520 Smallest = 2059
(vi) Greatest = 9631 Smallest = 1369
19. (i) Greatest = 6632 Smallest = 2236
(ii) Greatest = 6610 Smallest = 1006
(iii) Greatest = 9974 Smallest = 4479
(iv) Greatest = 5520 Smallest = 2005
20. (i) Greatest = 6987 Smallest = 6012
(ii) Greatest = 9487 Smallest = 1402
(iii) Greatest = 9876 Smallest = 1072
(iv) Greatest = 9871 Smallest = 2031
(v) Greatest = 9876 Smallest = 9012
(vi) Greatest =9087 Smallest = 1023
(vii) Greatest = 9857 Smallest = 1052
(viii) Greatest = 9873 Smallest = 1023
1. D 2. B 3. B 4. C
5. C 6. D 7. D 8. C
9. A 10. C 11. B 12. D
13. A 14. C 15. A 16. D
17. B 18. D 19. C 20. D
21. B 22. B 23. B 24. C
25. B 26. D
SUBJECTIVE :
1. No, zero is the only number
2. Both travels equal distance (320 km)
3. Both sold equal number of tickets. (50 tickets)
5. (i) 2364 (ii) 3774
6. (i) Whole Number
(ii) sum, same, commutative property
(iii) 7 × (32 × 56) = (7 × 32) × 56
(iv) 0 (zero)
7. 10010
8. 147
9. (i) n = 5 (ii) n = 7 (iii) n = 8
10. (i) 9720 (ii) 0 (iii) 957000
11. Rs. 1160
12. (i) 0 (ii) 0 (iii) 700
13. (i) True (ii) False (iii) False (iv) True (v) False
14. 204
15. 19
16. 47
17. 2970
18. 11300
19. 444
20. Tuesday
21. (a) 507 (b) 20 (c) 400 (d) 11 (e) 974
22. (a) False (b) False (c) False (d) True (e) True
PLAYING WITH NUMBERS
1. C 2. B 3. A 4. B
5. B 6. D 7. C 8. C
9. B 10. A 11. C 12. D
13. C 14. A 15. D
SUBJECTIVE :
1. 7
2. 1
3. 1
4. 0
5. 4
6. 1
7. (i) 1, 23
(ii) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
(iii) 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
8. (i) 112 (ii) 17, 51, 85
(iii) 55, 60, 65, 70, 75
9. 90, 91, 92, 93, 94, 95, 96
10. (i) 2 (ii) 2 (iii) 1
11. 4
12. 31L
13. 31
14. 20
15. (i) 300 (ii) 216 (iii) 5940
16. 151
17. 122m40cm
18. 9072
19. (a) 7, 11, 13, 17, 19, 23, 29, 31
(b) 71, 73, 79, 83, 89, 97
(c) 41, 43, 47, 53, 59, 61
(d) 79, 83, 89, 97, 101, 103, 109, 113, 127, 131, 139, 149, 151, 157
20. Yes, 9
21. (a) No (b) 1
(c) 4, 9, 25, 49
22. (a) 36 = 7 + 29 (b) 42 = 5 + 37 (c) 84 = 17 + 67 (d) 98 = 79 + 19
CONCEPTUAL PROBLEMS FOR NUMBER SYSTEM
1. C 2. C 3. D 4. B 5. D 6. D 7. C 8. B 9. D 10.C 11.D 12.C 13.D 14.D 15.B 16.A 17.C 18.C 19.B 20.B 21.D 22.B 23.B 24.A
25.C 26.D 27.B 28.A 29.C 30.B 31.D 32.D 33.B 34.A 35.A 36.C 37.B 38.C 39.T 40.F 41.T 42.T 43.F 44.T 45.F 46.T
47. F 48. F 49. F 50. T 51. F 52. F 53. T 54. F 55. F 56. F 57. F 58. T 59. F 60. F 61. T 62. T 63. T 64. F 65. F 66. T 67. F 68. T
69. T 70. F 71. T 72. T 73. F 74. T 75. T 76. F 77. T 78. T 79. T 80. F 81. F 82. F 83. T 84. F 85. T 86. F 87. T 88. F 89. T 90. T
91. F 92. F 93. T 94. T 95. T 96. F 97. F 98. T