Olympiad Level – Very Tricky
OLYMPIAD LEVEL – VERY TRICKY
61. Smallest number leaving remainder 2 when divided by 3 and 4:
Options: (a) 6 (b) 10 (c) 14 (d) 18
Ans: (c) 14
Explanation: LCM of 3 and 4 is 12; 12 + 2 = 14.
62. HCF of co-prime numbers 14 and 25:
Options: (a) 7 (b) 5 (c) 1 (d) 2
Ans: (c) 1
Explanation: Co-prime numbers always have HCF = 1.
63. Product of two numbers is 144 and HCF is 12. LCM = ?
Options: (a) 6 (b) 12 (c) 18 (d) 24
Ans: (b) 12
Explanation: Product = HCF × LCM → 144 = 12 × LCM → LCM = 12.
Options: (a) 6 (b) 12 (c) 18 (d) 24
Ans: (b) 12
Explanation: Product = HCF × LCM → 144 = 12 × LCM → LCM = 12.
64. Which number has the greatest number of factors?
Options: (a) 18 (b) 19 (c) 23 (d) 29
Ans: (a) 18
Explanation: 18 has factors 1,2,3,6,9,18 (6 factors); others are prime with only 2 factors.
Options: (a) 18 (b) 19 (c) 23 (d) 29
Ans: (a) 18
Explanation: 18 has factors 1,2,3,6,9,18 (6 factors); others are prime with only 2 factors.
65. Smallest 3-digit number divisible by 11:
Options: (a) 100 (b) 110 (c) 121 (d) 132
Ans: (b) 110
Explanation: 11 × 10 = 110, the first 3-digit multiple.
Options: (a) 100 (b) 110 (c) 121 (d) 132
Ans: (b) 110
Explanation: 11 × 10 = 110, the first 3-digit multiple.
66. If a number is divisible by 8, it must be divisible by:
Options: (a) 2 (b) 4 (c) Both (d) None
Ans: (c) Both
Explanation: Since 8 = 2³, it is automatically divisible by 2 and 4.
Options: (a) 2 (b) 4 (c) Both (d) None
Ans: (c) Both
Explanation: Since 8 = 2³, it is automatically divisible by 2 and 4.
67. Remainder when 500 is divided by 6:
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (b) 2
Explanation: 6 × 83 = 498; remainder = 2.
Options: (a) 1 (b) 2 (c) 3 (d) 4
Ans: (b) 2
Explanation: 6 × 83 = 498; remainder = 2.
68. Which is NOT a factor of 72?
Options: (a) 6 (b) 8 (c) 9 (d) 10
Ans: (d) 10
Explanation: 72 is not divisible by 10.
Options: (a) 6 (b) 8 (c) 9 (d) 10
Ans: (d) 10
Explanation: 72 is not divisible by 10.
69. Largest 2-digit prime:
Options: (a) 97 (b) 91 (c) 89 (d) 93
Ans: (a) 97
Explanation: 97 is prime; numbers after it (98, 99) are composite.
Options: (a) 97 (b) 91 (c) 89 (d) 93
Ans: (a) 97
Explanation: 97 is prime; numbers after it (98, 99) are composite.
70. If two numbers are multiples of 6, their HCF is always:
Options: (a) 6 (b) Multiple of 6 (c) 1 (d) 12
Ans: (b) Multiple of 6
Explanation: Both contain 6 as a factor, so HCF must include at least 6.
Options: (a) 6 (b) Multiple of 6 (c) 1 (d) 12
Ans: (b) Multiple of 6
Explanation: Both contain 6 as a factor, so HCF must include at least 6.
71. Which number is divisible by 99?
Options: (a) 198 (b) 297 (c) 396 (d) All
Ans: (d) All
Explanation: Each equals 99 × 2, 3, and 4 respectively.
Options: (a) 198 (b) 297 (c) 396 (d) All
Ans: (d) All
Explanation: Each equals 99 × 2, 3, and 4 respectively.
72. Prime factorization of 100:
Options: (a) 2²×5² (b) 4×25 (c) 10×10 (d) 20×5
Ans: (a) 2²×5²
Explanation: Only option written fully in prime factors.
Options: (a) 2²×5² (b) 4×25 (c) 10×10 (d) 20×5
Ans: (a) 2²×5²
Explanation: Only option written fully in prime factors.
73. Smallest number divisible by every number from 1–5:
Options: (a) 10 (b) 30 (c) 60 (d) 120
Ans: (c) 60
Explanation: LCM of 1,2,3,4,5 is 60.
Options: (a) 10 (b) 30 (c) 60 (d) 120
Ans: (c) 60
Explanation: LCM of 1,2,3,4,5 is 60.
74. Which number is divisible by 2,3,4,5,6 but NOT by 7?
Options: (a) 60 (b) 120 (c) 180 (d) 240
Ans: (a) 60
Explanation: 60 is divisible by all listed numbers except 7.
Options: (a) 60 (b) 120 (c) 180 (d) 240
Ans: (a) 60
Explanation: 60 is divisible by all listed numbers except 7.
75. HCF of three consecutive numbers:
Options: (a) 1 (b) 2 (c) 3 (d) Depends
Ans: (a) 1
Explanation: Consecutive numbers share no common factor other than 1.
Options: (a) 1 (b) 2 (c) 3 (d) Depends
Ans: (a) 1
Explanation: Consecutive numbers share no common factor other than 1.
76. Which is the smallest square number divisible by 3?
Options: (a) 3 (b) 6 (c) 9 (d) 12
Ans: (c) 9
Explanation: 3² = 9.
Options: (a) 3 (b) 6 (c) 9 (d) 12
Ans: (c) 9
Explanation: 3² = 9.
77. LCM of consecutive numbers 4 and 5:
Options: (a) 10 (b) 15 (c) 20 (d) 25
Ans: (c) 20
Explanation: Co-prime numbers → LCM = product (4×5).
Options: (a) 10 (b) 15 (c) 20 (d) 25
Ans: (c) 20
Explanation: Co-prime numbers → LCM = product (4×5).
78. Which number leaves remainder 1 when divided by any number?
Options: (a) 0 (b) 1 (c) Divisor+1 (d) Prime
Ans: (c) Divisor+1
Explanation: A number one more than the divisor always leaves remainder 1.
Options: (a) 0 (b) 1 (c) Divisor+1 (d) Prime
Ans: (c) Divisor+1
Explanation: A number one more than the divisor always leaves remainder 1.
79. If a number is divisible by both 9 and 11, it is divisible by:
Options: (a) 18 (b) 99 (c) 121 (d) 100
Ans: (b) 99
Explanation: 9 and 11 are co-prime → LCM = 99.
Options: (a) 18 (b) 99 (c) 121 (d) 100
Ans: (b) 99
Explanation: 9 and 11 are co-prime → LCM = 99.
80. Number of factors of 49:
Options: (a) 2 (b) 3 (c) 4 (d) 5
Ans: (b) 3
Explanation: Factors are 1, 7, 49.
Options: (a) 2 (b) 3 (c) 4 (d) 5
Ans: (b) 3
Explanation: Factors are 1, 7, 49.
81. Greatest multiple of 15 less than 200:
Options: (a) 180 (b) 195 (c) 190 (d) 175
Ans: (b) 195
Explanation: 15 × 13 = 195; next is 210 (>200).
Options: (a) 180 (b) 195 (c) 190 (d) 175
Ans: (b) 195
Explanation: 15 × 13 = 195; next is 210 (>200).
82. Which is divisible by 12?
Options: (a) 144 (b) 150 (c) 152 (d) 154
Ans: (a) 144
Explanation: Divisible by both 3 and 4.
Options: (a) 144 (b) 150 (c) 152 (d) 154
Ans: (a) 144
Explanation: Divisible by both 3 and 4.
83. The HCF of identical numbers is:
Options: (a) 1 (b) The number itself (c) 0 (d) Double
Ans: (b) The number itself
Explanation: Greatest common factor equals the number.
Options: (a) 1 (b) The number itself (c) 0 (d) Double
Ans: (b) The number itself
Explanation: Greatest common factor equals the number.
84. Which number is divisible by 15?
Options: (a) 45 (b) 46 (c) 47 (d) 48
Ans: (a) 45
Explanation: Must be divisible by 3 and 5.
Options: (a) 45 (b) 46 (c) 47 (d) 48
Ans: (a) 45
Explanation: Must be divisible by 3 and 5.
85. How many factors does 1 have?
Options: (a) 1 (b) 2 (c) 0 (d) Infinite
Ans: (a) 1
Explanation: Only divisor is 1 itself.
Options: (a) 1 (b) 2 (c) 0 (d) Infinite
Ans: (a) 1
Explanation: Only divisor is 1 itself.
86. Which is the smallest cube number?
Options: (a) 1 (b) 2 (c) 4 (d) 8
Ans: (a) 1
Explanation: 1³ = 1.
Options: (a) 1 (b) 2 (c) 4 (d) 8
Ans: (a) 1
Explanation: 1³ = 1.
87. If LCM is product, numbers are:
Options: (a) Equal (b) Co-prime (c) Even (d) Composite
Ans: (b) Co-prime
Explanation: Only co-prime numbers have LCM equal to their product.
Options: (a) Equal (b) Co-prime (c) Even (d) Composite
Ans: (b) Co-prime
Explanation: Only co-prime numbers have LCM equal to their product.
88. Which is divisible by both 8 and 3?
Options: (a) 16 (b) 18 (c) 24 (d) 32
Ans: (c) 24
Explanation: LCM of 8 and 3 is 24.
Options: (a) 16 (b) 18 (c) 24 (d) 32
Ans: (c) 24
Explanation: LCM of 8 and 3 is 24.
89. Prime factors of 77:
Options: (a) 7 (b) 11 (c) Both (d) 3
Ans: (c) Both
Explanation: 77 = 7 × 11.
Options: (a) 7 (b) 11 (c) Both (d) 3
Ans: (c) Both
Explanation: 77 = 7 × 11.
90. Smallest multiple of 9:
Options: (a) 0 (b) 9 (c) 18 (d) 27
Ans: (a) 0
Explanation: 0 is a multiple of every number (9×0=0).
Options: (a) 0 (b) 9 (c) 18 (d) 27
Ans: (a) 0
Explanation: 0 is a multiple of every number (9×0=0).
91. Which is NOT divisible by 5?
Options: (a) 115 (b) 125 (c) 132 (d) 145
Ans: (c) 132
Explanation: Numbers divisible by 5 end in 0 or 5.
Options: (a) 115 (b) 125 (c) 132 (d) 145
Ans: (c) 132
Explanation: Numbers divisible by 5 end in 0 or 5.
92. Even number divisible by 3 must be divisible by:
Options: (a) 5 (b) 6 (c) 9 (d) 12
Ans: (b) 6
Explanation: Divisible by both 2 and 3 → divisible by 6
Options: (a) 5 (b) 6 (c) 9 (d) 12
Ans: (b) 6
Explanation: Divisible by both 2 and 3 → divisible by 6
93. Smallest prime number:
Options: (a) 0 (b) 1 (c) 2 (d) 3
Ans: (c) 2
Explanation: Prime numbers start from 2.
Options: (a) 0 (b) 1 (c) 2 (d) 3
Ans: (c) 2
Explanation: Prime numbers start from 2.
94. Which number has only one factor?
Options: (a) 0 (b) 1 (c) 2 (d) 3
Ans: (b) 1
Explanation: 1 is neither prime nor composite.
Options: (a) 0 (b) 1 (c) 2 (d) 3
Ans: (b) 1
Explanation: 1 is neither prime nor composite.
95. LCM of same numbers is:
Options: (a) 1 (b) Number itself (c) Double (d) Zero
Ans: (b) Number itself
Explanation: Least common multiple equals the number.
Options: (a) 1 (b) Number itself (c) Double (d) Zero
Ans: (b) Number itself
Explanation: Least common multiple equals the number.
96. Which is a factor of all even numbers?
Options: (a) 1 (b) 2 (c) 3 (d) 5
Ans: (b) 2
Explanation: Every even number is divisible by 2.
Options: (a) 1 (b) 2 (c) 3 (d) 5
Ans: (b) 2
Explanation: Every even number is divisible by 2.
97. Greatest factor of any number is:
Options: (a) 1 (b) Number itself (c) Half (d) Double
Ans: (b) Number itself
Explanation: A number always divides itself.
Options: (a) 1 (b) Number itself (c) Half (d) Double
Ans: (b) Number itself
Explanation: A number always divides itself.
98. Which number is divisible by every number?
Options: (a) 0 (b) 1 (c) 2 (d) 10
Ans: (a) 0
Explanation: 0 ÷ any non-zero number = 0.
Options: (a) 0 (b) 1 (c) 2 (d) 10
Ans: (a) 0
Explanation: 0 ÷ any non-zero number = 0.
99. How many multiples does a number have?
Options: (a) Limited (b) Infinite (c) 10 (d) 100
Ans: (b) Infinite
Explanation: Multiples continue endlessly.
Options: (a) Limited (b) Infinite (c) 10 (d) 100
Ans: (b) Infinite
Explanation: Multiples continue endlessly.
100. True statement:
Options:
(a) Every prime is odd
(b) 2 is the only even prime
(c) All odd numbers are prime
(d) 1 is prime
Options:
(a) Every prime is odd
(b) 2 is the only even prime
(c) All odd numbers are prime
(d) 1 is prime
Ans: (b) 2 is the only even prime
Explanation: Every even number except 2 has more than two factors.