Mathematics
Number System
How many integers from 95 to 409, inclusive, are divisible by 11?
A. 30
B. 37
C. 28
D. 29
Correct Answer: D
Count = ⌊409/11⌋ - ⌊(95-1)/11⌋ = 37 - 8 = 29.
Mathematics
Number System
What least number must be subtracted from 217 so that the result is exactly divisible by 20?
A. 37
B. 17
C. 16
D. 3
Correct Answer: B
The remainder is 17; subtracting the remainder makes the number divisible by 20.
Mathematics
Number System
What is the greatest positive integer that can divide both 384 and 239 leaving the same remainder?
A. 144
B. 146
C. 72
D. 145
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 384-239 = 145; the greatest possible divisor is 145.
Mathematics
Number System
How many positive divisors does 56 have?
A. 8
B. 6
C. 10
D. 7
Correct Answer: A
56 = 2^3 × 7^1. Number of divisors = (3+1)(1+1) = 8.
Mathematics
Number System
Two positive integers have HCF 8 and LCM 840. What is their product?
A. 848
B. 6728
C. 840
D. 6720
Correct Answer: D
For two positive integers, product = HCF × LCM = 8 × 840 = 6720.
Mathematics
Number System
What is the greatest multiple of 25 that is less than 1690?
A. 1700
B. 1675
C. 1650
D. 1676
Correct Answer: B
1690 ÷ 25 has integer quotient 67; 25 × 67 = 1675.
Mathematics
Number System
Find the missing number: 28, 41, ?, 67, 80, 93
A. 67
B. 41
C. 80
D. 54
Correct Answer: D
This is an arithmetic series with common difference 13; the missing term is 54.
Mathematics
Number System
Find the next term: 6, 21, 27, 48, 75, 123, ?
A. 150
B. 246
C. 225
D. 198
Correct Answer: D
Each term is the sum of the previous two. Therefore 75 + 123 = 198.
Mathematics
Number System
Two positive integers have HCF 12 and LCM 240. What is their product?
A. 252
B. 240
C. 2880
D. 2892
Correct Answer: C
For two positive integers, product = HCF × LCM = 12 × 240 = 2880.
Mathematics
Number System
Find the LCM of 27 and 23.
A. 683
B. 27
C. 622
D. 621
Correct Answer: D
LCM = (27 × 23) ÷ HCF(27,23) = 621.
Mathematics
Number System
How is the integer 59 classified?
A. Irrational
B. Prime
C. Composite
D. Neither prime nor composite
Correct Answer: B
59 has exactly two positive divisors, 1 and 59; therefore it is prime.
Mathematics
Number System
Find the next term in the series: 25, 39, 57, 79, 105, ?
A. 139
B. 135
C. 161
D. 131
Correct Answer: B
The first differences are [14, 18, 22, 26]; their second difference is constant at 4. Continuing the pattern gives 135.
Mathematics
Number System
A two-digit number is 59. What is the absolute difference between the number and the number formed by reversing its digits?
A. 4
B. 36
C. 45
D. 27
Correct Answer: B
Reversed number = 95. Absolute difference = |59 - 95| = 36.
Mathematics
Number System
Find the next term: 73, 87, 85, 99, 97, 111, ?
A. 111
B. 95
C. 109
D. 125
Correct Answer: C
The operations alternate +14, -2. After the last +14, subtract 2: 111 - 2 = 109.
Mathematics
Number System
How many positive divisors does 1323 have?
A. 12
B. 11
C. 14
D. 7
Correct Answer: A
1323 = 3^3 × 7^2. Number of divisors = (3+1)(2+1) = 12.
Mathematics
Number System
How many integers from 24 to 234, inclusive, are divisible by 11?
A. 19
B. 21
C. 20
D. 18
Correct Answer: A
Count = ⌊234/11⌋ - ⌊(24-1)/11⌋ = 21 - 2 = 19.
Mathematics
Number System
Find the next term: 1, 17, 18, 35, 53, 88, ?
A. 106
B. 176
C. 141
D. 159
Correct Answer: C
Each term is the sum of the previous two. Therefore 53 + 88 = 141.
Mathematics
Number System
Find the next number: 7, 8, 13, 22, 35, ?
A. 56
B. 52
C. 48
D. 36
Correct Answer: B
The differences are 1, 5, 9, 13, increasing by 4. The next difference is 17, so the answer is 52.
Mathematics
Number System
How many integers from 98 to 466, inclusive, are divisible by 12?
A. 31
B. 38
C. 30
D. 29
Correct Answer: C
Count = ⌊466/12⌋ - ⌊(98-1)/12⌋ = 38 - 8 = 30.
Mathematics
Number System
Find the next number: 32, 33, 36, 41, 48, ?
A. 49
B. 55
C. 59
D. 57
Correct Answer: D
The differences are 1, 3, 5, 7, increasing by 2. The next difference is 9, so the answer is 57.