Mathematics
Number System
Find the next term: 11, 20, 35, 56, 83, ?
A. 80
B. 119
C. 152
D. 116
Correct Answer: D
The terms follow 3n² + 8 for consecutive n. For n = 6, the term is 3×6² + 8 = 116.
Mathematics
Number System
Two positive integers have HCF 7 and LCM 588. What is their product?
A. 4123
B. 588
C. 595
D. 4116
Correct Answer: D
For two positive integers, product = HCF × LCM = 7 × 588 = 4116.
Mathematics
Number System
What is the greatest positive integer that can divide both 545 and 501 leaving the same remainder?
A. 22
B. 45
C. 44
D. 43
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 545-501 = 44; the greatest possible divisor is 44.
Mathematics
Number System
Classify √44.
A. Irrational
B. Rational
C. Whole number
D. Prime number
Correct Answer: A
44 is not a perfect square, so √44 is irrational.
Mathematics
Number System
The sum of 5 consecutive integers is 345. What is the middle integer?
A. 69
B. 74
C. 68
D. 70
Correct Answer: A
The middle integer equals the average: 345 ÷ 5 = 69.
Mathematics
Number System
The sum of 5 consecutive integers is 230. What is the middle integer?
A. 46
B. 51
C. 45
D. 47
Correct Answer: A
The middle integer equals the average: 230 ÷ 5 = 46.
Mathematics
Number System
Find the next number in the series: 56, 62, 68, 74, 80, ?
A. 98
B. 92
C. 80
D. 86
Correct Answer: D
The common difference is 6. So the next term is 80 + 6 = 86.
Mathematics
Number System
Find the next term in the series: 9, 15, 23, 33, 45, ?
A. 57
B. 59
C. 71
D. 61
Correct Answer: B
The first differences are [6, 8, 10, 12]; their second difference is constant at 2. Continuing the pattern gives 59.
Mathematics
Number System
Find the next number: 14, 19, 29, 44, 64, ?
A. 69
B. 84
C. 89
D. 94
Correct Answer: C
The differences are 5, 10, 15, 20, increasing by 5. The next difference is 25, so the answer is 89.
Mathematics
Number System
Find the next term: 9, 28, 65, 126, ?
A. 223
B. 216
C. 109
D. 217
Correct Answer: D
Each term is n³ + 1. Thus the next term is 6³ + 1 = 217.
Mathematics
Number System
What is the greatest multiple of 18 that is less than 2406?
A. 2376
B. 2395
C. 2394
D. 2412
Correct Answer: C
2406 ÷ 18 has integer quotient 133; 18 × 133 = 2394.
Mathematics
Number System
How many positive divisors does 1372 have?
A. 12
B. 11
C. 14
D. 7
Correct Answer: A
1372 = 2^2 × 7^3. Number of divisors = (2+1)(3+1) = 12.
Mathematics
Number System
Find the next number: 6, 13, 25, 42, 64, ?
A. 91
B. 96
C. 86
D. 71
Correct Answer: A
The differences are 7, 12, 17, 22, increasing by 5. The next difference is 27, so the answer is 91.
Mathematics
Number System
Find the next number in the series: 6, 12, 24, 48, 96, ?
A. 194
B. 96
C. 98
D. 192
Correct Answer: D
Each term is multiplied by 2. Therefore 96 × 2 = 192.
Mathematics
Number System
What is the greatest multiple of 16 that is less than 3583?
A. 3568
B. 3569
C. 3584
D. 3552
Correct Answer: A
3583 ÷ 16 has integer quotient 223; 16 × 223 = 3568.
Mathematics
Number System
Find the next term: 13, 18, 25, 34, 45, ?
A. 44
B. 59
C. 72
D. 58
Correct Answer: D
The terms follow 1n² + 9 for consecutive n. For n = 7, the term is 1×7² + 9 = 58.
Mathematics
Number System
How is the integer 20 classified?
A. Neither prime nor composite
B. Irrational
C. Prime
D. Composite
Correct Answer: D
20 = 4 × 5, so it has factors other than 1 and itself and is composite.
Mathematics
Number System
What least number must be subtracted from 2597 so that the result is exactly divisible by 15?
A. 17
B. 1
C. 13
D. 2
Correct Answer: D
The remainder is 2; subtracting the remainder makes the number divisible by 15.
Mathematics
Number System
Two positive integers have HCF 13 and LCM 715. What is their product?
A. 728
B. 9308
C. 715
D. 9295
Correct Answer: D
For two positive integers, product = HCF × LCM = 13 × 715 = 9295.
Mathematics
Number System
What is the greatest positive integer that can divide both 640 and 553 leaving the same remainder?
A. 88
B. 86
C. 43
D. 87
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 640-553 = 87; the greatest possible divisor is 87.