Mathematics
Number System
Find the next number: 8, 30, 96, 294, 888, ?
A. 2664
B. 2667
C. 2670
D. 2676
Correct Answer: C
Each term is obtained by ×3 + 6. So 888 × 3 + 6 = 2670.
Mathematics
Number System
Find the next term: 65, 101, 145, 197, 257, ?
A. 397
B. 325
C. 329
D. 253
Correct Answer: B
The terms follow 4n² + 1 for consecutive n. For n = 9, the term is 4×9² + 1 = 325.
Mathematics
Number System
Find the next term: 24, 38, 36, 50, 48, 62, ?
A. 76
B. 46
C. 62
D. 60
Correct Answer: D
The operations alternate +14, -2. After the last +14, subtract 2: 62 - 2 = 60.
Mathematics
Number System
How many positive divisors does 40 have?
A. 8
B. 6
C. 7
D. 10
Correct Answer: A
40 = 2^3 × 5^1. Number of divisors = (3+1)(1+1) = 8.
Mathematics
Number System
How is the integer 31 classified?
A. Irrational
B. Prime
C. Composite
D. Neither prime nor composite
Correct Answer: B
31 has exactly two positive divisors, 1 and 31; therefore it is prime.
Mathematics
Number System
How many integers from 38 to 202, inclusive, are divisible by 14?
A. 14
B. 12
C. 11
D. 13
Correct Answer: B
Count = ⌊202/14⌋ - ⌊(38-1)/14⌋ = 14 - 2 = 12.
Mathematics
Number System
What is the least positive number exactly divisible by 11, 16, and 5?
A. 16
B. 880
C. 1760
D. 885
Correct Answer: B
The required number is LCM(11, 16, 5) = 880.
Mathematics
Number System
How is the integer 110 classified?
A. Irrational
B. Neither prime nor composite
C. Prime
D. Composite
Correct Answer: D
110 = 10 × 11, so it has factors other than 1 and itself and is composite.
Mathematics
Number System
How many positive divisors does 3375 have?
A. 16
B. 15
C. 8
D. 18
Correct Answer: A
3375 = 3^3 × 5^3. Number of divisors = (3+1)(3+1) = 16.
Mathematics
Number System
Find the next number: 2, 11, 27, 52, 88, ?
A. 130
B. 137
C. 144
D. 124
Correct Answer: B
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 137.
Mathematics
Number System
Find the next number: 2, 7, 22, 67, 202, ?
A. 607
B. 608
C. 604
D. 606
Correct Answer: A
Each term is obtained by ×3 + 1. So 202 × 3 + 1 = 607.
Mathematics
Number System
What is the remainder when 631 is divided by 14?
A. 1
B. 3
C. 4
D. 2
Correct Answer: A
631 = 14 × 45 + 1; therefore the remainder is 1.
Mathematics
Number System
Find the next number: 8, 20, 44, 92, 188, ?
A. 384
B. 376
C. 378
D. 380
Correct Answer: D
Each term is obtained by ×2 + 4. So 188 × 2 + 4 = 380.
Mathematics
Number System
Find the next number in the series: 38, 41, 44, 47, 50, ?
A. 53
B. 50
C. 59
D. 56
Correct Answer: A
The common difference is 3. So the next term is 50 + 3 = 53.
Mathematics
Number System
The sum of 5 consecutive integers is 280. What is the middle integer?
A. 61
B. 56
C. 55
D. 57
Correct Answer: B
The middle integer equals the average: 280 ÷ 5 = 56.
Mathematics
Number System
Find the next number in the alternating series: 15, 34, 21, 32, 27, 30, ?
A. 27
B. 39
C. 33
D. 28
Correct Answer: C
Odd-position terms are 15, 21, 27, ... with difference 6. Hence the next odd-position term is 33.
Mathematics
Number System
What is the remainder when 316 is divided by 14?
A. 11
B. 9
C. 8
D. 10
Correct Answer: C
316 = 14 × 22 + 8; therefore the remainder is 8.
Mathematics
Number System
Find the next number in the series: 8, 32, 128, 512, 2048, ?
A. 2048
B. 2052
C. 8192
D. 8196
Correct Answer: C
Each term is multiplied by 4. Therefore 2048 × 4 = 8192.
Mathematics
Number System
Find the next number in the series: 45, 51, 57, 63, 69, ?
A. 87
B. 81
C. 69
D. 75
Correct Answer: D
The common difference is 6. So the next term is 69 + 6 = 75.
Mathematics
Number System
What is the greatest multiple of 25 that is less than 1663?
A. 1651
B. 1650
C. 1625
D. 1675
Correct Answer: B
1663 ÷ 25 has integer quotient 66; 25 × 66 = 1650.