Mathematics
Number System
How many integers from 70 to 428, inclusive, are divisible by 10?
A. 42
B. 36
C. 35
D. 37
Correct Answer: B
Count = ⌊428/10⌋ - ⌊(70-1)/10⌋ = 42 - 6 = 36.
Mathematics
Number System
Find the next number: 11, 25, 53, 109, 221, ?
A. 443
B. 442
C. 445
D. 448
Correct Answer: C
Each term is obtained by ×2 + 3. So 221 × 2 + 3 = 445.
Mathematics
Number System
Find the next term: 97, 107, 102, 112, 107, 117, ?
A. 127
B. 102
C. 117
D. 112
Correct Answer: D
The operations alternate +10, -5. After the last +10, subtract 5: 117 - 5 = 112.
Mathematics
Number System
Find the next number: 13, 17, 26, 42, 67, ?
A. 109
B. 97
C. 103
D. 92
Correct Answer: C
The increments are consecutive squares: 4, 9, 16, 25; next add 6² = 36. So the answer is 103.
Mathematics
Number System
Find the next number: 26, 31, 40, 53, 70, ?
A. 87
B. 91
C. 95
D. 75
Correct Answer: B
The differences are 5, 9, 13, 17, increasing by 4. The next difference is 21, so the answer is 91.
Mathematics
Number System
Find the next term: 93, 100, 97, 104, 101, 108, ?
A. 115
B. 105
C. 108
D. 98
Correct Answer: B
The operations alternate +7, -3. After the last +7, subtract 3: 108 - 3 = 105.
Mathematics
Number System
Find the next number: 10, 12, 15, 20, 27, ?
A. 27
B. 40
C. 38
D. 45
Correct Answer: C
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 38.
Mathematics
Number System
The sum of 4 consecutive integers is 310. What is the smallest integer?
A. 76
B. 77
C. 80
D. 75
Correct Answer: A
Let the integers be n, n+1, ..., n+3. Their sum is 310; solving gives n = 76.
Mathematics
Number System
Classify 33/23.
A. Prime number
B. Whole number
C. Rational
D. Irrational
Correct Answer: C
33/23 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
How many positive divisors does 63 have?
A. 5
B. 7
C. 8
D. 6
Correct Answer: D
63 = 7^1 × 3^2. Number of divisors = (1+1)(2+1) = 6.
Mathematics
Number System
Two positive integers have HCF 2 and LCM 198. What is their product?
A. 200
B. 396
C. 398
D. 198
Correct Answer: B
For two positive integers, product = HCF × LCM = 2 × 198 = 396.
Mathematics
Number System
What is the remainder when 176 is divided by 7?
A. 4
B. 2
C. 3
D. 1
Correct Answer: D
176 = 7 × 25 + 1; therefore the remainder is 1.
Mathematics
Number System
Find the next number in the alternating series: 3, 64, 13, 67, 23, 70, ?
A. 23
B. 33
C. 43
D. 73
Correct Answer: B
Odd-position terms are 3, 13, 23, ... with difference 10. Hence the next odd-position term is 33.
Mathematics
Number System
How many trailing zeros are there in 146! ?
A. 14
B. 34
C. 36
D. 35
Correct Answer: D
Trailing zeros = ⌊146/5⌋ + ⌊146/25⌋ + ... = 29 + 5 + 1 = 35.
Mathematics
Number System
How many positive divisors does 675 have?
A. 12
B. 14
C. 11
D. 7
Correct Answer: A
675 = 3^3 × 5^2. Number of divisors = (3+1)(2+1) = 12.
Mathematics
Number System
What is the least positive number exactly divisible by 11, 15, and 9?
A. 15
B. 495
C. 504
D. 990
Correct Answer: B
The required number is LCM(11, 15, 9) = 495.
Mathematics
Number System
Find the next number: 39, 46, 57, 70, 87, ?
A. 87
B. 106
C. 123
D. 108
Correct Answer: B
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 106.
Mathematics
Number System
Two positive integers have HCF 7 and LCM 252. What is their product?
A. 1771
B. 1764
C. 252
D. 259
Correct Answer: B
For two positive integers, product = HCF × LCM = 7 × 252 = 1764.
Mathematics
Number System
Find the next number: 37, 39, 42, 47, 54, ?
A. 65
B. 72
C. 54
D. 67
Correct Answer: A
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 65.
Mathematics
Number System
Find the missing number: 63, 80, 97, ?, 131, 148
A. 97
B. 131
C. 148
D. 114
Correct Answer: D
This is an arithmetic series with common difference 17; the missing term is 114.