Mathematics
Number System
Find the next term: 3, 12, 27, 48, 75, ?
A. 108
B. 111
C. 144
D. 72
Correct Answer: A
The terms follow 3n² + 0 for consecutive n. For n = 6, the term is 3×6² + 0 = 108.
Mathematics
Number System
What least number must be subtracted from 2663 so that the result is exactly divisible by 19?
A. 16
B. 2
C. 3
D. 22
Correct Answer: C
The remainder is 3; subtracting the remainder makes the number divisible by 19.
Mathematics
Number System
Find the next number in the series: 49, 54, 59, 64, 69, ?
A. 69
B. 79
C. 84
D. 74
Correct Answer: D
The common difference is 5. So the next term is 69 + 5 = 74.
Mathematics
Number System
Find the next term: 68, 81, 78, 91, 88, 101, ?
A. 101
B. 85
C. 114
D. 98
Correct Answer: D
The operations alternate +13, -3. After the last +13, subtract 3: 101 - 3 = 98.
Mathematics
Number System
How many positive divisors does 784 have?
A. 15
B. 17
C. 8
D. 14
Correct Answer: A
784 = 2^4 × 7^2. Number of divisors = (4+1)(2+1) = 15.
Mathematics
Number System
What least number must be added to 2479 so that the result is exactly divisible by 6?
A. 11
B. 5
C. 1
D. 6
Correct Answer: B
2479 leaves remainder 1 on division by 6. Add 6 - 1 = 5.
Mathematics
Number System
Find the next number: 28, 31, 36, 43, 54, ?
A. 67
B. 78
C. 69
D. 54
Correct Answer: A
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 67.
Mathematics
Number System
What least number must be subtracted from 2541 so that the result is exactly divisible by 30?
A. 51
B. 20
C. 9
D. 21
Correct Answer: D
The remainder is 21; subtracting the remainder makes the number divisible by 30.
Mathematics
Number System
What is the units digit of 91^14?
A. 5
B. 7
C. 1
D. 3
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 91 gives units digit 1.
Mathematics
Number System
Find the next number: 16, 20, 29, 43, 62, ?
A. 91
B. 86
C. 66
D. 81
Correct Answer: B
The differences are 4, 9, 14, 19, increasing by 5. The next difference is 24, so the answer is 86.
Mathematics
Number System
Two positive integers have HCF 7 and LCM 126. What is their product?
A. 882
B. 133
C. 889
D. 126
Correct Answer: A
For two positive integers, product = HCF × LCM = 7 × 126 = 882.
Mathematics
Number System
What least number must be added to 1708 so that the result is exactly divisible by 17?
A. 8
B. 26
C. 9
D. 10
Correct Answer: C
1708 leaves remainder 8 on division by 17. Add 17 - 8 = 9.
Mathematics
Number System
What is the remainder when 140 is divided by 7?
A. 2
B. 0
C. 3
D. 1
Correct Answer: B
140 = 7 × 20 + 0; therefore the remainder is 0.
Mathematics
Number System
Find the next term: 34, 71, 132, 223, ?
A. 343
B. 350
C. 203
D. 357
Correct Answer: B
Each term is n³ + 7. Thus the next term is 7³ + 7 = 350.
Mathematics
Number System
How many integers from 21 to 270, inclusive, are divisible by 9?
A. 27
B. 29
C. 30
D. 28
Correct Answer: D
Count = ⌊270/9⌋ - ⌊(21-1)/9⌋ = 30 - 2 = 28.
Mathematics
Number System
Find the LCM of 14 and 30.
A. 212
B. 420
C. 210
D. 30
Correct Answer: C
LCM = (14 × 30) ÷ HCF(14,30) = 210.
Mathematics
Number System
Find the next term: 56, 63, 60, 67, 64, 71, ?
A. 61
B. 78
C. 71
D. 68
Correct Answer: D
The operations alternate +7, -3. After the last +7, subtract 3: 71 - 3 = 68.
Mathematics
Number System
What least number must be subtracted from 3303 so that the result is exactly divisible by 16?
A. 23
B. 7
C. 6
D. 9
Correct Answer: B
The remainder is 7; subtracting the remainder makes the number divisible by 16.
Mathematics
Number System
Find the next term in the series: 51, 80, 115, 156, 203, ?
A. 250
B. 256
C. 303
D. 262
Correct Answer: B
The first differences are [29, 35, 41, 47]; their second difference is constant at 6. Continuing the pattern gives 256.
Mathematics
Number System
Find the next term: 13, 21, 34, 55, 89, 144, ?
A. 288
B. 178
C. 267
D. 233
Correct Answer: D
Each term is the sum of the previous two. Therefore 89 + 144 = 233.