Mathematics
Number System
What least number must be added to 2813 so that the result is exactly divisible by 8?
A. 11
B. 3
C. 4
D. 5
Correct Answer: B
2813 leaves remainder 5 on division by 8. Add 8 - 5 = 3.
Mathematics
Number System
Find the next number in the alternating series: 10, 59, 14, 61, 18, 63, ?
A. 18
B. 22
C. 65
D. 26
Correct Answer: B
Odd-position terms are 10, 14, 18, ... with difference 4. Hence the next odd-position term is 22.
Mathematics
Number System
Find the next term: 28, 65, 126, 217, ?
A. 351
B. 344
C. 197
D. 343
Correct Answer: B
Each term is n³ + 1. Thus the next term is 7³ + 1 = 344.
Mathematics
Number System
Find the next number: 1, 3, 12, 60, 360, ?
A. 360
B. 2520
C. 2527
D. 2160
Correct Answer: B
The multipliers are ×3, ×4, ×5, ×6; the next multiplier is ×7. Thus 360 × 7 = 2520.
Mathematics
Number System
Find the next term in the series: 37, 65, 101, 145, 197, ?
A. 257
B. 249
C. 265
D. 309
Correct Answer: A
The first differences are [28, 36, 44, 52]; their second difference is constant at 8. Continuing the pattern gives 257.
Mathematics
Number System
Find the LCM of 6 and 19.
A. 19
B. 114
C. 115
D. 125
Correct Answer: B
LCM = (6 × 19) ÷ HCF(6,19) = 114.
Mathematics
Number System
Find the next term: 70, 77, 69, 76, 68, 75, ?
A. 60
B. 75
C. 82
D. 67
Correct Answer: D
The operations alternate +7, -8. After the last +7, subtract 8: 75 - 8 = 67.
Mathematics
Number System
What is the units digit of 15^55?
A. 7
B. 9
C. 5
D. 1
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 15 gives units digit 5.
Mathematics
Number System
Find the next number in the alternating series: 13, 54, 15, 51, 17, 48, ?
A. 19
B. 45
C. 17
D. 21
Correct Answer: A
Odd-position terms are 13, 15, 17, ... with difference 2. Hence the next odd-position term is 19.
Mathematics
Number System
What is the remainder when 50 is divided by 4?
A. 1
B. 2
C. 0
D. 3
Correct Answer: B
50 = 4 × 12 + 2; therefore the remainder is 2.
Mathematics
Number System
Find the next number: 18, 22, 31, 47, 72, ?
A. 102
B. 114
C. 97
D. 108
Correct Answer: D
The increments are consecutive squares: 4, 9, 16, 25; next add 6² = 36. So the answer is 108.
Mathematics
Number System
What least number must be added to 1612 so that the result is exactly divisible by 12?
A. 9
B. 20
C. 8
D. 4
Correct Answer: C
1612 leaves remainder 4 on division by 12. Add 12 - 4 = 8.
Mathematics
Number System
Find the HCF (GCD) of 154 and 140.
A. 15
B. 14
C. 28
D. 7
Correct Answer: B
The greatest common divisor of 154 and 140 is 14.
Mathematics
Number System
What is the units digit of 54^55?
A. 8
B. 6
C. 0
D. 4
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 54 gives units digit 4.
Mathematics
Number System
Find the next term: 4, 7, 12, 19, 28, ?
A. 27
B. 39
C. 40
D. 51
Correct Answer: B
The terms follow 1n² + 3 for consecutive n. For n = 6, the term is 1×6² + 3 = 39.
Mathematics
Number System
Find the missing number: 16, 24, 32, 40, ?, 56
A. 40
B. 48
C. 56
D. 64
Correct Answer: B
This is an arithmetic series with common difference 8; the missing term is 48.
Mathematics
Number System
Find the missing number: 80, 89, 98, ?, 116, 125
A. 116
B. 98
C. 125
D. 107
Correct Answer: D
This is an arithmetic series with common difference 9; the missing term is 107.
Mathematics
Number System
Find the next number: 26, 34, 43, 53, 64, ?
A. 75
B. 76
C. 72
D. 77
Correct Answer: B
The differences are 8, 9, 10, 11, increasing by 1. The next difference is 12, so the answer is 76.
Mathematics
Number System
What is the remainder when 1376 is divided by 11?
A. 1
B. 3
C. 4
D. 2
Correct Answer: A
1376 = 11 × 125 + 1; therefore the remainder is 1.
Mathematics
Number System
How many integers from 65 to 374, inclusive, are divisible by 13?
A. 24
B. 28
C. 25
D. 23
Correct Answer: A
Count = ⌊374/13⌋ - ⌊(65-1)/13⌋ = 28 - 4 = 24.