Mathematics
Number System
Find the next number in the alternating series: 14, 61, 16, 66, 18, 71, ?
A. 20
B. 76
C. 18
D. 22
Correct Answer: A
Odd-position terms are 14, 16, 18, ... with difference 2. Hence the next odd-position term is 20.
Mathematics
Number System
What least number must be subtracted from 2585 so that the result is exactly divisible by 8?
A. 1
B. 9
C. 7
D. 2
Correct Answer: A
The remainder is 1; subtracting the remainder makes the number divisible by 8.
Mathematics
Number System
Find the next number: 27, 28, 32, 41, 57, ?
A. 77
B. 87
C. 73
D. 82
Correct Answer: D
The increments are consecutive squares: 1, 4, 9, 16; next add 5² = 25. So the answer is 82.
Mathematics
Number System
Find the missing number: 19, 26, 33, 40, ?, 54
A. 47
B. 54
C. 40
D. 61
Correct Answer: A
This is an arithmetic series with common difference 7; the missing term is 47.
Mathematics
Number System
What is the greatest multiple of 34 that is less than 4269?
A. 4251
B. 4250
C. 4216
D. 4284
Correct Answer: B
4269 ÷ 34 has integer quotient 125; 34 × 125 = 4250.
Mathematics
Number System
What is the units digit of 67^69?
A. 9
B. 7
C. 3
D. 1
Correct Answer: B
Units digits repeat cyclically; applying the cycle for base 67 gives units digit 7.
Mathematics
Number System
Find the next number in the series: 10, 12, 14, 16, 18, ?
A. 20
B. 24
C. 22
D. 18
Correct Answer: A
The common difference is 2. So the next term is 18 + 2 = 20.
Mathematics
Number System
Find the next term in the series: 57, 92, 135, 186, 245, ?
A. 320
B. 304
C. 312
D. 371
Correct Answer: C
The first differences are [35, 43, 51, 59]; their second difference is constant at 8. Continuing the pattern gives 312.
Mathematics
Number System
Find the next number in the series: 21, 24, 27, 30, 33, ?
A. 39
B. 33
C. 42
D. 36
Correct Answer: D
The common difference is 3. So the next term is 33 + 3 = 36.
Mathematics
Number System
Find the next number in the alternating series: 12, 61, 20, 63, 28, 65, ?
A. 44
B. 36
C. 28
D. 67
Correct Answer: B
Odd-position terms are 12, 20, 28, ... with difference 8. Hence the next odd-position term is 36.
Mathematics
Number System
Find the next number: 1, 17, 42, 78, 127, ?
A. 191
B. 183
C. 176
D. 199
Correct Answer: A
The increments are consecutive squares: 16, 25, 36, 49; next add 8² = 64. So the answer is 191.
Mathematics
Number System
Find the next number: 10, 25, 55, 115, 235, ?
A. 475
B. 470
C. 480
D. 473
Correct Answer: A
Each term is obtained by ×2 + 5. So 235 × 2 + 5 = 475.
Mathematics
Number System
Find the LCM of 20 and 11.
A. 242
B. 221
C. 220
D. 20
Correct Answer: C
LCM = (20 × 11) ÷ HCF(20,11) = 220.
Mathematics
Number System
Find the next number in the alternating series: 21, 29, 30, 37, 39, 45, ?
A. 48
B. 57
C. 53
D. 39
Correct Answer: A
Odd-position terms are 21, 30, 39, ... with difference 9. Hence the next odd-position term is 48.
Mathematics
Number System
Find the next number: 2, 7, 17, 37, 77, ?
A. 154
B. 157
C. 160
D. 155
Correct Answer: B
Each term is obtained by ×2 + 3. So 77 × 2 + 3 = 157.
Mathematics
Number System
Find the next term: 4, 23, 27, 50, 77, 127, ?
A. 204
B. 154
C. 231
D. 254
Correct Answer: A
Each term is the sum of the previous two. Therefore 77 + 127 = 204.
Mathematics
Number System
What is the remainder when 1016 is divided by 13?
A. 2
B. 4
C. 5
D. 3
Correct Answer: A
1016 = 13 × 78 + 2; therefore the remainder is 2.
Mathematics
Number System
What is the greatest positive integer that can divide both 509 and 380 leaving the same remainder?
A. 64
B. 130
C. 129
D. 128
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 509-380 = 129; the greatest possible divisor is 129.
Mathematics
Number System
Find the next number: 10, 26, 51, 87, 136, ?
A. 208
B. 192
C. 185
D. 200
Correct Answer: D
The increments are consecutive squares: 16, 25, 36, 49; next add 8² = 64. So the answer is 200.
Mathematics
Number System
What is the least positive number exactly divisible by 5, 8, and 13?
A. 520
B. 1040
C. 13
D. 525
Correct Answer: A
The required number is LCM(5, 8, 13) = 520.