CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the alternating series: 6, 38, 11, 44, 16, 50, ?
A. 16
B. 21
C. 56
D. 26
Correct Answer: B
Odd-position terms are 6, 11, 16, ... with difference 5. Hence the next odd-position term is 21.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 8, 25, 76, 229, 688, ?
A. 2064
B. 2065
C. 2062
D. 2066
Correct Answer: B
Each term is obtained by ×3 + 1. So 688 × 3 + 1 = 2065.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the series: 28, 31, 34, 37, 40, ?
A. 40
B. 43
C. 49
D. 46
Correct Answer: B
The common difference is 3. So the next term is 40 + 3 = 43.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 22, 23, 27, 36, 52, ?
A. 77
B. 82
C. 68
D. 72
Correct Answer: A
The increments are consecutive squares: 1, 4, 9, 16; next add 5² = 25. So the answer is 77.
CSS - PMS - CCE - PCS - Mathematics
Number System
What least number must be subtracted from 3503 so that the result is exactly divisible by 13?
A. 19
B. 5
C. 6
D. 7
Correct Answer: C
The remainder is 6; subtracting the remainder makes the number divisible by 13.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 51, 56, 50, 55, 49, 54, ?
A. 59
B. 54
C. 43
D. 48
Correct Answer: D
The operations alternate +5, -6. After the last +5, subtract 6: 54 - 6 = 48.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the HCF (GCD) of 209 and 38.
A. 38
B. 9
C. 19
D. 20
Correct Answer: C
The greatest common divisor of 209 and 38 is 19.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 1, 9, 33, 105, 321, ?
A. 969
B. 963
C. 966
D. 975
Correct Answer: A
Each term is obtained by ×3 + 6. So 321 × 3 + 6 = 969.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the units digit of 53^44?
A. 5
B. 1
C. 3
D. 7
Correct Answer: B
Units digits repeat cyclically; applying the cycle for base 53 gives units digit 1.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest positive integer that can divide both 543 and 479 leaving the same remainder?
A. 64
B. 32
C. 63
D. 65
Correct Answer: A
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 543-479 = 64; the greatest possible divisor is 64.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the LCM of 27 and 20.
A. 27
B. 594
C. 540
D. 541
Correct Answer: C
LCM = (27 × 20) ÷ HCF(27,20) = 540.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 12, 28, 40, 68, 108, 176, ?
A. 284
B. 352
C. 324
D. 216
Correct Answer: A
Each term is the sum of the previous two. Therefore 108 + 176 = 284.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest positive integer that can divide both 633 and 532 leaving the same remainder?
A. 50
B. 101
C. 102
D. 100
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 633-532 = 101; the greatest possible divisor is 101.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 28, 31, 39, 52, 70, ?
A. 98
B. 73
C. 88
D. 93
Correct Answer: D
The differences are 3, 8, 13, 18, increasing by 5. The next difference is 23, so the answer is 93.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 27 to 201, inclusive, are divisible by 13?
A. 12
B. 14
C. 15
D. 13
Correct Answer: D
Count = ⌊201/13⌋ - ⌊(27-1)/13⌋ = 15 - 2 = 13.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 32, 35, 40, 47, 58, ?
A. 71
B. 58
C. 73
D. 82
Correct Answer: A
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 71.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 54, 81, 114, 153, 198, ?
A. 252
B. 195
C. 303
D. 249
Correct Answer: D
The terms follow 3n² + 6 for consecutive n. For n = 9, the term is 3×9² + 6 = 249.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 13, 25, 38, 63, 101, 164, ?
A. 265
B. 202
C. 328
D. 303
Correct Answer: A
Each term is the sum of the previous two. Therefore 101 + 164 = 265.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the least positive number exactly divisible by 6, 14, and 4?
A. 14
B. 84
C. 88
D. 168
Correct Answer: B
The required number is LCM(6, 14, 4) = 84.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 54 have?
A. 10
B. 6
C. 8
D. 7
Correct Answer: C
54 = 2^1 × 3^3. Number of divisors = (1+1)(3+1) = 8.