CSS - PMS - CCE - PCS - Mathematics
Number System
Two positive integers have HCF 12 and LCM 240. What is their product?
A. 252
B. 240
C. 2880
D. 2892
Correct Answer: C
For two positive integers, product = HCF × LCM = 12 × 240 = 2880.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the LCM of 27 and 23.
A. 683
B. 27
C. 622
D. 621
Correct Answer: D
LCM = (27 × 23) ÷ HCF(27,23) = 621.
CSS - PMS - CCE - PCS - Mathematics
Number System
How is the integer 59 classified?
A. Irrational
B. Prime
C. Composite
D. Neither prime nor composite
Correct Answer: B
59 has exactly two positive divisors, 1 and 59; therefore it is prime.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term in the series: 25, 39, 57, 79, 105, ?
A. 139
B. 135
C. 161
D. 131
Correct Answer: B
The first differences are [14, 18, 22, 26]; their second difference is constant at 4. Continuing the pattern gives 135.
CSS - PMS - CCE - PCS - Mathematics
Number System
A two-digit number is 59. What is the absolute difference between the number and the number formed by reversing its digits?
A. 4
B. 36
C. 45
D. 27
Correct Answer: B
Reversed number = 95. Absolute difference = |59 - 95| = 36.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 73, 87, 85, 99, 97, 111, ?
A. 111
B. 95
C. 109
D. 125
Correct Answer: C
The operations alternate +14, -2. After the last +14, subtract 2: 111 - 2 = 109.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 1323 have?
A. 12
B. 11
C. 14
D. 7
Correct Answer: A
1323 = 3^3 × 7^2. Number of divisors = (3+1)(2+1) = 12.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 24 to 234, inclusive, are divisible by 11?
A. 19
B. 21
C. 20
D. 18
Correct Answer: A
Count = ⌊234/11⌋ - ⌊(24-1)/11⌋ = 21 - 2 = 19.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 1, 17, 18, 35, 53, 88, ?
A. 106
B. 176
C. 141
D. 159
Correct Answer: C
Each term is the sum of the previous two. Therefore 53 + 88 = 141.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 7, 8, 13, 22, 35, ?
A. 56
B. 52
C. 48
D. 36
Correct Answer: B
The differences are 1, 5, 9, 13, increasing by 4. The next difference is 17, so the answer is 52.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 98 to 466, inclusive, are divisible by 12?
A. 31
B. 38
C. 30
D. 29
Correct Answer: C
Count = ⌊466/12⌋ - ⌊(98-1)/12⌋ = 38 - 8 = 30.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 32, 33, 36, 41, 48, ?
A. 49
B. 55
C. 59
D. 57
Correct Answer: D
The differences are 1, 3, 5, 7, increasing by 2. The next difference is 9, so the answer is 57.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the alternating series: 17, 60, 25, 58, 33, 56, ?
A. 54
B. 49
C. 33
D. 41
Correct Answer: D
Odd-position terms are 17, 25, 33, ... with difference 8. Hence the next odd-position term is 41.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the LCM of 13 and 24.
A. 343
B. 24
C. 312
D. 313
Correct Answer: C
LCM = (13 × 24) ÷ HCF(13,24) = 312.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the least positive number exactly divisible by 18, 7, and 9?
A. 126
B. 18
C. 252
D. 133
Correct Answer: A
The required number is LCM(18, 7, 9) = 126.
CSS - PMS - CCE - PCS - Mathematics
Number System
The sum of 4 consecutive integers is 250. What is the smallest integer?
A. 60
B. 65
C. 62
D. 61
Correct Answer: D
Let the integers be n, n+1, ..., n+3. Their sum is 250; solving gives n = 61.
CSS - PMS - CCE - PCS - Mathematics
Number System
What digit x makes the number 540x divisible by 9?
A. 3
B. 1
C. 0
D. 5
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 5+4+0+x must be a multiple of 9, giving x = 0.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the alternating series: 9, 56, 14, 62, 19, 68, ?
A. 19
B. 74
C. 24
D. 29
Correct Answer: C
Odd-position terms are 9, 14, 19, ... with difference 5. Hence the next odd-position term is 24.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term in the series: 19, 30, 43, 58, 75, ?
A. 111
B. 96
C. 94
D. 92
Correct Answer: C
The first differences are [11, 13, 15, 17]; their second difference is constant at 2. Continuing the pattern gives 94.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the LCM of 25 and 14.
A. 385
B. 350
C. 25
D. 351
Correct Answer: B
LCM = (25 × 14) ÷ HCF(25,14) = 350.