CSS - PMS - CCE - PCS - Mathematics
Number System
Classify 33/23.
A. Prime number
B. Whole number
C. Rational
D. Irrational
Correct Answer: C
33/23 is a ratio of two integers with a non-zero denominator, so it is rational.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 63 have?
A. 5
B. 7
C. 8
D. 6
Correct Answer: D
63 = 7^1 × 3^2. Number of divisors = (1+1)(2+1) = 6.
CSS - PMS - CCE - PCS - Mathematics
Number System
Two positive integers have HCF 2 and LCM 198. What is their product?
A. 200
B. 396
C. 398
D. 198
Correct Answer: B
For two positive integers, product = HCF × LCM = 2 × 198 = 396.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the remainder when 176 is divided by 7?
A. 4
B. 2
C. 3
D. 1
Correct Answer: D
176 = 7 × 25 + 1; therefore the remainder is 1.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the alternating series: 3, 64, 13, 67, 23, 70, ?
A. 23
B. 33
C. 43
D. 73
Correct Answer: B
Odd-position terms are 3, 13, 23, ... with difference 10. Hence the next odd-position term is 33.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many trailing zeros are there in 146! ?
A. 14
B. 34
C. 36
D. 35
Correct Answer: D
Trailing zeros = ⌊146/5⌋ + ⌊146/25⌋ + ... = 29 + 5 + 1 = 35.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 675 have?
A. 12
B. 14
C. 11
D. 7
Correct Answer: A
675 = 3^3 × 5^2. Number of divisors = (3+1)(2+1) = 12.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the least positive number exactly divisible by 11, 15, and 9?
A. 15
B. 495
C. 504
D. 990
Correct Answer: B
The required number is LCM(11, 15, 9) = 495.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 39, 46, 57, 70, 87, ?
A. 87
B. 106
C. 123
D. 108
Correct Answer: B
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 106.
CSS - PMS - CCE - PCS - Mathematics
Number System
Two positive integers have HCF 7 and LCM 252. What is their product?
A. 1771
B. 1764
C. 252
D. 259
Correct Answer: B
For two positive integers, product = HCF × LCM = 7 × 252 = 1764.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 37, 39, 42, 47, 54, ?
A. 65
B. 72
C. 54
D. 67
Correct Answer: A
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 65.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the missing number: 63, 80, 97, ?, 131, 148
A. 97
B. 131
C. 148
D. 114
Correct Answer: D
This is an arithmetic series with common difference 17; the missing term is 114.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 95 to 409, inclusive, are divisible by 11?
A. 30
B. 37
C. 28
D. 29
Correct Answer: D
Count = ⌊409/11⌋ - ⌊(95-1)/11⌋ = 37 - 8 = 29.
CSS - PMS - CCE - PCS - Mathematics
Number System
What least number must be subtracted from 217 so that the result is exactly divisible by 20?
A. 37
B. 17
C. 16
D. 3
Correct Answer: B
The remainder is 17; subtracting the remainder makes the number divisible by 20.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest positive integer that can divide both 384 and 239 leaving the same remainder?
A. 144
B. 146
C. 72
D. 145
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 384-239 = 145; the greatest possible divisor is 145.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 56 have?
A. 8
B. 6
C. 10
D. 7
Correct Answer: A
56 = 2^3 × 7^1. Number of divisors = (3+1)(1+1) = 8.
CSS - PMS - CCE - PCS - Mathematics
Number System
Two positive integers have HCF 8 and LCM 840. What is their product?
A. 848
B. 6728
C. 840
D. 6720
Correct Answer: D
For two positive integers, product = HCF × LCM = 8 × 840 = 6720.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest multiple of 25 that is less than 1690?
A. 1700
B. 1675
C. 1650
D. 1676
Correct Answer: B
1690 ÷ 25 has integer quotient 67; 25 × 67 = 1675.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the missing number: 28, 41, ?, 67, 80, 93
A. 67
B. 41
C. 80
D. 54
Correct Answer: D
This is an arithmetic series with common difference 13; the missing term is 54.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 6, 21, 27, 48, 75, 123, ?
A. 150
B. 246
C. 225
D. 198
Correct Answer: D
Each term is the sum of the previous two. Therefore 75 + 123 = 198.