CSS - PMS - CCE - PCS - Mathematics
Number System
What least number must be subtracted from 2268 so that the result is exactly divisible by 13?
A. 19
B. 5
C. 7
D. 6
Correct Answer: D
The remainder is 6; subtracting the remainder makes the number divisible by 13.
CSS - PMS - CCE - PCS - Mathematics
Number System
Classify 38/7.
A. Whole number
B. Prime number
C. Rational
D. Irrational
Correct Answer: C
38/7 is a ratio of two integers with a non-zero denominator, so it is rational.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the units digit of 43^83?
A. 9
B. 1
C. 7
D. 3
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 43 gives units digit 7.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 82, 87, 83, 88, 84, 89, ?
A. 94
B. 85
C. 80
D. 89
Correct Answer: B
The operations alternate +5, -4. After the last +5, subtract 4: 89 - 4 = 85.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 56 to 382, inclusive, are divisible by 11?
A. 28
B. 29
C. 30
D. 34
Correct Answer: B
Count = ⌊382/11⌋ - ⌊(56-1)/11⌋ = 34 - 5 = 29.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the alternating series: 4, 46, 10, 48, 16, 50, ?
A. 52
B. 16
C. 28
D. 22
Correct Answer: D
Odd-position terms are 4, 10, 16, ... with difference 6. Hence the next odd-position term is 22.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the HCF (GCD) of 20 and 25.
A. 5
B. 10
C. 6
D. 2
Correct Answer: A
The greatest common divisor of 20 and 25 is 5.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 45 have?
A. 7
B. 8
C. 5
D. 6
Correct Answer: D
45 = 3^2 × 5^1. Number of divisors = (2+1)(1+1) = 6.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the HCF (GCD) of 195 and 150.
A. 15
B. 16
C. 30
D. 7
Correct Answer: A
The greatest common divisor of 195 and 150 is 15.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 147 have?
A. 6
B. 5
C. 8
D. 7
Correct Answer: A
147 = 7^2 × 3^1. Number of divisors = (2+1)(1+1) = 6.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 28, 35, 46, 59, 76, ?
A. 76
B. 112
C. 97
D. 95
Correct Answer: D
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 95.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 28, 34, 32, 38, 36, 42, ?
A. 40
B. 48
C. 42
D. 34
Correct Answer: A
The operations alternate +6, -2. After the last +6, subtract 2: 42 - 2 = 40.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the HCF (GCD) of 165 and 88.
A. 5
B. 22
C. 11
D. 12
Correct Answer: C
The greatest common divisor of 165 and 88 is 11.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest multiple of 23 that is less than 2009?
A. 2002
B. 2001
C. 1978
D. 2024
Correct Answer: B
2009 ÷ 23 has integer quotient 87; 23 × 87 = 2001.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 26 to 395, inclusive, are divisible by 13?
A. 28
B. 30
C. 31
D. 29
Correct Answer: D
Count = ⌊395/13⌋ - ⌊(26-1)/13⌋ = 30 - 1 = 29.
CSS - PMS - CCE - PCS - Mathematics
Number System
What least number must be subtracted from 301 so that the result is exactly divisible by 22?
A. 37
B. 15
C. 7
D. 14
Correct Answer: B
The remainder is 15; subtracting the remainder makes the number divisible by 22.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many trailing zeros are there in 23! ?
A. 5
B. 3
C. 4
D. 2
Correct Answer: C
Trailing zeros = ⌊23/5⌋ + ⌊23/25⌋ + ... = 4 = 4.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 12, 25, 37, 62, 99, 161, ?
A. 260
B. 297
C. 322
D. 198
Correct Answer: A
Each term is the sum of the previous two. Therefore 99 + 161 = 260.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the missing number: 84, 104, 124, 144, ?, 184
A. 184
B. 164
C. 204
D. 144
Correct Answer: B
This is an arithmetic series with common difference 20; the missing term is 164.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 4, 12, 21, 31, 42, ?
A. 53
B. 54
C. 55
D. 50
Correct Answer: B
The differences are 8, 9, 10, 11, increasing by 1. The next difference is 12, so the answer is 54.