CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 12, 14, 17, 22, 29, ?
A. 42
B. 29
C. 47
D. 40
Correct Answer: D
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 40.
CSS - PMS - CCE - PCS - Mathematics
Number System
What least number must be subtracted from 2936 so that the result is exactly divisible by 22?
A. 12
B. 9
C. 32
D. 10
Correct Answer: D
The remainder is 10; subtracting the remainder makes the number divisible by 22.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 11, 38, 119, 362, 1091, ?
A. 3283
B. 3278
C. 3273
D. 3275
Correct Answer: B
Each term is obtained by ×3 + 5. So 1091 × 3 + 5 = 3278.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 1125 have?
A. 12
B. 11
C. 7
D. 14
Correct Answer: A
1125 = 3^2 × 5^3. Number of divisors = (2+1)(3+1) = 12.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest positive integer that can divide both 302 and 239 leaving the same remainder?
A. 62
B. 63
C. 64
D. 31
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 302-239 = 63; the greatest possible divisor is 63.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the units digit of 27^87?
A. 9
B. 7
C. 3
D. 5
Correct Answer: C
Units digits repeat cyclically; applying the cycle for base 27 gives units digit 3.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the units digit of 19^21?
A. 5
B. 1
C. 3
D. 9
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 19 gives units digit 9.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number in the series: 72, 89, 106, 123, 140, ?
A. 191
B. 140
C. 174
D. 157
Correct Answer: D
The common difference is 17. So the next term is 140 + 17 = 157.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 135 have?
A. 7
B. 8
C. 10
D. 6
Correct Answer: B
135 = 5^1 × 3^3. Number of divisors = (1+1)(3+1) = 8.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 27, 31, 39, 51, 67, ?
A. 87
B. 83
C. 71
D. 91
Correct Answer: A
The differences are 4, 8, 12, 16, increasing by 4. The next difference is 20, so the answer is 87.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 40, 68, 104, 148, 200, ?
A. 260
B. 324
C. 196
D. 264
Correct Answer: A
The terms follow 4n² + 4 for consecutive n. For n = 8, the term is 4×8² + 4 = 260.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many trailing zeros are there in 96! ?
A. 9
B. 21
C. 22
D. 23
Correct Answer: C
Trailing zeros = ⌊96/5⌋ + ⌊96/25⌋ + ... = 19 + 3 = 22.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 37, 40, 45, 52, 63, ?
A. 78
B. 87
C. 63
D. 76
Correct Answer: D
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 76.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 2, 8, 17, 29, 44, ?
A. 62
B. 59
C. 65
D. 50
Correct Answer: A
The differences are 6, 9, 12, 15, increasing by 3. The next difference is 18, so the answer is 62.
CSS - PMS - CCE - PCS - Mathematics
Number System
Classify 26/15.
A. Prime number
B. Irrational
C. Whole number
D. Rational
Correct Answer: D
26/15 is a ratio of two integers with a non-zero denominator, so it is rational.
CSS - PMS - CCE - PCS - Mathematics
Number System
What digit x makes the number 482x divisible by 9?
A. 7
B. 9
C. 4
D. 5
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+8+2+x must be a multiple of 9, giving x = 4.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many positive divisors does 6 have?
A. 3
B. 6
C. 5
D. 4
Correct Answer: D
6 = 3^1 × 2^1. Number of divisors = (1+1)(1+1) = 4.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 9, 29, 89, 269, 809, ?
A. 2427
B. 2426
C. 2431
D. 2429
Correct Answer: D
Each term is obtained by ×3 + 2. So 809 × 3 + 2 = 2429.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest positive integer that can divide both 444 and 305 leaving the same remainder?
A. 69
B. 138
C. 140
D. 139
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 444-305 = 139; the greatest possible divisor is 139.
CSS - PMS - CCE - PCS - Mathematics
Number System
What least positive number must be added to 1547 so that the result is divisible by 7?
A. 0
B. 1
C. 14
D. 7
Correct Answer: D
1547 is already divisible by 7; the least positive addition preserving divisibility is 7.