CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 73 to 370, inclusive, are divisible by 7?
A. 42
B. 43
C. 52
D. 41
Correct Answer: A
Count = ⌊370/7⌋ - ⌊(73-1)/7⌋ = 52 - 10 = 42.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the missing number: 16, 19, ?, 25, 28, 31
A. 19
B. 28
C. 25
D. 22
Correct Answer: D
This is an arithmetic series with common difference 3; the missing term is 22.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 35, 72, 133, 224, ?
A. 358
B. 351
C. 204
D. 343
Correct Answer: B
Each term is n³ + 8. Thus the next term is 7³ + 8 = 351.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the remainder when 310 is divided by 7?
A. 3
B. 5
C. 4
D. 2
Correct Answer: D
310 = 7 × 44 + 2; therefore the remainder is 2.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next number: 1, 7, 25, 79, 241, ?
A. 731
B. 724
C. 723
D. 727
Correct Answer: D
Each term is obtained by ×3 + 4. So 241 × 3 + 4 = 727.
CSS - PMS - CCE - PCS - Mathematics
Number System
What least positive number must be added to 915 so that the result is divisible by 15?
A. 15
B. 30
C. 0
D. 1
Correct Answer: A
915 is already divisible by 15; the least positive addition preserving divisibility is 15.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the remainder when 1043 is divided by 7?
A. 2
B. 0
C. 1
D. 3
Correct Answer: B
1043 = 7 × 149 + 0; therefore the remainder is 0.
CSS - PMS - CCE - PCS - Mathematics
Number System
Classify 34/4.
A. Irrational
B. Whole number
C. Prime number
D. Rational
Correct Answer: D
34/4 is a ratio of two integers with a non-zero denominator, so it is rational.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 15, 30, 51, 78, 111, ?
A. 150
B. 153
C. 192
D. 108
Correct Answer: A
The terms follow 3n² + 3 for consecutive n. For n = 7, the term is 3×7² + 3 = 150.
CSS - PMS - CCE - PCS - Mathematics
Number System
How is the integer 79 classified?
A. Composite
B. Neither prime nor composite
C. Prime
D. Irrational
Correct Answer: C
79 has exactly two positive divisors, 1 and 79; therefore it is prime.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 23, 43, 71, 107, 151, ?
A. 207
B. 203
C. 259
D. 147
Correct Answer: B
The terms follow 4n² + 7 for consecutive n. For n = 7, the term is 4×7² + 7 = 203.
CSS - PMS - CCE - PCS - Mathematics
Number System
How many integers from 61 to 337, inclusive, are divisible by 15?
A. 18
B. 17
C. 19
D. 22
Correct Answer: A
Count = ⌊337/15⌋ - ⌊(61-1)/15⌋ = 22 - 4 = 18.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the missing number: 86, 90, ?, 98, 102, 106
A. 102
B. 90
C. 98
D. 94
Correct Answer: D
This is an arithmetic series with common difference 4; the missing term is 94.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 6, 18, 38, 66, 102, ?
A. 194
B. 146
C. 150
D. 98
Correct Answer: B
The terms follow 4n² + 2 for consecutive n. For n = 6, the term is 4×6² + 2 = 146.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term in the series: 15, 22, 31, 42, 55, ?
A. 68
B. 70
C. 72
D. 83
Correct Answer: B
The first differences are [7, 9, 11, 13]; their second difference is constant at 2. Continuing the pattern gives 70.
CSS - PMS - CCE - PCS - Mathematics
Number System
Find the next term: 10, 22, 32, 54, 86, 140, ?
A. 226
B. 172
C. 258
D. 280
Correct Answer: A
Each term is the sum of the previous two. Therefore 86 + 140 = 226.
CSS - PMS - CCE - PCS - Mathematics
Number System
Two positive integers have HCF 8 and LCM 520. What is their product?
A. 4168
B. 520
C. 4160
D. 528
Correct Answer: C
For two positive integers, product = HCF × LCM = 8 × 520 = 4160.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the units digit of 90^62?
A. 4
B. 2
C. 6
D. 0
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 90 gives units digit 0.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest positive integer that can divide both 527 and 417 leaving the same remainder?
A. 55
B. 111
C. 109
D. 110
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 527-417 = 110; the greatest possible divisor is 110.
CSS - PMS - CCE - PCS - Mathematics
Number System
What is the greatest multiple of 7 that is less than 2756?
A. 2744
B. 2758
C. 2751
D. 2752
Correct Answer: C
2756 ÷ 7 has integer quotient 393; 7 × 393 = 2751.