Mathematics
Number System
Find the next term: 9, 19, 33, 51, 73, ?
A. 99
B. 71
C. 101
D. 127
Correct Answer: A
The terms follow 2n² + 1 for consecutive n. For n = 7, the term is 2×7² + 1 = 99.
Mathematics
Number System
Find the next term: 2, 8, 10, 18, 28, 46, ?
A. 92
B. 84
C. 56
D. 74
Correct Answer: D
Each term is the sum of the previous two. Therefore 28 + 46 = 74.
Mathematics
Number System
Find the next term: 19, 38, 75, 136, ?
A. 119
B. 233
C. 216
D. 227
Correct Answer: D
Each term is n³ + 11. Thus the next term is 6³ + 11 = 227.
Mathematics
Number System
Find the next number in the alternating series: 27, 67, 30, 73, 33, 79, ?
A. 39
B. 85
C. 33
D. 36
Correct Answer: D
Odd-position terms are 27, 30, 33, ... with difference 3. Hence the next odd-position term is 36.
Mathematics
Number System
Find the next number: 18, 21, 26, 33, 44, ?
A. 57
B. 44
C. 68
D. 59
Correct Answer: A
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 57.
Mathematics
Number System
What least number must be added to 1418 so that the result is exactly divisible by 7?
A. 10
B. 3
C. 2
D. 4
Correct Answer: B
1418 leaves remainder 4 on division by 7. Add 7 - 4 = 3.
Mathematics
Number System
How many trailing zeros are there in 34! ?
A. 8
B. 3
C. 7
D. 6
Correct Answer: C
Trailing zeros = ⌊34/5⌋ + ⌊34/25⌋ + ... = 6 + 1 = 7.
Mathematics
Number System
What is the greatest positive integer that can divide both 359 and 314 leaving the same remainder?
A. 44
B. 45
C. 22
D. 46
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 359-314 = 45; the greatest possible divisor is 45.
Mathematics
Number System
Find the missing number: 11, 19, 27, ?, 43, 51
A. 35
B. 51
C. 27
D. 43
Correct Answer: A
This is an arithmetic series with common difference 8; the missing term is 35.
Mathematics
Number System
What is the remainder when 1414 is divided by 13?
A. 10
B. 11
C. 0
D. 12
Correct Answer: A
1414 = 13 × 108 + 10; therefore the remainder is 10.
Mathematics
Number System
What is the greatest multiple of 13 that is less than 4831?
A. 4823
B. 4836
C. 4824
D. 4810
Correct Answer: A
4831 ÷ 13 has integer quotient 371; 13 × 371 = 4823.
Mathematics
Number System
How is the integer 43 classified?
A. Irrational
B. Neither prime nor composite
C. Composite
D. Prime
Correct Answer: D
43 has exactly two positive divisors, 1 and 43; therefore it is prime.
Mathematics
Number System
How many positive divisors does 75 have?
A. 6
B. 8
C. 5
D. 7
Correct Answer: A
75 = 3^1 × 5^2. Number of divisors = (1+1)(2+1) = 6.
Mathematics
Number System
What least number must be subtracted from 458 so that the result is exactly divisible by 7?
A. 10
B. 4
C. 3
D. 2
Correct Answer: C
The remainder is 3; subtracting the remainder makes the number divisible by 7.
Mathematics
Number System
What is the greatest multiple of 27 that is less than 1058?
A. 1054
B. 1053
C. 1026
D. 1080
Correct Answer: B
1058 ÷ 27 has integer quotient 39; 27 × 39 = 1053.
Mathematics
Number System
Find the missing number: 58, 66, 74, 82, ?, 98
A. 98
B. 82
C. 90
D. 106
Correct Answer: C
This is an arithmetic series with common difference 8; the missing term is 90.
Mathematics
Number System
Find the next number in the alternating series: 22, 74, 30, 72, 38, 70, ?
A. 38
B. 68
C. 46
D. 54
Correct Answer: C
Odd-position terms are 22, 30, 38, ... with difference 8. Hence the next odd-position term is 46.
Mathematics
Number System
Find the next term: 82, 92, 84, 94, 86, 96, ?
A. 96
B. 78
C. 88
D. 106
Correct Answer: C
The operations alternate +10, -8. After the last +10, subtract 8: 96 - 8 = 88.
Mathematics
Number System
What is the remainder when 2401 is divided by 19?
A. 10
B. 8
C. 9
D. 7
Correct Answer: D
2401 = 19 × 126 + 7; therefore the remainder is 7.
Mathematics
Number System
Find the next number: 2, 4, 9, 17, 28, ?
A. 42
B. 30
C. 45
D. 39
Correct Answer: A
The differences are 2, 5, 8, 11, increasing by 3. The next difference is 14, so the answer is 42.