Mathematics
Number System
What least number must be subtracted from 3411 so that the result is exactly divisible by 12?
A. 9
B. 15
C. 2
D. 3
Correct Answer: D
The remainder is 3; subtracting the remainder makes the number divisible by 12.
Mathematics
Number System
What is the greatest positive integer that can divide both 448 and 360 leaving the same remainder?
A. 88
B. 87
C. 44
D. 89
Correct Answer: A
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 448-360 = 88; the greatest possible divisor is 88.
Mathematics
Number System
Find the next term: 17, 27, 41, 59, 81, ?
A. 109
B. 79
C. 135
D. 107
Correct Answer: D
The terms follow 2n² + 9 for consecutive n. For n = 7, the term is 2×7² + 9 = 107.
Mathematics
Number System
Find the next number: 14, 19, 26, 37, 50, ?
A. 80
B. 69
C. 50
D. 67
Correct Answer: D
Successive prime numbers are added: 5, 7, 11, 13, 17. Add 17 next, giving 67.
Mathematics
Number System
What digit x makes the number 530x divisible by 9?
A. 2
B. 4
C. 6
D. 1
Correct Answer: D
A number is divisible by 9 when its digit sum is divisible by 9. Thus 5+3+0+x must be a multiple of 9, giving x = 1.
Mathematics
Number System
Find the next number: 28, 29, 33, 42, 58, ?
A. 78
B. 88
C. 74
D. 83
Correct Answer: D
The increments are consecutive squares: 1, 4, 9, 16; next add 5² = 25. So the answer is 83.
Mathematics
Number System
Find the next number: 15, 18, 24, 33, 45, ?
A. 63
B. 57
C. 48
D. 60
Correct Answer: D
The differences are 3, 6, 9, 12, increasing by 3. The next difference is 15, so the answer is 60.
Mathematics
Number System
Find the next term: 8, 24, 32, 56, 88, 144, ?
A. 264
B. 232
C. 288
D. 176
Correct Answer: B
Each term is the sum of the previous two. Therefore 88 + 144 = 232.
Mathematics
Number System
Find the missing number: 17, 35, 53, ?, 89, 107
A. 89
B. 107
C. 53
D. 71
Correct Answer: D
This is an arithmetic series with common difference 18; the missing term is 71.
Mathematics
Number System
The sum of 5 consecutive integers is 100. What is the middle integer?
A. 20
B. 21
C. 25
D. 19
Correct Answer: A
The middle integer equals the average: 100 ÷ 5 = 20.
Mathematics
Number System
Find the next term: 3, 8, 11, 19, 30, 49, ?
A. 79
B. 60
C. 98
D. 90
Correct Answer: A
Each term is the sum of the previous two. Therefore 30 + 49 = 79.
Mathematics
Number System
What is the greatest multiple of 18 that is less than 2095?
A. 2089
B. 2088
C. 2106
D. 2070
Correct Answer: B
2095 ÷ 18 has integer quotient 116; 18 × 116 = 2088.
Mathematics
Number System
How many positive divisors does 196 have?
A. 6
B. 11
C. 9
D. 8
Correct Answer: C
196 = 2^2 × 7^2. Number of divisors = (2+1)(2+1) = 9.
Mathematics
Number System
Find the HCF (GCD) of 22 and 33.
A. 12
B. 22
C. 11
D. 5
Correct Answer: C
The greatest common divisor of 22 and 33 is 11.
Mathematics
Number System
Find the next number in the alternating series: 16, 55, 24, 48, 32, 41, ?
A. 34
B. 48
C. 32
D. 40
Correct Answer: D
Odd-position terms are 16, 24, 32, ... with difference 8. Hence the next odd-position term is 40.
Mathematics
Number System
Find the next term: 9, 16, 35, 72, ?
A. 58
B. 138
C. 133
D. 125
Correct Answer: C
Each term is n³ + 8. Thus the next term is 5³ + 8 = 133.
Mathematics
Number System
What is the units digit of 62^41?
A. 8
B. 6
C. 4
D. 2
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 62 gives units digit 2.
Mathematics
Number System
Classify 17/4.
A. Prime number
B. Whole number
C. Rational
D. Irrational
Correct Answer: C
17/4 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
The sum of 4 consecutive integers is 118. What is the smallest integer?
A. 29
B. 28
C. 32
D. 27
Correct Answer: B
Let the integers be n, n+1, ..., n+3. Their sum is 118; solving gives n = 28.
Mathematics
Number System
Find the next term: 26, 37, 29, 40, 32, 43, ?
A. 54
B. 43
C. 35
D. 24
Correct Answer: C
The operations alternate +11, -8. After the last +11, subtract 8: 43 - 8 = 35.