Mathematics
Number System
Find the next number in the series: 9, 18, 27, 36, 45, ?
A. 63
B. 54
C. 45
D. 72
Correct Answer: B
The common difference is 9. So the next term is 45 + 9 = 54.
Mathematics
Number System
Classify 21/18.
A. Rational
B. Irrational
C. Whole number
D. Prime number
Correct Answer: A
21/18 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
What digit x makes the number 952x divisible by 9?
A. 7
B. 5
C. 2
D. 3
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 9+5+2+x must be a multiple of 9, giving x = 2.
Mathematics
Number System
Find the next term: 4, 9, 16, 25, 36, ?
A. 63
B. 49
C. 35
D. 50
Correct Answer: B
The terms follow 1n² + 0 for consecutive n. For n = 7, the term is 1×7² + 0 = 49.
Mathematics
Number System
Find the next number in the alternating series: 25, 53, 27, 46, 29, 39, ?
A. 29
B. 31
C. 32
D. 33
Correct Answer: B
Odd-position terms are 25, 27, 29, ... with difference 2. Hence the next odd-position term is 31.
Mathematics
Number System
What least number must be subtracted from 1049 so that the result is exactly divisible by 6?
A. 11
B. 5
C. 4
D. 1
Correct Answer: B
The remainder is 5; subtracting the remainder makes the number divisible by 6.
Mathematics
Number System
Find the next number: 12, 19, 29, 42, 58, ?
A. 80
B. 74
C. 77
D. 65
Correct Answer: C
The differences are 7, 10, 13, 16, increasing by 3. The next difference is 19, so the answer is 77.
Mathematics
Number System
What least number must be subtracted from 358 so that the result is exactly divisible by 29?
A. 10
B. 9
C. 39
D. 19
Correct Answer: A
The remainder is 10; subtracting the remainder makes the number divisible by 29.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.