Mathematics
Number System
How is the integer 72 classified?
A. Prime
B. Neither prime nor composite
C. Irrational
D. Composite
Correct Answer: D
72 = 6 × 12, so it has factors other than 1 and itself and is composite.
Mathematics
Number System
Find the next number: 22, 29, 40, 53, 70, ?
A. 91
B. 106
C. 70
D. 89
Correct Answer: D
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 89.
Mathematics
Number System
What is the greatest positive integer that can divide both 433 and 366 leaving the same remainder?
A. 33
B. 67
C. 68
D. 66
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 433-366 = 67; the greatest possible divisor is 67.
Mathematics
Number System
What digit x makes the number 926x divisible by 9?
A. 6
B. 2
C. 1
D. 4
Correct Answer: C
A number is divisible by 9 when its digit sum is divisible by 9. Thus 9+2+6+x must be a multiple of 9, giving x = 1.
Mathematics
Number System
How many positive divisors does 10 have?
A. 6
B. 3
C. 5
D. 4
Correct Answer: D
10 = 2^1 × 5^1. Number of divisors = (1+1)(1+1) = 4.
Mathematics
Number System
What least number must be subtracted from 1055 so that the result is exactly divisible by 6?
A. 5
B. 4
C. 11
D. 1
Correct Answer: A
The remainder is 5; subtracting the remainder makes the number divisible by 6.
Mathematics
Number System
Find the next number: 4, 6, 9, 14, 21, ?
A. 32
B. 39
C. 34
D. 21
Correct Answer: A
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 32.
Mathematics
Number System
Two positive integers have HCF 15 and LCM 495. What is their product?
A. 510
B. 495
C. 7425
D. 7440
Correct Answer: C
For two positive integers, product = HCF × LCM = 15 × 495 = 7425.
Mathematics
Number System
Find the next number in the series: 26, 31, 36, 41, 46, ?
A. 56
B. 46
C. 51
D. 61
Correct Answer: C
The common difference is 5. So the next term is 46 + 5 = 51.
Mathematics
Number System
Find the next number: 3, 5, 8, 13, 20, ?
A. 31
B. 33
C. 38
D. 20
Correct Answer: A
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 31.
Mathematics
Number System
Find the next number: 28, 31, 35, 40, 46, ?
A. 54
B. 52
C. 53
D. 49
Correct Answer: C
The differences are 3, 4, 5, 6, increasing by 1. The next difference is 7, so the answer is 53.
Mathematics
Number System
What is the greatest multiple of 35 that is less than 3136?
A. 3080
B. 3150
C. 3116
D. 3115
Correct Answer: D
3136 ÷ 35 has integer quotient 89; 35 × 89 = 3115.
Mathematics
Number System
Find the next number in the alternating series: 27, 61, 35, 59, 43, 57, ?
A. 59
B. 43
C. 51
D. 55
Correct Answer: C
Odd-position terms are 27, 35, 43, ... with difference 8. Hence the next odd-position term is 51.
Mathematics
Number System
How many positive divisors does 250 have?
A. 10
B. 8
C. 7
D. 6
Correct Answer: B
250 = 5^3 × 2^1. Number of divisors = (3+1)(1+1) = 8.
Mathematics
Number System
What least number must be subtracted from 755 so that the result is exactly divisible by 27?
A. 26
B. 25
C. 1
D. 53
Correct Answer: A
The remainder is 26; subtracting the remainder makes the number divisible by 27.
Mathematics
Number System
Find the HCF (GCD) of 84 and 132.
A. 6
B. 12
C. 24
D. 13
Correct Answer: B
The greatest common divisor of 84 and 132 is 12.
Mathematics
Number System
Find the HCF (GCD) of 182 and 168.
A. 28
B. 7
C. 14
D. 15
Correct Answer: C
The greatest common divisor of 182 and 168 is 14.
Mathematics
Number System
Find the next number: 5, 10, 30, 120, 600, ?
A. 600
B. 3600
C. 3000
D. 3606
Correct Answer: B
The multipliers are ×2, ×3, ×4, ×5; the next multiplier is ×6. Thus 600 × 6 = 3600.
Mathematics
Number System
Classify √46.
A. Prime number
B. Irrational
C. Whole number
D. Rational
Correct Answer: B
46 is not a perfect square, so √46 is irrational.
Mathematics
Number System
What digit x makes the number 988x divisible by 9?
A. 7
B. 3
C. 5
D. 2
Correct Answer: D
A number is divisible by 9 when its digit sum is divisible by 9. Thus 9+8+8+x must be a multiple of 9, giving x = 2.