Mathematics
Number System
Find the next number: 18, 25, 36, 49, 66, ?
A. 102
B. 85
C. 66
D. 87
Correct Answer: B
Successive prime numbers are added: 7, 11, 13, 17, 19. Add 19 next, giving 85.
Mathematics
Number System
Find the next number in the alternating series: 23, 23, 27, 27, 31, 31, ?
A. 31
B. 38
C. 39
D. 35
Correct Answer: D
Odd-position terms are 23, 27, 31, ... with difference 4. Hence the next odd-position term is 35.
Mathematics
Number System
What least number must be subtracted from 2073 so that the result is exactly divisible by 27?
A. 21
B. 20
C. 6
D. 48
Correct Answer: A
The remainder is 21; subtracting the remainder makes the number divisible by 27.
Mathematics
Number System
What digit x makes the number 429x divisible by 9?
A. 8
B. 3
C. 6
D. 4
Correct Answer: B
A number is divisible by 9 when its digit sum is divisible by 9. Thus 4+2+9+x must be a multiple of 9, giving x = 3.
Mathematics
Number System
Two positive integers have HCF 5 and LCM 105. What is their product?
A. 105
B. 525
C. 110
D. 530
Correct Answer: B
For two positive integers, product = HCF × LCM = 5 × 105 = 525.
Mathematics
Number System
Find the next number: 6, 24, 78, 240, 726, ?
A. 2178
B. 2184
C. 2190
D. 2181
Correct Answer: B
Each term is obtained by ×3 + 6. So 726 × 3 + 6 = 2184.
Mathematics
Number System
Find the next number in the series: 75, 89, 103, 117, 131, ?
A. 145
B. 159
C. 173
D. 131
Correct Answer: A
The common difference is 14. So the next term is 131 + 14 = 145.
Mathematics
Number System
The sum of 3 consecutive integers is 30. What is the middle integer?
A. 9
B. 13
C. 11
D. 10
Correct Answer: D
The middle integer equals the average: 30 ÷ 3 = 10.
Mathematics
Number System
Classify 36/23.
A. Rational
B. Irrational
C. Whole number
D. Prime number
Correct Answer: A
36/23 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next number in the series: 24, 37, 50, 63, 76, ?
A. 89
B. 102
C. 76
D. 115
Correct Answer: A
The common difference is 13. So the next term is 76 + 13 = 89.
Mathematics
Number System
Find the missing number: 35, 50, ?, 80, 95, 110
A. 80
B. 50
C. 95
D. 65
Correct Answer: D
This is an arithmetic series with common difference 15; the missing term is 65.
Mathematics
Number System
Find the next number: 31, 33, 37, 43, 51, ?
A. 63
B. 59
C. 61
D. 53
Correct Answer: C
The differences are 2, 4, 6, 8, increasing by 2. The next difference is 10, so the answer is 61.
Mathematics
Number System
How many trailing zeros are there in 43! ?
A. 10
B. 8
C. 4
D. 9
Correct Answer: D
Trailing zeros = ⌊43/5⌋ + ⌊43/25⌋ + ... = 8 + 1 = 9.
Mathematics
Number System
Find the next term in the series: 25, 44, 69, 100, 137, ?
A. 186
B. 180
C. 217
D. 174
Correct Answer: B
The first differences are [19, 25, 31, 37]; their second difference is constant at 6. Continuing the pattern gives 180.
Mathematics
Number System
Find the missing number: 55, 58, 61, ?, 67, 70
A. 67
B. 70
C. 61
D. 64
Correct Answer: D
This is an arithmetic series with common difference 3; the missing term is 64.
Mathematics
Number System
How many integers from 4 to 240, inclusive, are divisible by 12?
A. 19
B. 22
C. 20
D. 21
Correct Answer: C
Count = ⌊240/12⌋ - ⌊(4-1)/12⌋ = 20 - 0 = 20.
Mathematics
Number System
What is the units digit of 89^56?
A. 7
B. 5
C. 3
D. 1
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 89 gives units digit 1.
Mathematics
Number System
Find the next term: 11, 30, 67, 128, ?
A. 111
B. 225
C. 219
D. 216
Correct Answer: C
Each term is n³ + 3. Thus the next term is 6³ + 3 = 219.
Mathematics
Number System
How many positive divisors does 200 have?
A. 7
B. 11
C. 12
D. 14
Correct Answer: C
200 = 2^3 × 5^2. Number of divisors = (3+1)(2+1) = 12.
Mathematics
Number System
What least number must be subtracted from 2398 so that the result is exactly divisible by 20?
A. 18
B. 2
C. 38
D. 17
Correct Answer: A
The remainder is 18; subtracting the remainder makes the number divisible by 20.