Mathematics
Number System
What digit x makes the number 514x divisible by 9?
A. 3
B. 1
C. 9
D. 8
Correct Answer: D
A number is divisible by 9 when its digit sum is divisible by 9. Thus 5+1+4+x must be a multiple of 9, giving x = 8.
Mathematics
Number System
Find the next number: 4, 8, 24, 96, 480, ?
A. 2880
B. 2886
C. 2400
D. 480
Correct Answer: A
The multipliers are ×2, ×3, ×4, ×5; the next multiplier is ×6. Thus 480 × 6 = 2880.
Mathematics
Number System
What is the units digit of 48^91?
A. 8
B. 2
C. 4
D. 6
Correct Answer: B
Units digits repeat cyclically; applying the cycle for base 48 gives units digit 2.
Mathematics
Number System
The sum of 3 consecutive integers is 162. What is the middle integer?
A. 53
B. 57
C. 55
D. 54
Correct Answer: D
The middle integer equals the average: 162 ÷ 3 = 54.
Mathematics
Number System
What is the greatest positive integer that can divide both 599 and 575 leaving the same remainder?
A. 23
B. 12
C. 24
D. 25
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 599-575 = 24; the greatest possible divisor is 24.
Mathematics
Number System
Find the next number in the series: 4, 16, 64, 256, 1024, ?
A. 4100
B. 1024
C. 4096
D. 1028
Correct Answer: C
Each term is multiplied by 4. Therefore 1024 × 4 = 4096.
Mathematics
Number System
What is the least positive number exactly divisible by 9, 7, and 17?
A. 1071
B. 17
C. 2142
D. 1078
Correct Answer: A
The required number is LCM(9, 7, 17) = 1071.
Mathematics
Number System
Two positive integers have HCF 5 and LCM 715. What is their product?
A. 3580
B. 720
C. 3575
D. 715
Correct Answer: C
For two positive integers, product = HCF × LCM = 5 × 715 = 3575.
Mathematics
Number System
Find the missing number: 75, 89, 103, ?, 131, 145
A. 117
B. 103
C. 131
D. 145
Correct Answer: A
This is an arithmetic series with common difference 14; the missing term is 117.
Mathematics
Number System
Find the next number in the series: 70, 76, 82, 88, 94, ?
A. 112
B. 100
C. 106
D. 94
Correct Answer: B
The common difference is 6. So the next term is 94 + 6 = 100.
Mathematics
Number System
Find the LCM of 24 and 21.
A. 24
B. 504
C. 168
D. 171
Correct Answer: C
LCM = (24 × 21) ÷ HCF(24,21) = 168.
Mathematics
Number System
Find the next number: 5, 7, 10, 15, 22, ?
A. 35
B. 22
C. 33
D. 40
Correct Answer: C
Successive prime numbers are added: 2, 3, 5, 7, 11. Add 11 next, giving 33.
Mathematics
Number System
Find the next term: 13, 22, 35, 57, 92, 149, ?
A. 276
B. 298
C. 184
D. 241
Correct Answer: D
Each term is the sum of the previous two. Therefore 92 + 149 = 241.
Mathematics
Number System
A two-digit number is 49. What is the absolute difference between the number and the number formed by reversing its digits?
A. 54
B. 36
C. 45
D. 5
Correct Answer: C
Reversed number = 94. Absolute difference = |49 - 94| = 45.
Mathematics
Number System
Find the next number: 30, 39, 55, 80, 116, ?
A. 152
B. 172
C. 165
D. 158
Correct Answer: C
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 165.
Mathematics
Number System
Find the next number in the series: 3, 15, 75, 375, 1875, ?
A. 1880
B. 1875
C. 9380
D. 9375
Correct Answer: D
Each term is multiplied by 5. Therefore 1875 × 5 = 9375.
Mathematics
Number System
Find the next number: 7, 8, 11, 16, 23, ?
A. 32
B. 24
C. 34
D. 30
Correct Answer: A
The differences are 1, 3, 5, 7, increasing by 2. The next difference is 9, so the answer is 32.
Mathematics
Number System
What least number must be subtracted from 3243 so that the result is exactly divisible by 12?
A. 2
B. 15
C. 9
D. 3
Correct Answer: D
The remainder is 3; subtracting the remainder makes the number divisible by 12.
Mathematics
Number System
The sum of 5 consecutive integers is 40. What is the middle integer?
A. 8
B. 7
C. 13
D. 9
Correct Answer: A
The middle integer equals the average: 40 ÷ 5 = 8.
Mathematics
Number System
Find the next number in the alternating series: 8, 22, 16, 19, 24, 16, ?
A. 40
B. 24
C. 13
D. 32
Correct Answer: D
Odd-position terms are 8, 16, 24, ... with difference 8. Hence the next odd-position term is 32.