Mathematics
Number System
What digit x makes the number 680x divisible by 9?
A. 9
B. 4
C. 5
D. 7
Correct Answer: B
A number is divisible by 9 when its digit sum is divisible by 9. Thus 6+8+0+x must be a multiple of 9, giving x = 4.
Mathematics
Number System
Find the HCF (GCD) of 12 and 15.
A. 6
B. 1
C. 4
D. 3
Correct Answer: D
The greatest common divisor of 12 and 15 is 3.
Mathematics
Number System
Find the next number: 25, 27, 32, 40, 51, ?
A. 62
B. 53
C. 65
D. 68
Correct Answer: C
The differences are 2, 5, 8, 11, increasing by 3. The next difference is 14, so the answer is 65.
Mathematics
Number System
What is the greatest positive integer that can divide both 240 and 210 leaving the same remainder?
A. 31
B. 29
C. 30
D. 15
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 240-210 = 30; the greatest possible divisor is 30.
Mathematics
Number System
A two-digit number is 26. What is the absolute difference between the number and the number formed by reversing its digits?
A. 4
B. 36
C. 45
D. 27
Correct Answer: B
Reversed number = 62. Absolute difference = |26 - 62| = 36.
Mathematics
Number System
Find the next number in the series: 38, 51, 64, 77, 90, ?
A. 129
B. 116
C. 90
D. 103
Correct Answer: D
The common difference is 13. So the next term is 90 + 13 = 103.
Mathematics
Number System
Find the next term: 6, 12, 18, 30, 48, 78, ?
A. 144
B. 96
C. 156
D. 126
Correct Answer: D
Each term is the sum of the previous two. Therefore 48 + 78 = 126.
Mathematics
Number System
What least number must be subtracted from 364 so that the result is exactly divisible by 16?
A. 12
B. 4
C. 11
D. 28
Correct Answer: A
The remainder is 12; subtracting the remainder makes the number divisible by 16.
Mathematics
Number System
How many trailing zeros are there in 108! ?
A. 26
B. 24
C. 10
D. 25
Correct Answer: D
Trailing zeros = ⌊108/5⌋ + ⌊108/25⌋ + ... = 21 + 4 = 25.
Mathematics
Number System
Find the next term in the series: 23, 34, 47, 62, 79, ?
A. 96
B. 98
C. 100
D. 115
Correct Answer: B
The first differences are [11, 13, 15, 17]; their second difference is constant at 2. Continuing the pattern gives 98.
Mathematics
Number System
Find the missing number: 66, 71, ?, 81, 86, 91
A. 81
B. 86
C. 71
D. 76
Correct Answer: D
This is an arithmetic series with common difference 5; the missing term is 76.
Mathematics
Number System
What digit x makes the number 606x divisible by 9?
A. 9
B. 7
C. 1
D. 6
Correct Answer: D
A number is divisible by 9 when its digit sum is divisible by 9. Thus 6+0+6+x must be a multiple of 9, giving x = 6.
Mathematics
Number System
Find the next number: 36, 38, 43, 51, 62, ?
A. 64
B. 79
C. 73
D. 76
Correct Answer: D
The differences are 2, 5, 8, 11, increasing by 3. The next difference is 14, so the answer is 76.
Mathematics
Number System
Find the next number: 5, 15, 60, 300, 1800, ?
A. 10800
B. 12600
C. 1800
D. 12607
Correct Answer: B
The multipliers are ×3, ×4, ×5, ×6; the next multiplier is ×7. Thus 1800 × 7 = 12600.
Mathematics
Number System
What is the units digit of 72^90?
A. 0
B. 4
C. 6
D. 8
Correct Answer: B
Units digits repeat cyclically; applying the cycle for base 72 gives units digit 4.
Mathematics
Number System
Find the next number in the series: 9, 16, 23, 30, 37, ?
A. 37
B. 58
C. 44
D. 51
Correct Answer: C
The common difference is 7. So the next term is 37 + 7 = 44.
Mathematics
Number System
Find the next number: 11, 13, 17, 23, 31, ?
A. 39
B. 43
C. 41
D. 33
Correct Answer: C
The differences are 2, 4, 6, 8, increasing by 2. The next difference is 10, so the answer is 41.
Mathematics
Number System
Two positive integers have HCF 2 and LCM 312. What is their product?
A. 626
B. 314
C. 624
D. 312
Correct Answer: C
For two positive integers, product = HCF × LCM = 2 × 312 = 624.
Mathematics
Number System
Find the next term: 97, 102, 96, 101, 95, 100, ?
A. 105
B. 100
C. 94
D. 89
Correct Answer: C
The operations alternate +5, -6. After the last +5, subtract 6: 100 - 6 = 94.
Mathematics
Number System
Find the next term: 34, 52, 74, 100, 130, ?
A. 200
B. 166
C. 164
D. 128
Correct Answer: C
The terms follow 2n² + 2 for consecutive n. For n = 9, the term is 2×9² + 2 = 164.