Mathematics
Number System
Find the next number in the alternating series: 30, 37, 34, 35, 38, 33, ?
A. 42
B. 31
C. 38
D. 46
Correct Answer: A
Odd-position terms are 30, 34, 38, ... with difference 4. Hence the next odd-position term is 42.
Mathematics
Number System
Find the next number: 3, 19, 44, 80, 129, ?
A. 178
B. 201
C. 193
D. 185
Correct Answer: C
The increments are consecutive squares: 16, 25, 36, 49; next add 8² = 64. So the answer is 193.
Mathematics
Number System
Find the next number in the alternating series: 19, 30, 29, 28, 39, 26, ?
A. 49
B. 24
C. 59
D. 39
Correct Answer: A
Odd-position terms are 19, 29, 39, ... with difference 10. Hence the next odd-position term is 49.
Mathematics
Number System
Find the next number: 25, 41, 66, 102, 151, ?
A. 223
B. 215
C. 207
D. 200
Correct Answer: B
The increments are consecutive squares: 16, 25, 36, 49; next add 8² = 64. So the answer is 215.
Mathematics
Number System
A two-digit number is 28. What is the absolute difference between the number and the number formed by reversing its digits?
A. 6
B. 54
C. 45
D. 63
Correct Answer: B
Reversed number = 82. Absolute difference = |28 - 82| = 54.
Mathematics
Number System
What least number must be subtracted from 1669 so that the result is exactly divisible by 7?
A. 2
B. 3
C. 10
D. 4
Correct Answer: B
The remainder is 3; subtracting the remainder makes the number divisible by 7.
Mathematics
Number System
Find the next number: 18, 26, 36, 48, 62, ?
A. 80
B. 70
C. 76
D. 78
Correct Answer: D
The differences are 8, 10, 12, 14, increasing by 2. The next difference is 16, so the answer is 78.
Mathematics
Number System
What is the greatest positive integer that can divide both 292 and 265 leaving the same remainder?
A. 28
B. 26
C. 27
D. 13
Correct Answer: C
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 292-265 = 27; the greatest possible divisor is 27.
Mathematics
Number System
Find the next number: 17, 26, 42, 67, 103, ?
A. 145
B. 152
C. 139
D. 159
Correct Answer: B
The increments are consecutive squares: 9, 16, 25, 36; next add 7² = 49. So the answer is 152.
Mathematics
Number System
Find the LCM of 11 and 7.
A. 11
B. 78
C. 77
D. 84
Correct Answer: C
LCM = (11 × 7) ÷ HCF(11,7) = 77.
Mathematics
Number System
A two-digit number is 92. What is the absolute difference between the number and the number formed by reversing its digits?
A. 63
B. 54
C. 7
D. 72
Correct Answer: A
Reversed number = 29. Absolute difference = |92 - 29| = 63.
Mathematics
Number System
What digit x makes the number 825x divisible by 9?
A. 4
B. 8
C. 6
D. 3
Correct Answer: D
A number is divisible by 9 when its digit sum is divisible by 9. Thus 8+2+5+x must be a multiple of 9, giving x = 3.
Mathematics
Number System
Find the HCF (GCD) of 32 and 20.
A. 5
B. 8
C. 2
D. 4
Correct Answer: D
The greatest common divisor of 32 and 20 is 4.
Mathematics
Number System
What is the remainder when 1241 is divided by 23?
A. 0
B. 2
C. 1
D. 22
Correct Answer: D
1241 = 23 × 53 + 22; therefore the remainder is 22.
Mathematics
Number System
Find the next term in the series: 38, 57, 80, 107, 138, ?
A. 177
B. 173
C. 204
D. 169
Correct Answer: B
The first differences are [19, 23, 27, 31]; their second difference is constant at 4. Continuing the pattern gives 173.
Mathematics
Number System
What is the units digit of 76^44?
A. 8
B. 2
C. 0
D. 6
Correct Answer: D
Units digits repeat cyclically; applying the cycle for base 76 gives units digit 6.
Mathematics
Number System
Find the next term: 35, 53, 75, 101, 131, ?
A. 201
B. 165
C. 167
D. 129
Correct Answer: B
The terms follow 2n² + 3 for consecutive n. For n = 9, the term is 2×9² + 3 = 165.
Mathematics
Number System
What is the least positive number exactly divisible by 9, 13, and 5?
A. 13
B. 590
C. 585
D. 1170
Correct Answer: C
The required number is LCM(9, 13, 5) = 585.
Mathematics
Number System
How many integers from 4 to 235, inclusive, are divisible by 3?
A. 78
B. 76
C. 84
D. 77
Correct Answer: D
Count = ⌊235/3⌋ - ⌊(4-1)/3⌋ = 78 - 1 = 77.
Mathematics
Number System
Find the HCF (GCD) of 105 and 75.
A. 15
B. 7
C. 30
D. 16
Correct Answer: A
The greatest common divisor of 105 and 75 is 15.