Mathematics
Number System
What is the greatest positive integer that can divide both 633 and 532 leaving the same remainder?
A. 50
B. 101
C. 102
D. 100
Correct Answer: B
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 633-532 = 101; the greatest possible divisor is 101.
Mathematics
Number System
Find the next number: 28, 31, 39, 52, 70, ?
A. 98
B. 73
C. 88
D. 93
Correct Answer: D
The differences are 3, 8, 13, 18, increasing by 5. The next difference is 23, so the answer is 93.
Mathematics
Number System
How many integers from 27 to 201, inclusive, are divisible by 13?
A. 12
B. 14
C. 15
D. 13
Correct Answer: D
Count = ⌊201/13⌋ - ⌊(27-1)/13⌋ = 15 - 2 = 13.
Mathematics
Number System
Find the next number: 32, 35, 40, 47, 58, ?
A. 71
B. 58
C. 73
D. 82
Correct Answer: A
Successive prime numbers are added: 3, 5, 7, 11, 13. Add 13 next, giving 71.
Mathematics
Number System
Find the next term: 54, 81, 114, 153, 198, ?
A. 252
B. 195
C. 303
D. 249
Correct Answer: D
The terms follow 3n² + 6 for consecutive n. For n = 9, the term is 3×9² + 6 = 249.
Mathematics
Number System
Find the next term: 13, 25, 38, 63, 101, 164, ?
A. 265
B. 202
C. 328
D. 303
Correct Answer: A
Each term is the sum of the previous two. Therefore 101 + 164 = 265.
Mathematics
Number System
What is the least positive number exactly divisible by 6, 14, and 4?
A. 14
B. 84
C. 88
D. 168
Correct Answer: B
The required number is LCM(6, 14, 4) = 84.
Mathematics
Number System
How many positive divisors does 54 have?
A. 10
B. 6
C. 8
D. 7
Correct Answer: C
54 = 2^1 × 3^3. Number of divisors = (1+1)(3+1) = 8.
Mathematics
Number System
A two-digit number is 80. What is the absolute difference between the number and the number formed by reversing its digits?
A. 81
B. 8
C. 63
D. 72
Correct Answer: D
Reversed number = 8. Absolute difference = |80 - 8| = 72.
Mathematics
Number System
Find the next number in the series: 5, 25, 125, 625, 3125, ?
A. 3130
B. 15630
C. 3125
D. 15625
Correct Answer: D
Each term is multiplied by 5. Therefore 3125 × 5 = 15625.
Mathematics
Number System
Find the next number: 4, 9, 19, 39, 79, ?
A. 158
B. 159
C. 160
D. 157
Correct Answer: B
Each term is obtained by ×2 + 1. So 79 × 2 + 1 = 159.
Mathematics
Number System
What least number must be subtracted from 2152 so that the result is exactly divisible by 27?
A. 19
B. 8
C. 18
D. 46
Correct Answer: A
The remainder is 19; subtracting the remainder makes the number divisible by 27.
Mathematics
Number System
Find the missing number: 5, 8, 11, ?, 17, 20
A. 14
B. 20
C. 17
D. 11
Correct Answer: A
This is an arithmetic series with common difference 3; the missing term is 14.
Mathematics
Number System
What least number must be added to 603 so that the result is exactly divisible by 8?
A. 5
B. 6
C. 3
D. 13
Correct Answer: A
603 leaves remainder 3 on division by 8. Add 8 - 3 = 5.
Mathematics
Number System
The sum of 4 consecutive integers is 90. What is the smallest integer?
A. 25
B. 22
C. 20
D. 21
Correct Answer: D
Let the integers be n, n+1, ..., n+3. Their sum is 90; solving gives n = 21.
Mathematics
Number System
Classify √19.
A. Prime number
B. Rational
C. Whole number
D. Irrational
Correct Answer: D
19 is not a perfect square, so √19 is irrational.
Mathematics
Number System
Find the next term in the series: 18, 32, 50, 72, 98, ?
A. 124
B. 154
C. 132
D. 128
Correct Answer: D
The first differences are [14, 18, 22, 26]; their second difference is constant at 4. Continuing the pattern gives 128.
Mathematics
Number System
Classify 27/8.
A. Prime number
B. Rational
C. Irrational
D. Whole number
Correct Answer: B
27/8 is a ratio of two integers with a non-zero denominator, so it is rational.
Mathematics
Number System
Find the next term: 66, 72, 65, 71, 64, 70, ?
A. 70
B. 57
C. 63
D. 76
Correct Answer: C
The operations alternate +6, -7. After the last +6, subtract 7: 70 - 7 = 63.
Mathematics
Number System
What is the units digit of 82^58?
A. 4
B. 6
C. 8
D. 0
Correct Answer: A
Units digits repeat cyclically; applying the cycle for base 82 gives units digit 4.