Mathematics
Number System
Find the next number: 2, 10, 19, 29, 40, ?
A. 53
B. 48
C. 52
D. 51
Correct Answer: C
The differences are 8, 9, 10, 11, increasing by 1. The next difference is 12, so the answer is 52.
Mathematics
Number System
What is the greatest multiple of 29 that is less than 4246?
A. 4235
B. 4205
C. 4234
D. 4263
Correct Answer: C
4246 ÷ 29 has integer quotient 146; 29 × 146 = 4234.
Mathematics
Number System
Find the missing number: 80, 92, ?, 116, 128, 140
A. 92
B. 104
C. 116
D. 128
Correct Answer: B
This is an arithmetic series with common difference 12; the missing term is 104.
Mathematics
Number System
Find the next term in the series: 9, 17, 29, 45, 65, ?
A. 85
B. 93
C. 89
D. 109
Correct Answer: C
The first differences are [8, 12, 16, 20]; their second difference is constant at 4. Continuing the pattern gives 89.
Mathematics
Number System
Find the next number: 31, 37, 44, 52, 61, ?
A. 70
B. 72
C. 71
D. 67
Correct Answer: C
The differences are 6, 7, 8, 9, increasing by 1. The next difference is 10, so the answer is 71.
Mathematics
Number System
What is the least positive number exactly divisible by 6, 18, and 17?
A. 312
B. 306
C. 612
D. 18
Correct Answer: B
The required number is LCM(6, 18, 17) = 306.
Mathematics
Number System
What least number must be subtracted from 2107 so that the result is exactly divisible by 9?
A. 8
B. 10
C. 2
D. 1
Correct Answer: D
The remainder is 1; subtracting the remainder makes the number divisible by 9.
Mathematics
Number System
How many trailing zeros are there in 122! ?
A. 29
B. 12
C. 28
D. 27
Correct Answer: C
Trailing zeros = ⌊122/5⌋ + ⌊122/25⌋ + ... = 24 + 4 = 28.
Mathematics
Number System
Find the next term: 94, 108, 106, 120, 118, 132, ?
A. 132
B. 130
C. 146
D. 116
Correct Answer: B
The operations alternate +14, -2. After the last +14, subtract 2: 132 - 2 = 130.
Mathematics
Number System
Find the next number: 7, 22, 67, 202, 607, ?
A. 1822
B. 1823
C. 1819
D. 1821
Correct Answer: A
Each term is obtained by ×3 + 1. So 607 × 3 + 1 = 1822.
Mathematics
Number System
What is the greatest positive integer that can divide both 662 and 596 leaving the same remainder?
A. 33
B. 65
C. 67
D. 66
Correct Answer: D
If both numbers leave the same remainder, their difference must be divisible by the divisor. Their difference is 662-596 = 66; the greatest possible divisor is 66.
Mathematics
Number System
Classify √30.
A. Whole number
B. Irrational
C. Rational
D. Prime number
Correct Answer: B
30 is not a perfect square, so √30 is irrational.
Mathematics
Number System
A two-digit number is 35. What is the absolute difference between the number and the number formed by reversing its digits?
A. 27
B. 2
C. 9
D. 18
Correct Answer: D
Reversed number = 53. Absolute difference = |35 - 53| = 18.
Mathematics
Number System
What is the greatest multiple of 25 that is less than 4314?
A. 4300
B. 4301
C. 4325
D. 4275
Correct Answer: A
4314 ÷ 25 has integer quotient 172; 25 × 172 = 4300.
Mathematics
Number System
A two-digit number is 62. What is the absolute difference between the number and the number formed by reversing its digits?
A. 27
B. 4
C. 45
D. 36
Correct Answer: D
Reversed number = 26. Absolute difference = |62 - 26| = 36.
Mathematics
Number System
What digit x makes the number 620x divisible by 9?
A. 2
B. 1
C. 6
D. 4
Correct Answer: B
A number is divisible by 9 when its digit sum is divisible by 9. Thus 6+2+0+x must be a multiple of 9, giving x = 1.
Mathematics
Number System
Find the next number: 20, 28, 40, 56, 76, ?
A. 84
B. 104
C. 100
D. 96
Correct Answer: C
The differences are 8, 12, 16, 20, increasing by 4. The next difference is 24, so the answer is 100.
Mathematics
Number System
The sum of 4 consecutive integers is 86. What is the smallest integer?
A. 24
B. 21
C. 19
D. 20
Correct Answer: D
Let the integers be n, n+1, ..., n+3. Their sum is 86; solving gives n = 20.
Mathematics
Number System
Find the next term: 6, 13, 32, 69, ?
A. 135
B. 125
C. 130
D. 55
Correct Answer: C
Each term is n³ + 5. Thus the next term is 5³ + 5 = 130.
Mathematics
Number System
Find the next number in the series: 17, 22, 27, 32, 37, ?
A. 52
B. 47
C. 42
D. 37
Correct Answer: C
The common difference is 5. So the next term is 37 + 5 = 42.